Business Valuation Parts 1 - 5 plus Example.pdf

Christopher F. Agar FCA FCT
[email protected]
(October 2025)

BUSINESS VALUATION

BUSINESS VALUATION

Part 1 Cash Flows & Value

Overview of Valuation Series 1.1
Cash Flows Profits & Rates of Return 1.2
Free Cash Flows to the Firm (FCFF) 1.2
Net Operating Profits After Tax (NOPAT) 1.3
Rates of Return 1.4
Return On Invested Capital (ROIC) 1.4
Return on New Invested Capital (RONIC) 1.5
Forecasting Cash Flows 1.6
General Approach 1.6
Operating Profits 1.6
Investing for Operating Profits 1.7
Taxes 1.8
Towards the Terminal Value: Achieving Steady State 1.8
Integrated Forecast Financial Statements 1.9
Terminal Value 1.10
Scenarios 1.11
DCF Values 1.11
Appendix 1 - Present Value Formulae 1.13
Appendix 2 - Terminal Value Driver Formulae 1.17
Appendix 3 - Enterprise Value Example 1.21

Part 2 Discount Rates & Tax Shields

Leverage 2.1
Debt & Cash 2.2
Cost of Debt 2.3
Cost of Equity 2.4
WACC 2.5
Cross Border WACC 2.6
Appendix 1 - WACC Theory & Tax Shields 2.9
MM Theory 2.9
General Equations with Tax Shield 2.10
Tax shield discounted at Ungeared Cost of Equity 2.13
Tax shield discounted at Cost of Debt 2.14
Beta relevering 2.15
Appendix 2 - Cross Border WACC 2.19
Foreign Risk 2.19
CAPM approach 2.19
Basic DCF principles 2.20

Part 3 Alternative DCF Methods & Multiples

Alternative DCF Methods 3.1
Free Cash Flows to the Firm (post-tax WACC) 3.1
Economic Operating Profits (post-tax WACC) 3.4
Capital Cash Flows (pre-tax WACC) 3.6
Adjusted Present Value (APV)(ungeared cost of equity, pre-tax cost debt) 3.8
Free Cash Flows to Equity (geared cost of equity) 3.8
Residual Income Model (geared cost of equity) 3.9
Dividend Discount Model (geared cost of equity) 3.11
Multiples 3.12
Types of Multiple 3.12
Adjustments 3.13
Appendix – Multiples Perpetuity Formulae 3.15
Growth & Returns 3.15
Returns & Risk 3.17
ROIC Multiples 3.18

Part 4 The Value Bridge - Part I

Net Operating Assets 4.1
Cash 4.1
Deferred Tax Assets 4.1
Debt & Debt Equivalents 4.2
Straight Debt 4.2
Leases 4.6
Pension Deficits 4.8
Appendix – Leveraged Lease Example 4.11

Part 5 The Value Bridge - Part II

Debt & Debt Equivalents 5.1
Convertible Debt 5.1
Equity Equivalents 5.3
Employee Stock Options 5.3
Appendix 1 - Option Pricing Models (with examples) 5.8
Binomial Model (BM) – single period 5.8
Black-Scholes Model (BSM) 5.11
Binomial Model (BM) – multi period 5.12
BM – BSM Convergence 5.13
Dividends 5.16
Appendix 2 – Convertible Bond Pricing (with example) 5.18

Part 6 Detailed DCF Example 6.1 – 6.19

[email protected] 1. 1
BUSINESS VALUATION
Part 1: Cash Flows and Value

Overview of Valuation Series

The intrinsic value of a business can be estimated using techniques that consider future cash flows or
income or consider what a comparable business might be worth if it was quoted or acquired (relative
valuation with multiples). A value estimated by discounting future cash flows at a ‘Discount Rate’ to
their ‘Present Value’ (‘PV’) (‘Discounted Cash Flow’ / ‘DCF’ valuation), represents the value expected to
be received from the business in the future, expressed in economically equivalent terms as if received
today. A DCF requires cash flows to be estimated over a forecast period, usually 5 – 10 years, at the end
of which a single formula can be used to capture the PV of remaining cash flows in perpetuity (‘Terminal
Value’ / ‘TV’). Part 1 discusses the general DCF methodology, including basic PV formulae (Appendix 1),
forecast period cash flows, ‘steady state’ assumptions and TV formulae (Appendix 2), with a simplified
example (Appendix 3).

A discount rate is adjusted to reflect the riskiness of the expected cash flows being valued (uncertainty
as to their amount and timing), and represents the return required by the providers of capital (‘Cost of
Capital’). Discount rates are discussed in Part 2 of this series, along with theory relating to the tax
benefits of debt finance and impact on the cost of capital (‘Tax Shield’).

A number of different approaches can be used to value cash flows or income, which should give the
same value. The first set of cash flows to forecast are pre-financing operating cash flows net of
operating taxes paid (‘Free Cash Flows to the Firm’ / ‘FCFF’), the subject of this paper. These are
available for distribution to all providers of financial capital, starting with debt investors who have
priority over equity investors. The second type of cash flows (‘Free Cash Flows to Equity’ / ‘FCFE’) equal
FCFF less debt cash flows (net borrowings / (repayments) less interest paid net of tax relief) that are
free to be distributed to equity investors. These are the two main DCF approaches, but other methods
can be used (discussed in Part 3 of the series, along with a multiples approach that applies a factor to
a specific financial measure, like net profits, to estimate a value).

When FCFF are discounted, the resulting PV is the operating Enterprise Value (‘Ent’V’). Net non-operating
assets that do not generate FCFF (e.g.surplus cash, head office properties, investments in associates
and joint ventures, equity investments etc) need to be valued separately and added to produce the total
EntV. The market value of debt (e.g.borrowings, preference shares, leases) and ‘debt-equivalents’ (e.g.
pension deficits) is then deducted to arrive at the Equity Value (‘EqV’). This amount is shared between
current equity investors (ordinary shareholders) and ‘equity equivalents’ (e.g. employee stock options).
Some of the many claims to total EntV that lie ahead of the residual entitlement of ordinary shareholders
(the ‘Bridge’) are discussed in Parts 4 and 5 of this series.
C.F. Agar 12 Sept. 2025

[email protected] 1. 2
Cash Flows, Profits & Rates of Return

Free Cash Flows to the Firm (FCFF)

FCFF can be defined in a number of ways when providing non-GAAP financial information in annual
reports, but for the purpose of a DCF valuation they are defined as after-tax cash flows derived from
operating activities (ignoring after-tax financing cash flows), being operating income and operating
investments required to generate the operating income. FCFF can be calculated from the cash flow or
income statement, shown here with some numbers:

[email protected] 1. 3

Net Operating Profits After Tax (‘NOPAT’)

Operating ‘Invested Capital’ (‘IC’) represents operating net assets used to generate FCFF and NOPAT:

In this example, net cash in excess of the amount estimated as required for daily operations (‘operating
cash’) is paid out in full to shareholders. The dividend equals the Free Cash Flow to Equity (this assumes
sufficient distributable profits under company law exist).

NOPAT represents operating Earnings Before Interest & Tax (EBIT) after operating taxes paid have been
deducted. NOPAT can be used for valuation purposes because of its relationship to FCFF:

NOPAT x
less: New Invested Capital (‘NIC’ = capex – depreciation + increase in working capital) (x.)
FCFF x

Where NIC is the increase in IC:

Property, Plant & Equipment x
Working Capital x
Other operating net assets and intangibles x
IC at start x
NIC (capex – depreciation + change in working capital) x
IC at end x

[email protected] 1. 4

The proportion of NOPAT that is reinvested in NIC is the ‘Reinvestment Rate’ (‘RR”):

RR % = NIC__
NOPAT

FCFF = NOPAT (1 - RR %)

Rates of Return

ROIC

‘Return on Invested Capital’ (‘ROIC’) equals NOPAT for the period t (NOPATt) divided by opening (or
average) Invested Capital (ICt-1):

ROIC t = NOPAT t ∴ NOPAT t = ROIC t x ICt-1
ICt-1

ROICt can be expressed in terms of a margin and net operating asset turnover ratio:

ROIC t = NOPATt x Revenues t
Revenuet ICt-1

= NOPAT margin
Net PP&E t-1 + Working Capital t-1
Revenues t Revenues t

Taking the example in Appendix 3

[email protected] 1. 5

RONIC

Part of ROIC will incorporate the return on new invested capital, termed marginal ROIC or ‘Return On
New Invested Capital’ (‘RONIC’), which can be calculated on the assumption that the growth in NOPAT
in the period is due to NIC made at the end of the prior period:

RONIC t = Change in NOPAT in year
NIC in previous year

= NOPAT t - NOPAT t-1
NIC t-1

= g. NOPATt-1
NICt-1

∴ gt = RONIC t x NIC t-1
NOPAT t-1

= RONIC t x RR t-1

∴ RR t-1 = Growth NOPAT t
RONIC t

NOPAT t-1 = NOPAT t + RONIC t x NIC t-1

Taking the example in Appendix 3:

ROIC and RONIC

Average ROIC is the return on all invested capital, including NIC made this year and in prior years, so
will incorporate RONIC

ROIC t = NOPAT prior year + Change in NOPAT this year
Invested Capital at start of last year + New Invested Capital last year

[email protected] 1. 6

= NOPAT t-1 + gNOPAT t x NOPAT t-1
IC t-2 + gIC t-1 x ICt-2

= NOPATt-1 x 1 + gNOPAT t
IC t-2 1 + gIc t-1

= ROIC t-1 x 1 + gNOPAT t
1 + gIC t-1

= ROIC t-1 x 1 + [ RRt-1 x RONIC t ]
1 + gIC t-1
From Appendix 3:

Forecasting Cash Flows

General Approach

The length of the forecast period and when cash flows are deemed to arise during the year (usually at
the end of the year or mid year) needs to be determined first. The accuracy of any forecast beyond two
or three years has to be questioned, meaning a long term forecast period creates more uncertainty.
However, if the value of the business calculated at the end of the forecast period is based on a single
formula, as is popular for a TV calculation, the components of that formula need to be reasonably
justifiable over the long term terminal period. This requires a long enough time period for cash flows
and other relevant financial measures to reach some ‘Steady State’ (when growth in income and net
assets is sustainable), which would depend on where the business is in its life cycle, competition in the
industry, growth rates, risk profile etc.

Operating profits

A forecast would typically start with revenue, with annual price and volume estimates based on either
a top-down (market share) or bottom-up approach (simulation or scenario analysis can also be used to

[email protected] 1. 7

derive expected revenues based on weighted probabilities), growing at various rates over the period.
Fixed costs that do not vary with revenue should be treated separately, whilst other operating costs
(excluding depreciation and amortisation) can be assumed to be a percentage of revenues. A review of
financial statements over the past few years, once adjusted for abnormal items (acquisitions,
discontinued operations, restructuring, capitalised expenses, etc), should help forecasting.

Earnings Before Interest Tax Depreciation & Amortisation (EBITDA) can be calculated directly by applying
an assumed EBITDA margin to revenues or indirectly by calculating operating expenses (ignoring
depreciation and amortisation), as a percentage of revenues.

Investing for operating profits

EBITDA should be adjusted for non-cash items, which, in this simple case, involves deducting the
increase in operating working capital (‘OWC’)(or adding a decrease), calculated as the closing less
opening OWC balance. OWC represents net current assets used in the daily operations which are
expected to be consumed or converted into cash in the year or operating cycle (inventory + trade
receivables – trade payables) and which require financing. Each component can be estimated based on
a percentage of sales.

Capex (net of disposals) represents the increase in operating Gross Property, Plant & Equipment (PP&E)
after adding back asset retirements that have been removed. As the closing book value of PP&E (cost
net of accumulative depreciation) equals the opening net PP&E + capex – depreciation charge, capex
will be the balancing item if net PP&E and depreciation are assumed (this avoids the need to forecast
retirements).

Net PP&E can be based on a percentage of revenues (inverse of the Asset Turnover):

Net PP&En = Assumed % x Rn

Depreciation can be estimated as a percentage of opening gross or net PP&E (the latter is preferred to
avoid problems with retirements):

Depreciationn = Assumed % x Net PP&E n - 1

Capex will then be the balancing figure from:

Net PP&En = Net PP&En - 1 + Capexn - Depreciationn

⸫ Capexn = Net PP&En - Net PP&E n - 1 + Depreciationn

(see Koller et al. (McKinsey) (2025) p.266, p.273)

[email protected] 1. 8

A more detailed estimate would assume a depreciation profile for PP&E existing at the valuation date
balance sheet and would calculate depreciation on capex each year in the forecast period using a
‘vintage’ approach (straight line depreciation on each year’s capex based on average asset lives).

Depreciation could also be a multiple of capex if capex is assumed to be a percentage of revenues rather
than as estimated as above. Capex is required to increase the productive capacity (‘growth’ capex) and
maintain existing capacity (‘maintenance’ capex). The latter would represent true economic depreciation
rather than accounting depreciation, which is often used as a proxy. Ignoring OWC, Invested Capital will
only grow if capex exceeds accounting depreciation, so the capex / depreciation ratio must exceed 1.0
if growth is assumed. Capex and the increase in OWC represent the gross cash investment in Invested
Capital (before depreciation), required to generate the forecast EBITDA.

Taxes

The final calculation to arrive at FCFF (in this simple case) is to deduct the operating cash taxes that
would be paid on pre-financing operating and investing cash flows. A tax computation based on taxable
profits (net of permanent differences to pre-tax profits), incorporating tax relief on capex rather than
depreciation (capital allowances in the UK) and adjustments for accumulated tax losses, would be
preferred, but the required information is unlikely be available. An estimate of taxable profits from the
income statement should be made, excluding financing items, to which the statutory tax rate can be
applied before the increase in operating ‘Deferred Taxes’ (discussed in Part 4) is deducted to arrive at
taxes paid on operating cash flows (see Koller et al. (McKinsey) (2025) ch.20, Damodaran (2025) ch.10,
Bodmer (2015) ch.12).

Towards the Terminal Value: Achieving Steady State

Competition should drive down ROIC (see Appendix 2), so that new investments generate less value
(zero value if the returns equal the discount rate) and the returns and growth rates remain constant
thereafter. Once the final forecast period has been reached, a steady state should be in place to allow
a reasonable long term growth rate to be assumed in the TV calculation (such as the long term economic
growth rate in the country where the business operates) and to ensure revenues, net profits and balance
sheet items grow at the same rate.

The steady state growth rate g* (usually revenue growth) should be in place by the final year of the
forecast period (year n), so that in the first year of the terminal period (n+1) all balance sheet items
(including debt and equity) and flows (free cash flows, profit after tax, dividends and ‘Residual Income’
– discussed in Part 3) also grow at g*. If interest expense is calculated on opening balances, then
steady state should apply to year n-1 (so that debt grows at g* in year n-1 and interest grows at g* in
year n).

Appendx 3 provides a simple illustration of steady state (3.0% growth is achieved in year n-1 or year 4).
The following assumptions are made:

[email protected] 1. 9

 Revenues grow at g* and margins are constant from year 4.

 Other assumptions are made to ensure all income components and balance sheet items grow at g*
(including debt and equity):

○ The carrying amount of operating fixed assets (Property, Plant & Equipment ‘PP&E’) at the year
end is calculated as a % of revenues for the year:

Net PP&E n + 1 = ( Net PP&En / Revenuen ) x Revenuen+1

= Net PP&En x (1 + g*)

○ The depreciation expense for the year is calculated a % of opening Net PP&E

Depreciation (D)n + 1 = Net PP&En x assumed depreciation rate %

○ Capex is implied from the above:

Capexn+1 = Net PP&E n + 1 - Net PP&En + Dn + 1 = g*. Net PP&E + Dn+1

○ The carrying amount of working capital at the year end is calculated as a % of revenues for the
year:

Working capital (WC)n + 1 = ( WCn / Rn ) x Rn+1

= WCn x (1 + g*)

⸫ Change in WC n + 1 = g* . WCn

 As a result RONIC and the Reinvestment Rate are constant and equal to the final forecast year (the
average ROIC is also constant)

Integrated Forecast Financial Statements

Once the main components of FCFF have been forecasted (revenues, operating costs, changes in
invested capital, tax), non-operating forecasts can be made, principally debt and equity cash flows (after
tax), which allows forecast financial statements to be prepared. Although a DCF using FCFF to estimate
the EntV does not require financial statements for each forecast period, it is useful to produce them for
a number of reasons:

 to identify risk and return measures: credit risk ratios can indicate financial strain, whilst return
measures are an important ‘value driver’

[email protected] 1. 10

 to calculate net profits and equity cash flows for other calculation methods (discussed in Part 3):
residual net income and equity cash flow methods that should give similar equity values as under
the traditional FCFF valuation method (after debt is deducted from Enterprise Value)

 to compare capital structure to assumptions used in the discount rate: the discount rate is calculated
based on capital structure assumptions that may or may not be consistent with forecast leverage
ratios

Terminal Value

TV based on FCFF

The TV can be determined using a growing perpetuity model:

TVn = FCFFn+1
r – g*

Where n is the last year of the forecast period, FCFFn+1 the steady state FCFF in the first year of the
terminal period, r the discount rate and g* the steady state growth rate. This would then be discounted
back over the forecast period to the valuation date:

PV at valuation date = TVn
(1 + r )
n

TV based on‘NOPAT’

We can replace the FCFF growing perpetuity formula with the following:

TVn = NOPATn+1 x ( 1 - RR )
r - g*

= NOPATn+1 x 1 - g*
RONICn+1
r - g*

In the presence of inflation, g* and RONIC should be expressed in real terms (see Appendix 2).

TV based on multiples

An alternative would be to calculate the TV based on a multiple applied to FCFFn+1 (the equivalent to 1 /
(r – g*) ) or some other measure such as EBITDA, so long as the multiple was suitable for enterprise
value (i.e. a Price / Earnings multiple could not be used):

[email protected] 1. 11

TVn = EBITDA n+1 x multiple

A perpetuity approach would be more traditional, although this could be used to derive the implied
multiple as a reasonableness check.

Scenarios

The assumptions that significantly affect the DCF value should be identified so that scenarios can be
modelled to indicate a valuation range. Typical ‘value drivers’ would be revenue growth (including the TV
growth rate), EBITDA margins, investments and the discount rate. In the simple case, a best and worst
case scenario would be shown in addition to the base case.

DCF Values

The sum of the PV of FCFF over the forecast period (n years) and the PV of the TV represents the operating
Enterprise Value:
Stready state FCFF

Enterprise Value0 = FCFF1 + FCFF2 + ……… + FCFFn-1 + FCFFn + FCFFn + 1
(1 + r)
1
(1 + r)
2
(1 + r)
n-1
(1 + r)
n
(1 + r)
n

Forecast FCFF PV TV PV

This assumes the discount rate is constant and FCFF is received at the end of the year.

______________________________________

Copyright © 2025 Christopher F. Agar

The information contained in this article has been prepared for general information and educational purposes only, and should not be
construed in any way as investment, tax, accounting or other professional advice, or any recommendation to buy, sell or hold any
security or other financial instrument. Readers should seek independent financial advice, including advice as to tax consequences,
before making any investment decision.

While the author has used their best efforts in preparing this article, they make no representations or warranties (express or implied)
with respect to the accuracy, completeness, reliability or suitability of the content. The content reflects the author’s own interpretation
of financial theory, accounting standards and tax requirements. The author accepts no responsibility for any loss which may arise,
directly or indirectly, from reliance on information contained in the article.

All content is the copyright of the author except where stated and a source is acknowledged. The whole or any part of this article may
not be directly or indirectly reproduced, copied, modified, published, posted or transmitted without the author’s express written
consent.

[email protected] 1. 12

Suggested reading

Books:

Arzac, E.R. (2008) Valuation for Mergers, Buyouts and Restructurings (2
nd
ed.) Wiley.
Benninga, S. & Sarig, O.H.(1996) Corporate Finance: A Valuation Approach, McGraw Hill
Bodmer, E. (2015) Corporate and Project Finance Modeling Wiley
Damodaran, A. (2025) Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (4
th
ed.) Wiley
Fernàndez, P. (2002) Valuation Methods and Shareholder Value Creation. San Diego/London: Academic Press.
Holthausen, R.W & Zmijewski, M.E. (2020) Corporate Valuation: Theory, Evidence & Practice (2
nd
ed.). Cambridge.
Koller, T.,Goedhart, D.,Wesells, D., McKinsey & Co. (2025) Valuation: Measuring and Managing the Value of Companies (8
th
ed.). Wiley.
Penman, S. & Pope, P. (2025) Financial Statement Analysis for Value Investing, Columbia University Press
Tham, J. & Vélez Pareja, I. (2004) Principles of Cash Flow Valuation. Elsevier.

Papers:

Bradley, M. & Jarrell, G.A. (2003) “Inflation and the Constant-Growth Valuation Model: A Clarification” http://ssrn.com/abstract=356540
Buttignon, F. (2012) “Terminal Value, Growth and Inflation in DCF Models: Some Problems and Practical Solutions”
http://ssrn.com/abstract=2041289
Caness, J.L. & Jarrell, G.A (2022) “The Proper Treatment of Cash Holdings in DCF Valuation Theory and Practice” Journal of Business
Valuation and Economic Loss Analysis 2022: 17(1) pp.39-64
Cooper, I.A. (2019) “Setting the horizon value using DCF-based methods: Teaching note” https://ssrn.com/abstract=3159030
Cooper, I.A. (2021) “Using the constant growth formula to set the horizon value in corporate valuation: The case of growth firms and
why you need a longer horizon” https://ssrn.com/abstract=4094896
Cornell, B. & Gerger, R. (2017) “Estimating Terminal Values with Inflation: The Inputs Matter—It Is Not a Formulaic Exercise” Business
Valuation Review Vol.36 No.4
Forsyth, J.A. (2018) “An alternative formula for the constant growth model”
https://www.researchgate.net/publication/332952318_An_alternative_formula_for_the_constant_growth_model
Fuller, R.J. & Hsia, C-C (1984), “A Simplified Common Stock Valuation Model” Financial Analysts Journal Sept-Oct 1984
Gordon, M.J and Shapiro, E. (1956) "Capital Equipment Analysis: The Required Rate of Profit," Management Science, 3,(1) (October
1956)
Gordon, M. J. (1959). "Dividends, Earnings and Stock Prices". Review of Economics and Statistics. 41 (2). The MIT Press: 99–105
Holland, D.A., and Matthews, B (2016): “Don’t Suffer from a Terminal Flaw, Add Fade to Your DCF” (Credit Suisse, Holt Market
Commentary, 14 June 2016)
Holland, D.A. (2018) “An Improved Method for Valuing Mature business and Estimating Terminal Value” Journal of Applied Corporate
Finance, Winter 2018
Jennergren, L.P. (2008) “Continuing Value in Firm Valuation by the Discounted Cash Flow Model”. European Journal of Operational
Research, 185, 1548-1563.
Jennergren, L.P. (2011) “A Tutorial on the Discounted Cash Flow Model for Valuation of Companies” Stockholm School of Economics,
https://swoba.hhs.se/hastba/papers/hastba0001.pdf
Mauboussin, M.J. & Callahan, D. (2022) “Return on Invested Capital: How to Calculate ROIC and Handle Common Issues”, Morgan
Stanley 6 October 2022
Nissim, D. (2022) “Profitability Analysis” https://ssrn.com/abstract=4064824
Nissim, D. (2022) “Reformulated Financial Statements” https://ssrn.com/abstract=4064722
O’Brien, T (2003) “A Simple and Flexible DCF Valuation Formula”, Journal of Applied Finance, Fall / Winter 2003
Vélez–Pareja,I. (2009) “Constructing Consistent Financial Planning Models for Valuation” http://ssrn.com/abstract=1455304

[email protected] 1. 13

Appendix 1: Present Value Formulae

Finite Period

If an amount invested (capital or principle) is certain to be recovered at some future date, together with
income (investment or interest income based on some rate of return), we can say the investment is risk
free as to the amount and timing of the cash flow. The risk free rate of return should apply, meaning the
investor is rewarded for the ‘time value of money’.

An investment or deposit of PV would, in this case, grow to C at the risk free rate, such that after 1 year
C = PV x (1 + r), where C = the cash flow received at the end of the year or the Future Value, PV = Present
Value and r = the risk free rate (effective annual rate). The risk free rate is the rate required by the
investor for the zero risk investment. Of course, business cash flows are risky and investors will expect
a risk premium to be added to the risk free rate.

If C is received after more than 1 year, PV will be compounded if interest is retained on deposit: interest
(assumed in this case to be paid annually at the end of each year) will accrue on the opening balance
(interest on interest). The future value will equal the present value when the income return has been
factored out (discounted, the reverse of compounding):

PV = C C received after 1 year
(1 + r)

PV = C = C C received after n years
(1 + r) (1 + r) (1 + r) …. (1 + r)
n

The present value of multiple cash flows received over a specified forecast period can be estimated
from:

PV = C + C + C + ……….. C__
(1 + r)
1
(1 + r)
2
(1 + r)
3
(1 + r)
n

This can be simplified to:

PV = C x 1 x 1 - 1 _
r (1 + r)
n

[email protected] 1. 14

If PV is already known (the fair price in the market), the rate r* that discounts cash flows to PV is the
‘Internal Rate of Return’ or ‘IRR’ (if the IRR is greater than the required return r, making the investment
and paying PV for it would be worthwhile). The IRR can be calculated in Excel using the XIRR function
or determined using trial and error (goal seek). Problems arise (i.e. multiple IRR can result) if there is
more than one change in the sign of the cash flow, although this can be avoided using another method
to calculate IRR (as when calculating the effective interest rate for measuring amortised cost or the
implicit rate for a lease, discussed in Part 4).

If C grows at a rate g over the finite period n:

PV = C (1 + g)
1
+ C (1 + g)
2
+ C (1 + g)
3
+ ………… C (1 + g)
n

(1 + r)
1
(1 + r)
2
(1 + r)
3
(1 + r)
n

This can be simplified to:

PV = C x 1 x 1 - (1 + g)
n

r - g (1 + r)
n

If C varies each year, as one would expect in a DCF, we have to discount each period, using the long
formulae, until such time as we assume it is constant or growing at a constant rate.

Perpetuity

If C is received in perpetuity (infinite period) without growing (an annuity):

PV = C x 1
r

If F is received in perpetuity growing at g each year:

PV = C x 1
r - g

[email protected] 1. 15

This is the Gordon Growth Model, used in the Dividend Discount Model (discussed in Part 3 of this
series) (Gordon & Shapiro (1956), Gordon (1959))

The constant growth perpetuity formula can be adjusted to allow for g to reduce or ‘fade’ at a linear
rate ‘f’ over time (Holland (2016)):

PV = C x 1
r - g + f

One Finite Period + Perpetuity (’2-Stage Model’)

The 2-stage model combines the equations for finite (time 0 to n) and infinite (time n+1 on) cash flows,
allowing for different growth rates (for example an initial high rate gH followed by a low rate gL):

PV = C1 x 1 x 1 - (1 + gH)
n
+ Cn+1 x 1__ x 1__
r - gH (1 + r)
n
r - gL (1 + r)
n

PV at tn of stage 2

PV today of stage 1 PV today of stage 2
where

Cn+1 is the cash flow at the end of the first period after the finite period (n + 1). As C1 is the cash flow
received at the end of year 1, Cn+1 = C1 x (1 + gH)
n - 1
x (1 + gL)

If we assume a cash flow received today (C0) grows at gH to C1 after one year, then the above formula
becomes:

PV = C0 x 1 + gH x 1 - (1 + gH)
n
+ (1 + gH)
n
(1 + gL) x 1__
r - gH (1 + r)
n
r - gL (1 + r)
n

[email protected] 1. 16

If there is an immediate linear decrease in the growth rate from gH to gL over period 2H followed by a
constant growing perpetuity at gL, the ‘H’ fade model can be used (Fuller and Hsia 1984):

PV at time 0 = C0 1 + gL + C0 H (gH – gL)
r - gL r - gL

(see Damodaran (2025) ch.14 for further discussion on the H model)

Two Finite Periods + Perpetuity (‘3-Stage Model’)

The 3-stage model shows cash flows growing at three different rates, an initial phase (with growth g1),
an interim phase (with growth g2) and a perpetuity phase (with growth g3). Growth rates would typically
reduce from g1 to g3, although the transition period can incorporate a reducing growth rate that ‘fades’
over the period from g1 to g3, following the H model above.

The 3-stage model can be shown as:

PV = C1 x 1 x 1 - (1 + g1)
n1
1
st
stage
r - g1 (1 + r)
n1

+ Cn1+1 x 1 x 1 - (1 + g2)
n2
2
nd
stage (Typically modelled as a ‘fade’ period)
r - g2 (1 + r)
n2

+ Cn2+1 x 1__ x 1__ 3
rd
stage
r - g3 (1 + r)
n2

[email protected] 1. 17

Appendix 2 : Terminal Value Driver Formulae

The main growing perpetuity TV formula that decomposes FCF into NOPAT, g and RONIC is:

TVn = NOPATn+1 x 1 - g*
RONICn+1

r - g*
where:
NOPAT = Free Cash Flows to the Firm (FCFF) + New Invested Capital (NIC)
NIC = ( Capital expenditures – Depreciation ) + Increase / (decrease) in working capital
RONIC = Return On New Invested Capital
g* = Steady state (sustainable) growth rate of NOPAT (and Invested Capital)

Replacing NOPAT with ROIC n+1 x ICn:

TVn = ROIC n+1 x ICn x 1 - g*
RONIC n+1

r - g*
The TV in Appendix 3 can be shown as:

As Invested Capital grows at the steady state rate of g* and NIC = growth x Invested Capital at the
start of the period:

NICn+1 = g* x ICn

We can replace these expression in the FCFF – NOPAT equation:

FCFFn+1 = NOPATn+1 - NIC n+1

= ( ROIC n+1 x ICn ) - ( g* x ICn )
A2.1

[email protected] 1. 18

= ICn x ( ROIC n+1 - g*)

TVn = ICn x ROIC n+1 - g*
r – g*

The TV in Appendix 3 can be shown as:

This TV formula can be rewritten in a number of ways:

TVn = ICn + ICn ROIC n+1 - r
r - g*

This formula will be mentioned again when alternative DCF methods are covered in Part 3 of this series.
The formula shows the TV as the value of net operating assets (Invested Capital) existing at the start of
the terminal period (ICn) and the value derived from future investments (NIC) made in perpetuity. Value
will be created if the expected return on assets (ROIC) exceeds the required return (‘excess returns’).
The average return on all assets (ROIC) is used here as it is being calculated on total net operating
assets (IC).

The second term can also be shown as follows:

= ICn ( ROIC n+1 - r ) +

r r - g*

(see Koller et al. (McKinsey) 2025 p.866, p288)
(see Koller et al. (McKinsey) 2025 p.288)
A2.2
A2.3
A2.4

[email protected] 1. 19

=
+

This breaks the return on all assets down into a constant perpetuity value (first terminal year excess
returns on all assets received in perpetuity) and a growing perpetuity value (second terminal year excess
returns on new investments growing in perpetuity). If RONIC = r the second term is zero as new
investments will not create value (until RONIC is greater than r).

We can also write the TV as a no growth value (NOPAT / r) plus the value of future growth:

TVn = NOPATn+1 + NOPATn+1 ROIC n+1 - r g*
r r ROIC n+1 r – g*

Inflation

In a high inflation environment growth, rates and returns should be expressed in real terms to account
for inflation:

TVn = NOPATn+1 x 1 - g*
real

RONICn+1
real

( r
real
- g*
real
) (1 + i)
(see Arzac 2008 p.90)
A2.5

[email protected] 1. 20

where

i = the inflation rate
g*
real
= (1 + g*
nominal
) / ( 1 + i ) - 1 = (g*
nominal
- i ) / ( 1 + i )
RONICn+1
real
= reinvestment rax x g*
real

The real RONIC is here implied from the fixed reinvestment rate, so that the implied RONICn+1
nominal
will
differ when ignoring inflation. From Appendix 3, if we assume inflation is 1.98% so the real growth rate
is 1.0%, the implied nominal RONIC drops from 12.40% if inflation is zero to 6.19% taking into account
inflation (this is based on Arzac 2005 p.17 - see Koller et al. (McKinsey) 2025 p.502 for a discussion
about converting all figures, including NOPAT, into real terms).

[email protected] 1. 21

Appendix 3: Enterprise Value Simplified Example

This simplified example illustrates the basic principles of DCF Enterprise Valuation, particularly the
requirement for a steady state towards the end of the forecast period. A detailed discussion of steady
state cash flows, along with a DCF model can be found in Jennergren (2011). To simplify things, deferred
tax and adjustments to the EntV to arrive at Equity Value (‘EqV’)(see Parts 4 and 5) have been ignored.

In the base case, revenues have reached the long term sustainable growth rate used in the perpetuity
(3.0%) by year 3, and by year 4 all flows and balances in the financial statements grow at this rate. ROIC
and RONIC are both constant and equal at 12.40% (and will remain this way happily forever), since the
proportion of NOPAT reinvested as New Invested Capital (NIC) is fixed at the year 5 level
1
. Discounting
the year 5 TV and forecast period cash flows at a constant 10.0% gives a base case EnV of 750.00 and
EqV of 600.00.

If revenue growth, operating expenses / revenues and the discount rate are changed by 1.0% increase
/ decrease, 0.5% decrease / increase and 1.0% decrease / increase respectively, the EntV ranges from
1,120.87 to 544.69. Over 85% of the variation is due to the TV, because the based case growth adjusted
perpetuity discount rate ranges 7.0% +/- 2.0%. Also RONIC in the worst case scenario has decreased
below the discount rate (WACC), meaning new investments are value destructive.

It is assumed the book value of debt equals market value (‘MV’) and all ‘excess cash’ is paid out to
shareholders. This valuation illustrates the approach of some experts by assuming cash required to
operate the business (‘Operating Cash’) approximates 2.0% of annual revenue (see Koller et al.
(McKinsey) 2025 p.213, p.336). Some argue that cash should not be separated into operating and excess
cash (see Caness & Jarrell (2022)), but is shown in this example. Some also question whether operating
cash should be included in working capital rather than treated separately as cash. It is treated here as
part of working capital, so the increase in working capital includes the increase in operating cash. How
cash is treated in general will be discussed in Parts 2 and 4 of this Series.

Calculation of the discount rate assumes the MV of debt as a percentage of the MV of debt and equity
(the EntV) is constant at 20%, and debt levels have been set to ensure this occurs. This requires
circularity and a ‘recursive’ procedure, where the EntV Terminal Value (‘TV’) is first calculated in order
to set the debt at the end of the forecast period. The EntV at the prior period (year 4) equals the TV plus
the year 5 Free Cash Flow to the Firm (FCFF) both discounted back one period, which allows year 4 debt
to be calculated. This procedures is carried on back to the valuation date, at which time interest can be
calculated (going forward) and net income determined (allowing for tax relief).

1
If, instead, RR were to increase to 30% and growth rates remain at 3.0%, RONIC would reduce to 10.0%
(ROIC reduces to 10.0% very slowly over some 200 years) since more investment would be required to
generate the same growth (RONIC = g / RR). As this equals the discount rate, the NIC will not add any value.

[email protected] 1. 22

[email protected] 1. 23

WACC is the discount rate, or the ‘Weighted Average Cost of Capital’, which is the subject of Part 2 of
this Valuation Series.

[email protected] 1. 24

[email protected] 2.1

BUSINESS VALUATION
Part 2: Discount Rates and Tax Shields

Introduction

The average after-tax rate of return required by all providers of financial capital, adjusted for the
perceived riskiness of the cash flows distributable to them (‘Free Cash Flows to the Firm’ / ‘FCFF’) and
weighted by the market values of each source of financing, is called the ‘Weighted Average Cost of
Capital’ (‘WACC’). In Part 1, the discount rate ‘r’ is the WACC.

Taking the simple case of debt and equity as the only sources of financing, WACC can be shown as:

Post-tax WACC = Required return for x E + Required return for x D
equity investors D + E debt providers D + E

where the required return (income and capital growth) comprises a risk free rate (Rf) plus a premium for
equity or debt risk:

 Equity return (Cost of Equity Ke) = Rf + Equity Risk Premium (‘ERP’)

 Debt return (Cost of Debt Kd) = Rf + Debt Risk Premium (‘DRP’)

Kd represents the expected yield from holding the debt to maturity (if issued at par or face value, the
yield at issue would be the coupon or interest rate). As debt interest is tax deductible, whereas equity
dividends are not, the pre-tax cost of debt must be adjusted to the after-tax equivalent (Kd (1 – tax rate
t) ), assuming tax relief is available in the same period the interest is paid.

Leverage

Leverage (‘L’) measures debt as a proportion of financial capital (in book value or market value terms): L
= D / (D + E) (assuming equity is the only other source of finance – any other financial claims, such as
preference shares, leases, or pension deficits would be added in). Gearing (‘G’) is the ratio D / E (so G
= L / (1 – L)). Leverage (L = G / (1 + G)), measured at market value, features in the above WACC
calculation, and gearing in the Cost of Equity, if using the ‘Capital Asset Pricing Model’ (‘CAPM’). The
market value of a debt instrument should be the same as its book value, assuming recognised at
amortised cost (to be discussed in Part 4), if the yield to maturity at the valuation date is the same as
when issued.

For equity investors, leverage adds financial risk (a greater chance the business defaults on its debt) to
the business risk (the uncertainty as to the amount and timing of future operating cash flows). Equity
investors will require a higher ‘geared’ (or ‘levered’) cost of equity (Kg) when facing both types of risk,
whereas an ungeared (or unlevered) all-equity financed business will be expected to generate an
ungeared cost of equity (Ku) that compensates them for business risk only.

C.F. Agar 16 Sept. 2025

[email protected] 2.2

In theory, the capital structure should be adjusted towards some optimum level. As the cost of debt is
less than the cost of equity, due to lower risk and the tax deductibility of interest, increasing debt in the
capital structure should reduce WACC (and hence increases value for equity investors), but at some level
this benefit will reverse as the risk of financial distress and default increases both the cost of debt and
equity. In practice, capital structure may be adjusted so as to align with the sector peer group (the
industry average for comparable companies with similar growth and business risk), so as not to alarm
investors.

If leverage changes during the forecast period, the WACC will change. It is usually assumed that the
business will adjust its capital structure to its target level before the end of the forecast period, and so
a constant WACC assumption might be justifiable (the leverage set in the WACC equation would then
be this target leverage, using market values). Adjusting the capital structure can be done by changing
debt (borrowing or repaying debt) and/or changing equity (paying special dividends from debt funding
or buying back shares). However, assuming a constant WACC may not be appropriate for some
businesses or projects if leverage is required to change (in leveraged buyouts or project finance, for
example, where debt repayments are scheduled and often not discretionary).

A DCF valuation for a private business poses a bit of a challenge if we need to verify that market value
leverage reaches the target level, since no market price exists for the debt and equity. The Enterprise
Value (‘EntV’) can be used as market value (i.e. fair value), so at any date we can set debt based on the
required leverage using the EntV at that date. In practice, this means working backwards from the EntV
at the end of the forecast period (‘Terminal Value’ / ‘TV’), setting debt at this date and then calculating
the EntV at the previous period (this will equal the TV plus final year FCFF, both discounted back one
period) and setting debt at this date and so on.

This process obviously causes circularity, as leverage depends on the EntV which depends on the WACC
which depends on leverage. Alternatively, we could assume a leverage figure in the WACC calculation
and avoid the need to calculate debt each period (not required for a FCFF valuation, but required when
valuing equity directly, as discussed in the next Part).

Debt and Cash

Excess cash (and liquid investments) that could be used to repay some debt at any time (with no impact
on operating cash flows), can be netted off ‘gross debt’ to ‘net debt’ (gross debt – cash). This means the
following must be based on net debt:

 Debt deducted from EntV when calculating Equity Value (‘EqV’) (amongst other ‘bridge’ items –
discussed in Parts 4 and 5)

 Leverage in the WACC: L = net debt / (net debt + equity)

 Equity beta in CAPM Cost of Equity, when re-gearing using Net D / E

 Cost of debt in the WACC (see Damodaran (2025) ch.15):

[email protected] 2.3

Cost of net debt Kdnet = (Cost of gross debt Kdgross x Debt) - (Return on cash Rcash x Cash)
Gross debt - Cash

The required return for cash would typically be the risk free rate (Rf), so that Kdgross = (Rf + DRP) and
Kdnet = Rf + ( Debt / Net Debt x DRP )

Some argue that total cash on the balance sheet (and liquid investments), and not just a proportion
deemed (arbitrarily) to be excess cash, should be deducted off gross debt (which would remove the issue
of whether or not operating cash is treated on its own or part of working capital) or treated separately.
Ignoring the net debt option and going for gross debt means cash is treated as a non-operating asset
like other such items (e.g. investments in associates, equity investments, head office property etc.).

In the example in Part 1 of this Series (the WACC for that valuation is shown below), all excess cash is
paid out and only operating cash is on the balance sheet (treated as part of working capital, so the
WACC is calculated based on gross debt).

Cost of Debt

The pre-tax cost of debt represents the ‘marginal return’ expected at the valuation date on new
borrowing with a maturity and currency matching the cash flow forecast. It should be based on the
expected cash flows from a debt instrument, representing the contractual (promised) cash flows
adjusted downwards for likelihood of non-payment (probability weighted cash flows) over the period to
maturity, meaning the promised yield to maturity will be more than the expected yield (as for Rf in the
CAPM, the time to maturity should be long term as well to match the forecast cash flows in the
valuation).

A quoted debt instrument could be used, issued by the company being valued itself or issued by a ‘proxy’
company with a similar credit risk (for example, by estimating a likely ‘synthetic’ credit rating for the
business using a credit rating model and determining what yield is available in the market for such a
rating). Alternatively, an estimate could be made for the actual cost of debt the business would incur if
it borrowed new long term funds (the marginal or incremental pre-tax cost of debt).

Assuming debt interest obtains full tax relief in the year paid (the ‘tax shield’ being interest x tax rate –
discussed in more detail in Appendix 1), the pre-tax cost of debt should be reduced to reflect the lower
after tax cost (post-tax cost of debt = pre-tax cost of debt x (1 – tax rate)). The tax rate should be the
actual rate that would apply to the interest paid, typically the ‘marginal’ rate, which may or may not be
the same as the statutory rate.

The tax deductibility of debt interest effectively generates a tax cash inflow (‘Tax Shield’) which can be
forecasted and discounted at an assumed risk-adjusted rate (discussed in more detail in Appendix 1).
The value of the geared company (Vg) should, in theory, equal the value of the ungeared company (Vu)
plus the value of the Tax Shield (VTS). In the WACC formula, deductibility of interest is included by
reducing the cost of debt by the marginal tax rate (t):

[email protected] 2.4

WACCpost-tax = Kg E + Kd (1 – t) D
D + E D + E

Cost of Equity

The total return achieved over a single period for an equity investor in a quoted company is the sum of
the cash inflow assumed to arise during the period (dividend) plus the change in market value (ex-
dividend) over the period (capital gain), as a percentage of the opening market value (ex-dividend),
representing the dividend yield and capital growth. If this return was expected at the start of the period,
it would represent the required return or cost of equity. As expectations change in the future (risk,
operating returns, growth, dividends, etc), so the cost of equity changes.

Expected return increases with risk, as indicated by the level of volatility or standard deviation of returns.
Equity risk will depend on market risk (share price volatility due to market volatility, as measured by
some market index), business risk (riskiness associated with FCFF) and financial risk (risk associated
with leverage affecting Free Cash Flows to Equity ‘FCFE’, used to pay dividends, subject to sufficient
legally distributable profits being available).

Asset pricing models try to identify which risks are relevant to equity investors and how to capture such
risk in the required return. The CAPM assumes only some of the total risk of any stock (uncertainty about
the future amount and timing of any income or capital gains) needs to be rewarded. Assuming an
investor is sufficiently diversified and constructs a portfolio of investments with a total risk that is less
than the risk of the individual portfolio stocks (selecting securities that are negatively correlated with
each other, such that negative factors for one stock are positive for another), some of the risk of the
stock (the specific, unique or unsystematic part) can be eliminated, leaving residual risk that relates to
the market as a whole (systematic or market risk). This means that, ignoring leverage for now, the
sensitivity of the stock to market risk is all that needs to be considered. Other models have expanded
on CAPM to introduce additional risk factors (Fama & French 2015).

The volatility of the return on the stock may or may not exactly match volatility of the market index (as
measured by the ratio of the standard deviation of their returns: stock / market). This relationship, when
adjusted by how closely the returns match each other (correlation coefficient of stock vs. market
returns), indicates the sensitivity of the stock to market risk, as measured by the equity ‘beta’ (=
correlation coefficient stock vs market returns x stock / market ).

If the stock risk matches market risk, beta = 1.0 and the required return would be the market return,
comprising the Risk Free Rate (Rf)
1
and the ‘Equity Risk Premium’ (‘ERP’)
2
. The stock’s sector is likely,
however, to have different risk to the whole market, so the beta
3
reflecting business risk (asset beta ßa
or ungeared / unlevered beta ßu) would not be 1.0, but lower or higher if the risk was lower or higher,
respectively, than the market as a whole: Cost of Equity (ungeared)(Ku) = Rf + ßa x ERP. If financial
risk is introduced via leverage, the asset beta needs to be increased to the equity beta (or geared /
levered beta ßg) to reflect the extra risk. This can be done using formulae discussed in Appendix 1: Cost
of Equity (geared)(Kg) = Rf + ßg x ERP.

[email protected] 2.5

For a private business, the ungeared cost of equity can be estimated by taking the average or median
of a sample of ‘proxy’ equity betas observed in the market (reflecting the same business risk
characteristics as the private business), and adjusting for leverage to arrive at an average asset beta
that can be used for the valuation and geared up to reflect leverage chosen for the valuation.

WACC

An example of how the WACC is built up is shown below. This version (9.75%) would be suitable when
an amount of debt is assumed and the value of the tax shield does not depend on FCFF or the EntV (beta
is re-geared adjusting D/E by (1 – t)). An alternative financing policy assumption is for the amount of
debt to be based on an assumed leverage ratio applied to EntV, when the tax shield would depend on
FCFF (beta is re-geared ignoring the tax adjustment, resulting in 10.0% in the example). Also, it is
assumed here that the debt beta is ignored when re-levering the asset beta (see Appendix 1 for further
discussion on tax shields and betas).

[email protected] 2.6

9.75% = Rf + a (1 + D (1 – t) ) ERP x E__ + ( Rf + Debt Risk Premium
4
)(1 – t) x D__
E D + E D + E

10.0% = Rf + a (1 + D ) ERP x E__ + ( Rf + Debt Risk Premium
4
)(1 – t) x D__
E D + E D + E

Cross -border WACC

The return required by investors for investing in a business located outside their ‘home’ country will
reflect the different risks compared to a business located in their jurisdiction. Cross border DCF
approaches, including CAPM adjustments, are discussed briefly in Appendix 2.

The next paper will discuss how alternative DCF valuation methods can be used (Economic Profits,
Adjusted Present Value, Capital Cash Flows, Residual Income), incorporating some of the information in
Appendix 1.

[email protected] 2.7

Notes

1 Rf is typically measured using the yield to maturity, at the valuation date, for a government bond maturing in
10 years, in the same currency as the stock currency / cash flows. This yield is meant to estimate the risk
free return over the period for which the cost of equity is being calculated, which for a constant cost of equity
(or WACC) would be the life of the business or project. As risk free yields comprise a real risk free rate, a
premium for expected inflation and a premium for market risk (the general level of interest rates affecting
bond prices), a longer term bond might be more sensitive to unexpected changes in inflation and not risk
free.

2
ERP should be a forward looking estimate, but may, in practice, be based on observed historic returns over
a long term period, on the assumption that the ERP will revert to the long term average. An ERP, however,
can be implied from current market prices using stock valuation tools. The ERP should be the market required
return in excess of whatever risk free rate is used in the WACC

3
Asset betas can be estimated by de-levering observed quoted company equity betas, and are available from
beta consultancy firms or other providers (e.g. Bloomberg).

4
The ‘Debt Risk Premium’ (‘DRP’) or ‘Credit Spread’ is the required return for debt holders (pre-tax cost of
debt) in excess of the risk free rate: Kd = Rf + DRP. As for the cost of equity, DRP can be expressed in terms
of ERP: DRP = ßd x ERP, where ßd is the ‘Debt Beta’ equal to DRP / ERP (see https://edbodmer.com/debt-
beta-and-credit-spreads/).

__________________________________________

Copyright © 2025 Christopher F. Agar

The information contained in this article has been prepared for general information and educational purposes only, and should not be
construed in any way as investment, tax, accounting or other professional advice, or any recommendation to buy, sell or hold any
security or other financial instrument. Readers should seek independent financial advice, including advice as to tax consequences,
before making any investment decision.

While the author has used their best efforts in preparing this article, they make no representations or warranties (express or implied)
with respect to the accuracy, completeness, reliability or suitability of the content. The content reflects the author’s own interpretation
of financial theory, accounting standards and tax requirements. The author accepts no responsibility for any loss which may arise,
directly or indirectly, from reliance on information contained in the article.

All content is the copyright of the author except where stated and a source is acknowledged. The whole or any part of this article may
not be directly or indirectly reproduced, copied, modified, published, posted or transmitted without the author’s express written
consent.

Suggested reading

Books:

Abrams, J.B. (2010) Quantitative Business Valuation: A Mathematical Approach for Today's Professionals (2
nd
edn.) Wiley
Arzac, E.R. (2008) Valuation for Mergers, Buyouts and Restructurings (2
nd
ed.).Wiley
Buckley, A (1995) International Capital Budgeting, Prentice Hall
Damodaran, A. (2025) Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (4
th
ed.) Wiley
Fernàndez, P. (2002) Valuation Methods and Shareholder Value Creation. San Diego/London: Academic Press.
Holthausen, Robert.W & Zmijewski, Mark.E. (2020) Corporate Valuation. (2
nd
ed.). Cambridge.

[email protected] 2.8

Koller, T.,Goedhart, D.,Wesells, D., McKinsey & Co. (2025) Valuation: Measuring and Managing the Value of Companies (8
th
ed.). Wiley
Pereiro, L.E. (2002) Valuation of Companies in Emerging Markets. Wiley
Pratt, S.P. & Grabowski, R,J,(2014) Cost of Capital: Applications and Examples. (5
th
ed.) Wiley
Tham, J. & Vélez Pareja, I. (2004) Principles of Cash Flow Valuation. Elsevier.

Papers

Ansay, T. (2009) “Firm valuation: tax shields discount rates”, MPRA Paper No. 23027 https://mpra.ub.uni-muenchen.de/23027/
Campani, C.H. (2015) “On the Correct Evaluation of Cost of Capital for Project Valuation” (2015), Applied Mathematical Sciences, Vol. 9,
2015, no. 132, 6583 – 6604 (https://www.m-hikari.com/ams/ams-2015/ams-131-132-2015/59571.html)
Cooper, I.A. & Nyborg, K.G. (2007) “Valuing the Debt Tax Shield” http://ssrn.com/abstract=979910
Damodaran, A. (2025) “Country Risk: Determinants, Measures and Implications”
https://pages.stern.nyu.edu/~adamodar/New_Home_Page/home.htm
Estrada, J (2007) “Discount Rates in Emerging Markets: Four Models and An Application” Journal of applied Corporate Finance, Spring
2007
Fama, E.F., and K.R. French (2015), " A five-factor asset pricing model", Journal of Financial Economics, 116, 2015, 1-22
Fernandez, P. (2011) “WACC: Definition, Misconceptions And Errors”, https://www.iese.edu/media/research/pdfs/DI-0914-E.pdf
Godfrey, S. & Espinoza, R. (1996) “A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets” Journal of
Applied Corporate Finance, Fall 1996
Hamada, R.S. (1972), "The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stock", Journal of Finance, 27, 1972,
435-452.
Harrington, J.P., Nunes, C.S. & Aboulamer, A (2023) “Valuation Handbook International Guide To Cost Of Capital 2023 Summary Edition”, Kroll
& CFA Institute Research Foundation
Harris, R.S., and J.J. Pringle (1985), "Risk-Adjusted Discount Rates: Extensions from the Average-Risk Case", Journal of Financial Research,
8, 1985, 237-244.
Holthausen, Robert.W & Zmijewski, Mark.E. (2012) “Pitfalls in Levering and Unlevering Beta and Cost of Capital Estimates in DCF
Valuations”, Journal of Applied Corporate Finance, Summer 2012
Kolari, J.W. (2017) “Gross and Net Tax Shield Valuation” https://ssrn.com/abstract=3088735
Kumar, V. (2021) “A Contribution Towards Integrating Theories of Asset Pricing and Corporate Finance, and Resolving the Tax Shield Puzzle”
https://ssrn.com/abstract=3902008
Lessard, D.R. (1996) “Incorporating Country Risk in the Valuation of Offshore Projects”, Journal of Applied Corporate Finance Fall 1996
Mariscal, J.O. & Lee, R.M. (1993) “The Valuation of Mexican Stocks: An Extension of the Capital Asset Pricing Model”, 1993, Goldman Sachs
Mejia-Pelaez, F. & Vélez–Pareja,I. (2011) “Cost of Equity and WACC for Perpetuities with Constant Growth”
http://ssrn.com/abstract=1651662
Miles, J., and R. Ezzell (1980), "The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life: A Clarification", Journal of
Financial and Quantitative Analysis, 15, 1980, 719-730.
Modigliani, F., and M.H. Miller (1958), "The Cost of Capital, Corporate Finance, and the Theory of Investment", American Economic Review,
48, 1958, 261-297.
Modigliani, F., and M.H. Miller (1961), " Dividend Policy, Growth, and the Valuation Of Shares", The Journal of Business, 34, 1961, 411-433
Modigliani, F., and M.H. Miller (1963), "Corporate Income Taxes and the Cost of Capital: A Correction", American Economic Review, 53,
1963, 433-443.
Myers, S.C. (1974), "Interactions of Corporate Financing and Investment Decisions - Implications for Capital Budgeting", Journal of Finance,
29, 1974, 1-25.
Oded, J., Michel, A. & Feinstein, S.P. (2011) “Distortion in corporate valuation: implications of capital structure changes, Managerial
Finance, Vol 37/8 (2011) https://www.academia.edu/download/66493494/Distortion_in_corporate_valuation_implic20210421-
16049-vxf9fl.pdf
Tham, J. & Vélez–Pareja,I.(2019)“An Embarrassment of Riches: Winning Ways to Value with the WACC”
https://www.researchgate.net/publication/5007340_An_Embarrassment_of_Riches_Winning_Ways_to_Value_with_the_WACC
Vélez–Pareja,I. (2003) “A Practical Guide for Consistency in Valuation: Cash Flows, Terminal Value and Cost of Capital”
https://www.researchgate.net/publication/26431792_A_Practical_Guide_for_Consistency_in_Valuation_Cash_Flows_Terminal
_Value_and_Cost_of_Capital
Vélez–Pareja,I. (2005) “A New Approach to WACC, Value of Tax Savings and Value for Growing and Non Growing Perpetuities: A Clarification”
https://ssrn.com/abstract=873686
Vélez–Pareja,I & Tham, J. (2007) “WACC, Value of Tax Savings and Terminal Value for Growing and Non Growing Perpetuities”
http://ssrn.com/abstract=789025
Vélez–Pareja,I., Ibragimov, R. & Tham, J. (2008) “Constant Leverage and Constant Cost of Capital: A Common Knowledge Half-Truth”,
https://www.sciencedirect.com/science/article/pii/S0123592308700354

[email protected] 2.9

Appendix 1 : WACC Theory & Tax Shields

MM Theory

Ignoring the tax benefits of debt, Modigliani & Miller (MM 1958) stated that the value of a business
should not be affected by how it is financed, as FCFF will be the same (FCFF ungeared = FCFF geared), implying
the WACC will be the same with or without any leverage. If the tax deductibility of interest is considered
(MM 1961), the value of the geared business will be greater than the value of the ungeared business
due to the present value of the tax inflows (‘Tax Shield’ / ‘TS’) from interest deductibility (Value of the
‘Tax Shield’ / ‘VTS’):

Value of geared firm (Vg) = Value of ungeared (Vu) + VTS

and since Vg = Equity Market Value (E) + Debt Market Value (D)

Vu + VTS = E + D

so Vu = E + D - VTS

Assuming perpetual debt of D (a constant amount each year), with interest at the cost of debt Kd paid
annually in perpetuity, VTS can be calculated using the no-growth perpetuity formula (see Part 1),
discounted at a rate Ψ that reflects the riskiness of the tax shield, so that:

Vg = Vu + Kd.t.D  VTS
Ψ

Assuming Ψ = Kd (MM also assumed Kd = Rf), this expression simplifies to:

Vg = Vu + t.D

Myers (1974) assumed Ψ = Kd (but not Kd = Rf) on the basis that debt levels do not depend on FCFF or
the EntV and the risk of tax shields relates to the ability of the business to generate sufficient income
to offset the tax deductions. Miles and Ezzell (1980) assumed debt was adjusted based on the assumed
leverage as from the end of the first year rather than the valuation date. As the interest in the first year
would be known, based on an assumed amount of debt at the valuation date (not dependent on the
value of the business), the tax shield in the first year would be discounted at the risk free rate and
thereafter at the ungeared cost of equity. The valuation at any future date would follow the same
principle in respect of new debt issues in the first year after the valuation date. Harris and Pringle (‘HP’)
(1985) assumed Ψ = Ku on the basis that debt levels (leverage) depend on the EntV and hence FCFF and
business risk. As the tax shield cash flows depend on the value of the business, they should be
discounted at the ungeared cost of equity (it is assumed that debt is continually adjusted to ensure
leverage is constant with effect from the valuation date)

[email protected] 2.10

General Equations with Tax Shield

♦ Finite period (general equation):

Cash flows distributable to equity investors (‘Cash Flows to Equity’ / ‘CFE’ = dividends + stock
repurchases) are what remain of FCFF after payments to debt providers (‘Cash Flows to Debt’ / ‘CFD’ =
pre-tax interest + debt principal net payments (- net new borrowings) less of tax relief on interest (Tax
Shield cash flows = pre-tax interest x tax rate):

CFD Tax Shield (TS)

CFE = FCFF - debt decr. (+ debt incr.) - Interest + tax rate x interest

= FCFF - ( Dn-1 - Dn ) - Dn-1 Kd + t. Dn-1 . Kd.

⸫ FCFF = CFE + CFD - t. Dn-1 . Kd.

Cash flows can be expressed in terms of the opening value to which they related times the required
return (FCFF = Vg,WACCg, CFE = E,Kg, CFD = D. Kd), TS = VTS Ψ):

Vgn-1 . WACCgn = En-1. Kgn + Dn-1. Kdn - Dn-1 . Kdn t

WACCgn = En-1. Kgn + Dn-1. Kdn ( 1 - t )
Vgn-1 Vgn-1

= En-1 Kgn + Dn-1 Kdn ( 1 - t )
(D + E)n-1 (D + E)n-1

where:
VTS, D, E - market values of tax shields, debt and equity, respectively
Kg, Kd, Ψ - required return on equity and debt and the discount rate for tax shields

As FCFF = E. Kg + D. Kd - VTS Ψ

And FCFF = Vu Ku = Ku . ( Vg - VTS ) (from Vg = Vu + VTS )

⸫ Ku . ( Vg - VTS ) = E. Kg + D. Kd - VTS . Ψ

The value of the tax shield can now be incorporated in the cost of equity formula by substituting D + E
for Vg and re-arranging, to give a general equation for Kg (see: Koller et al. (McKinsey)(2025) Eq.C.6
p.878); Tham & Vélez–Pareja (2019) Eq.14; Mejia-Pelaez & Vélez–Pareja (2011) Eq.2; Vélez–Pareja,
Ibragimov & Tham (2008) p.17):

The traditional WACC formula
(see: Fernandez (2011) Exhibit 1;
Mejia-Pelaez & Vélez–Pareja
(2011) App.C)

[email protected] 2.11

Kg = Ku + ( Ku - Kd ) D - ( KU -  ) VTS
E E

Note: D / E = L / (1 – L), where L is the leverage % D / D + E (or D / Vg)

Since FCFF = CFE + CFD - TS

WACCg . Vg + TS = Kg. E + Kd. D

Substituting Kg in the general equation (A1.1) into the above:

WACCg . Vg + TS = E + Kd. D

After re-arranging, this becomes the general WACC formula (see: Tham & Vélez–Pareja,I (2019) Eq. 28;
Mejia-Pelaez & Vélez–Pareja (2011) Eq.3):

WACC = Ku - ( Ku -  ) VTS - TS
D + E D + E

Note: TS = Kd. t. D where D = D / D + E and D + E = Vg

♦ Perpetuity (general equation):

With constant growth, the value of the tax shield is (see: Mejia-Pelaez & Vélez–Pareja (2011) Eq.6):

VTS = TS = Kd.t.D
Ψ - g Ψ - g

The general equation Kg for a constant growth perpetuity is the finite equation (A1.1) with VTS adjusted
for growth:

Kg = K + ( Ku - Kd ) D - ( Ku -  )
E E

Kg = K + ( Ku - Kd ) D - ( Ku -  ) Kd.t D
E  - g E

The general equation WACCg for a constant growth perpetuity is:

WACC = Ku - ( Ku - g ) VTS
D + E

A1.1
A1.2
A1.3
(see Fernandez (2011) Eq.10):

[email protected] 2.12

= Ku - ( Ku - g )
D + E

WACC = Ku - ( Ku - g ) Kd . t. L
 - g

The general equations Kg and WACC for a zero growth perpetuity is (setting g = 0 in A1.3 and A1.4):

Kg = Ku + ( Ku - Kd ) D - ( KU -  ) Kd.t.D 1
E  E
WACC = Ku 1 - Kd . t. L


= Ku 1 - VTS
Vg

Since Kd.t.L = Kd. t. ( D / Vg ) and VTS = t.D when g = 0
  

♦ Beta:

Weighted average betas can be applied to each component of the equation above:

Vu + VTS = E + D

ßu VU + ßTS PVTS_ = ßg E + ßd D _
D + E D + E D + E D + E

In terms of the equity or geared beta, this can be re-arranged into a general equation:

ßg = ßu + ( ßu - ßd ) D - ( ßu - ßTS ) VTS
E E

A1.4
A1.5
(see Vélez–Pareja (2005)
Eq. B7d)

[email protected] 2.13

Assuming Ψ = Ku (Harris & Pringle)

♦ Finite Period (Ψ = Ku )

If Ψ = Ku, it is assumed tax shield cash flows vary with FCFF and depend on the business risk.

The general equation for Kg over a finite period (eq. A1.1) with Ψ = Ku is adjusted to (see: Vélez–Pareja,
Ibragimov & Tham (2008) p.17):

Kg = Ku + ( Ku - Kd ) D - ( KU - KU ) VTS
E E

⸫ Kg = Ku + ( Ku - Kd ) D
E

The general equation for WACCg over a finite period (eq.A1.2) with Ψ = Ku is adjusted to (see: Vélez–
Pareja, Ibragimov & Tham (2008) p.17):

WACC = Ku - ( Ku - KU ) VTS - TS
D + E D + E

⸫ WACC = Ku - TS
D + E
⸫ WACC = Ku - Kd.t. D
D + E

⸫ WACC = Ku - Kd.t. L

This is the general equation for finite WACC with Ku replacing Ψ

WACC = Ku 1 - Kd . t. L  Ku 1 - Kd . t. L  Ku - Kd.t.L
 Ku

♦ Perpetuity (Ψ = Ku )

With constant growth and Ψ = Ku, the value of the tax shield is (see: Fernandez (2011) Eq.4):

VTS = TS = Kd.t.D
Ku - g Ku - g

The general equation Kg for a constant growth perpetuity (eq.A1.3) with Ψ = Ku is adjused to:

A1.6
A1.7

[email protected] 2.14

Kg = K + ( Ku - Kd ) D - ( Ku - Ku ) Kd.t D
E Ku - g E

Kg = Ku + ( Ku - Kd ) D same as finite
E

The general equation WACCg for a constant growth perpetuity (eq.A1.4) with Ψ = Ku is adjusted to

WACC = Ku - ( Ku - g ) Kd . t. L
Ku - g

WACC = Ku - Kd.t. L same as finite

Note: The equations for perpetuities are the same whether or not g = 0

Assuming Ψ = Kd (Myers)

♦ Finite Period (Ψ = Kd )

If Ψ = Kd, it is assumed tax shield cash flows do not depend on FCFF and business risk.

The general equation for Kg over a finite period with Ψ = Kd is adjusted to (see: Vélez–Pareja, Ibragimov
& Tham (2008) p.18):

Kg = Ku + ( Ku - Kd ) D - ( KU - Kd ) VTS
E E

⸫ Kg = Ku + ( Ku - Kd ) D - VTS
E E

The general equation for WACCg over a finite period with Ψ = Kd is adjusted to (see: Vélez–Pareja,
Ibragimov & Tham (2008) p.18):

WACC = Ku - ( Ku - Kd ) VTS - TS
D + E D + E

♦ Perpetuity (Ψ = Kd )

With positive growth and Ψ = Kd, the value of the tax shield is:

A1.9
A1.10

[email protected] 2.15

VTS = Kd.t.D
Kd - g

The general equation Kg for a growing perpetuity with Ψ = Kd is adjusted to:

Kg = Ku + ( Ku - Kd ) D - ( Ku - Kd ). Kd. t D
E Kd - g E

Kg if Ψ = Ku

Kg = K + ( Ku - Kd ) D 1 - Kd.t
E Kd - g

The general equation WACCg for a growing perpetuity with Ψ = Kd is adjusted to:

WACC = Ku - ( Ku - g ) Kd . t. L
Kd - g

This assumes D grows at g

The general equations for Kg and WACC for a zero growth perpetuity with Ψ = Kd are adjusted to (setting
g = 0 in A1.11 and A1.12)(see Holthausen & Zmijewski (2012) p.63):

Kg = Ku + ( Ku - Kd ) D ( 1 - t )
E
WACC = Ku 1 - t. L

Note: VTS = t.D (with zero growth and Ψ = Kd)

Beta Relevering

If debt is set as a proportion of the EntV (D = leverage x EntV), the amount of debt will depend on
business risk, so ßu = ßTS. The general beta equation (eq. A1.5) can be adjusted (see: Koller et al.
(McKinsey)(2025) Exhibit C.3 p.880): Oded, Michel & Feinstein (2011) p.687):

ßg = ßu + ( ßu - ßd ) D - ( ßu - ßu ) VTS
E E

ßg = ßu + ( ßu - ßd ) D
E

A1.11
A1.12

[email protected] 2.16

If we assume ßd = 0 (‘Practioners’ formula’)

ßg = ßu 1 + D
E

If the amount of D is known and does not depend on the value of the business, the riskiness of the tax
shield can be assumed the same as the riskiness of debt, so that  = Kd and ßTS = ßD. The equity beta
formula (A1.5) becomes:

ßg = ßu + ( ßu - ßd ) D - ( ßu - ßd ) VTS
E E

ßg = ßu + ( ßu - ßd ) D (1 - t)
E

Where VTS = Kd.t.D
Kd

If it is assumed ßd = 0, the general beta equation is the ‘Hamada’ equation (see: Koller et al.
(McKinsey)(2025) Exhibit C.3 p.880): Oded, Michel & Feinstein (2011) p.684; Hamada (1972)):

ßg = ßu 1 + D ( 1 – t ) D is constant
E

As Arzac (2005) states: [The Hamada] “equation … is a special result that applies only when the level
of net debt is constant and the tax shield is riskless…… [and] does not apply in the important case in
which the ﬁrm maintains a constant net debt ratio and cash ﬂows are discounted at the weighted
average cost of capital (WACC)” (see also Koller et al. (McKinsey) (2025) p.318). Therefore, the
Practioners formula (eq. A1.8) should be used when adjusting the asset beta for financial risk in a DCF
valuation where WACC uses leverage based on market values (forecast debt theoretically should be be
based on this leverage as applied to period end EntVs).

Based on the WACC example in the main text, there are a six different results depending on whether (1)
the beta re-levering includes or excludes the adjustment (1 – t) and (2) the beta re-levering includes or
excludes the debt beta, and for both cases whether the WACC is on a post-tax or pre-tax basis (there
are four different beta and cost of equity results):

A1.13
A1.8

[email protected] 2.17

Other possibilities include (equation references shown):

[email protected] 2.18

[email protected] 2.19

Appendix 2 : Cross Border WACC

Foreign Risk

A number of variations to the general CAPM have been suggested to estimate the return required by
equity investors (‘home’ investors) when they invest in entities located outside their jurisdiction (‘foreign’
entities), where the risks are likely to be different to an otherwise identical business based in their home
country. Such risks include: political risk (e.g. default on government bonds making them risky and not
risk free, or tax changes), currency risk (e.g. exchange rate fluctuations affecting conversion of foreign
currency to home currency denominated cash flows), and inflation risk (affecting nominal cash flows
and discount rates). How these incremental risks are quantified and incorporated into the discount rate
has led to a variety of approaches.

As for the general CAPM, the risk reflected in the discount rate should, the theory says, be total risks
that cannot be diversified away via portfolio allocation. The discount rate for an investor in a fully
integrated market who holds a globally diversified portfolio that allows country risk to be diversified
away is likely to be different to the rate for an investor in a segmented market who only holds
investments in that market.

CAPM Models

If markets are fully integrated, so that the price of non-currency risk for a company based at home is the
same as for an otherwise identical company based in another country, each market has the same risk
(markets are perfectly correlated with each other) and so the beta of any company can be measured
against the world equity risk premium (ERP). The same real WACC (same real risk free rate and risk
premium) can be used for valuation purposes. In such a market, it is assumed investors hold diversified
global portfolios, so that the return required for home based investors from investing in the foreign
entity is:

World CAPM KeH = RF World + World x ERPWorld

where:
RF World typically the US risk-free rate
ERP measured in the same currency as RF World
World represents the foreign company beta as measured against the world market index.

If markets are not integrated but fully segmented, then investors based in the same jurisdiction as the
foreign entity will only invest in the local market. The inputs for this ‘Local CAPM’ would be those for the
country and expressed in that country’s currency:

Local CAPM KeL = RF Local + Local x ERPLocal

Between these two extremes there are a number of variations that incorporate country risk (see
Harrington, Nunes & Aboulamer - Kroll (2023)). These include the following:

[email protected] 2.20

 Country Risk Premium (CRP): adding a CRP to a CAPM that has world inputs (World CAPM above),
mature market inputs (such as the US) or inputs for the market where the investor are based (home
investors). The Country Yield Spread model (CYSM) (Mariscal & Lee, Goldman Sachs (1993))
measures the CRP as the yield on a government bond issued in the foreign country (in local currency)
less the yield on a government bond issued in the home country (in home currency, taken as US$ Rf).
Ideally the foreign country bond would be issued in the same currency as the home government
bond.

Home (CYSM) CAPM KeH = RF Homel + Home x ERPHome + CRP Foreign

 Relative Volatility Models:

○ Adjusting the ERP by the relative volatility of the foreign market versus the home market:

Home (RV) CAPM KeH = RF Homel + Home x ERPHome Foreign stock market
 Home stock market

○ Adjust the CRP by the relative volatility (from the point of view of U.S. investors, so ‘Home’ is the
U.S.)(Damodaran (2025)):

Home (RVDamodaran) KeH = RF Homel + Home . ERPHome + λ . CRPForeign Foreign stock market
Foreign bond market

Where λ is a measure of exposure to local risk and the CRP (as measured by the yield differential
on local versus home government bonds), adjusted by the relative volatility of the local stock
market returns to local bond market market returns

Basic DCF Principles

Cash flows of the foreign operation can be forecasted in the foreign currency and:

 discounted at a rate that reflects that currency, in either real or nominal terms, and the present value
translated into the home currency at the valuation date spot rate, or

 translated into home currency at expected future exchange rates and discounted at a rate based on
the home currency.

The discount rate must be consistent with how the cash flows are measured, so a nominal or real foreign
(WACCFn,WACCFr) or home (WACCHn,WACCHr) rate must match with nominal or real foreign or home
currency cash flows. If only inflation and exchange rates are determining factors, real home and real
foreign discount rates should in theory be the same according to the International Fisher Effect, where
(1 + WACCHn) / (1 + home inflation rate) = (1 + WACCFn) / (1 + foreign inflation rate). This assumes all

[email protected] 2.21

cash flow components are affected equally by inflation, which might not arise in practice. A simplified
example show how the two approaches would equal each other is given below:

[email protected] 3.1

BUSINESS VALUATION
Part 3: Alternative DCF Methods & Multiples

Alternative DCF Methods

Introduction

This paper introduces some alternative approaches to DCF valuation, including methods to value the
equity cash flows or income streams directly, and multiples valuation. It will refer to Parts 1 and 2 when
discussing rates of return, discount rates and tax shield valuation. The methods are:

Cash flows Pre / post tax Discount rate Value

1

Free Cash Flows to the Firm (FCFF)

Post-tax

Post-tax WACC

Enterprise

2 Economic Profits
+
Existing Invested Capital
Post-tax

n / a
Post-tax WACC

n / a

Enterprise
3 Free Cash Flows to the Firm
+
Tax cash flows on debt interest
Post-tax

Tax
Pre-tax WACC

Pre-tax WACC

Enterprise
‘Capital Cash
Flows’

4 Free Cash Flows to the Firm
+
Tax cash flows on debt interest
Post-tax

Tax
Ungeared Cost of Equity

Pre-tax Cost of Debt

Enterprise
‘Adjusted PV’

5 Free Cash Flows to Equity Post-tax Geared Cost of Equity

Equity

6 Residual Income
+
Existing Book Value of Equity

Post-tax

n / a
Geared Cost of Equity

n / a

Equity
7 Dividends Post-tax Geared Cost of Equity Equity

Method 1: Free Cash Flows to the Firm (FCFF)

Method 1 was discussed in Part 1 of this Valuation Series (see Appendix 3 of that Part for an example).
Details of how the WACC is calculated were provided in Part 2. As the debt levels were set as a
proportion of the Enterprise Value (‘EntV’), the tax shields should be discounted at the ungeared cost of
equity and hence re-levering of the beta ignores the tax adjustment (1 – t) (see Part 2 Appendix 1).

Highlights of the valuation are reproduced here:

C.F. Agar
19 Sept. 2025

[email protected] 3.2

[email protected] 3.3

The FCFF can be thought of as the probability weighted expected cash flows, based on possible future
up or down ‘routes’ or ‘paths’ in a ‘Binomial Tree’ (used for option pricing – to be discussed in Part 5).
Assuming 40% volatility, the FCFF could be shown as follows (expected FCFF = sum of routes x
probability x FCFF at each node):

[email protected] 3.4

Method 2: Economic Operating Profits

Net Operating Profit After Tax (‘NOPAT’) and Invested Capital (‘IC’) were introduced in Part 1 and
discussed in the context of the perpetuity Terminal Value (‘TV’) in Appendix 2, particularly the idea that
the EnV TV could be calculated based on IC plus the value of excess residual operating income or
Economic Profits (‘EP’):

TVn = ICn + ICn ROICav n+1 - r see App 2 in Part 1
r – g

From Part 2, we can now replace r with WACC.

Economic return models (such as Economic Value Added (EVA®), created by Stern Value Management),
value a business as the value of existing net operating assets (IC) plus the present value of future EP,
representing residual net operating profits (NOPAT) after a charge for capital has been made:

Economic profit (EPn+1) = NOPATn+1 - ( ICn x WACC )

= ICn x ( ROICav n+1 – WACC )

Where ROICav n+1 = NOPATn+1
ICn

In the TV equation above, the PV of the future EP is calculated as the first terminal year EPn+1 (= ICn x
(ROICav n+1 - WACC) ) discounted at the growing perpetuity formula (WACC – g). If the final forecast
year is in a steady state, where the rate of growth of NOPAT and IC (gNOPAT and gIC) equals the perpetuity
growth rate, then the final forecast year EP can be increased by the growth rate and used for the first
terminal period (EPn+1 = EPn x (1 + g) ). This is because the ‘spread’ (ROIC – WACC) will be the same in
both years, so EP will grow because of the NOPAT growth rate.

Using the example from Part 1:

[email protected] 3.5

The terminal value is the PV of first year economic profits growing at 3.0% in perpetuity:

From the Appendix 2 of Part 1, this can also be shown as (equation A2.4) (replacing r with WACC):

TV = ICn ( ROIC n+1 - WACC ) +

WACC WACC - g

where RONIC is the Return On New Invested Capital (increase in NOPAT this year / New Invested Capital
last year). The above shows the PV of first terminal year economic profits received in perpetuity without
growth and the PV of economic profits from New Invested Capital made each year in perpetuity.

=

WACC
RONICn+1 - WACC

[email protected] 3.6

We can split the TV into a two stage model by assuming RONIC reduces over a given number of years,
due to competitive advantages being eroded, so that it ‘fades’ down to WACC, after which zero value
will be added. This is best modelled explicitly in Excel but a single formula can be used (see Professor
Dr. Bernhard Schwetzler for more discussion on this:
https://www.youtube.com/watch?v=aJflGpTj_S0&t=10s)

Method 3: Capital Cash Flows (CCF)

Part 2 of this Series discusses the tax benefits of leverage (‘tax shield’) arising from the tax relief on
debt interest and the additional value they create for a geared company compared to an ungeared one.
In Appendix 1, FCFF was shown as follows:

FCFF + TS = CFE + CFD

Where:
TS Tax Shield cash flows = pre-tax interest x tax rate
CFE ‘Cash Flows to Equity’ = dividends + stock repurchases
CFD ‘Cash Flows to Debt’ = debt principal net payments + pre-tax interest

CFE and CFD are termed ‘Capital Cash Flows’ (‘CCF’) (Kaplan & Ruback (1994)). As the effect of tax relief
has been captured in a cash flow (TS), tax in the WACC can be ignored. Discounting at the pre-tax WACC
(10.39% in the example below – see note 9 in the example in Appendix 1 of Part 2) gives the same EntV
as under method 1:

[email protected] 3.7

If tax is ignored, the traditional WACC formula is modified:

Post-tax WACC = Kg . (1 – L) + Kd . (1 – t) L

Pre-tax WACC = Kg . (1 – L) + Kd . L

= Rf + g. ERP (1 – L) + Kd . L

= Rf + u (1 + L ) . ERP (1 – L) + ( Rf + DRP). L
1 – L
= Rf + u . ERP (1 – L) + ( Rf + DRP) L
1 - L

= Ku + DRP. L = Ku + ( Kd - Rf ). L )

10.39% = 9.79% + 3.00% x 20%

Where:
L Leverage (D/(D+E)) where D/E = L/(1-L)
Kg,Kd Geared cost of equity, pre-tax cost of debt
a, g Asset beta, equity beta (here re-levered ignoring debt beta d = DRP/ERP
ERP Equity Risk Premium
DRP Debt Risk Premium (Kd - Risk Free Rate Rf)

It can also be showns as:

Pre-tax WACC = Post-tax WACC + (Tax Shield / Enterprise Value) x (1 + growth rate)

When valuation with CCF was originally presented (1994), the beta was re-geared with a debt beta (see
Ruback (2000) note 1 on page 10 and note 6 on page 12). This produces a different post-tax WACC (9.40%
- see note 7 in the example in Appendix 1 of Part 2 – equal to Ku - Kd.t.L = 9.79% - 7.84% x 25% x 20%),
which on a pre-tax basis equals the ungeared cost of equity (Ku - Kd.t.L with t = 0 = 9.79%)(discounting
FCFF at 9.40% rather than 10.00% will obviously increase the EntV). Ignoring the debt beta when re-
gearing gives the 10.39% pre-tax WACC (10.00% post-tax), reconciled to ungeared cost of equity as
debt beta x ERP x L (10.39% - 9.79% = 0.6667 x 4.5% x 20%).

[email protected] 3.8

Method 4: Valuing FCFF and tax shield cash flows at pre-tax cost of debt (Kd)(‘APV’)

The Adjusted Present Value (Myers (1974)) is similar to method 3 in that the Ent.V comprises the value
of an all equity financed firm plus the value of the tax shield, however the discount rates are different.
In the APV, FCFF are discounted at the ungeared cost of equity and tax shields at the pre-tax cost of debt
(if debt levels depended on FCFF or the ungeared enterprise value, the discount rate would be the
ungeared cost of equity, to reflect business risk).

Method 5: Valuing FCFE at the geared cost of equity (Kg)

The amount of FCFF remaining after payments (net of tax relief) to financial capital providers with
superior claims to equity providers (‘Equity Cash Flows’ or ‘Free Cash Flows to Equity’ / ‘FCFE’) can be
distributed as equity cash flows in the form of dividends and / or share repurchases. The present value
of FCFE when discounted at the return required by the providers of equity capital (cost of equity) will
represent the Equity Value. We can reconcile Enterprise Value to Equity Value (the ‘Bridge’) as follows:

Operating Enterprise Value (FCFF discounted at the cost of capital) x
Fair value of non-operating net assets x
Total Enterprise Value x
Less: net debt (gross debt less surplus cash) (x.)
Less: other non-equity claims and debt-equivalents (e.g. pension deficit) (x.)
Equity Value (FCFE discounted at the geared cost of equity) x
Less: equity claims (e.g. employee stock options value) (x.)
Equity Value for current shareholders x

This method requires forecasting all financing cash flows and related tax in order to calculate residual
post-tax cash flows available for distribution to equity holders (via ordinary dividends, special dividends
or share buybacks), assuming all excess cash is distributed. The steps are as follows:
 Determine funding requirements, allocate to debt facilities, calculate net interest, pre-tax profit and
tax
 Calculate FCFE
1
& reconcile to net profit
2

 Calculate the Equity Value Terminal Value (Eq.TV) at the end of the forecast period
 Calculate the PV of FCFE and Eq.TV at the valuation date (Equity Value)
 Add net debt and equivalents to the Equity Value to determine the Enterprise Value

1
The interest cash flows need to be consistent with what is used in the WACC calculation, so that if leverage is
based on net debt and debt equivalents, the equity cash flows should be after interest is calculated based on net
debt and debt equivalents, meaning a notional interest may have to be applied to match the two.
2
See Part 1 of this series for a reconciliation of net profit to FCFE

From method 3 above, we can start with the equity cash flows for our example:

[email protected] 3.9

Method 6: Residual Income Model

The Residual Income (RI) model is similar to the residual operating income method 2, but uses profits
after tax and the book value of equity (BVE) rather than NOPAT and Invested Capital (Ohlson (1995)). The
equity value is calculated as BVE at the valuation date plus the present value of future residual income.
The perpetuity value is:

Equity TVn = BVEn + BVEn ROE n+1 - Kg
Kg – g
where:
BVEn book value of equity at the end of the forecast period
ROEn+1 the return on equity (= profits after taxn+1 / BVEn)
Kg geared cost of equity
g stable growth in profits after tax

If the change in BVE reflects profits after tax net of dividends paid (‘Clean Surplus’ accounting), this
method should give the same equity value as the equity cash flow method (5).

This value can also be shown as the value of profits after tax in the first year of the terminal period
(PATn+1) if received in perpetuity without growth and capitalised at the geared cost of equity (= PATn+1 /
Kg) plus the present value of growth from the second year in perpetuity (measured as the growth in PAT
less a charge for equity capital based on the prior year change in BVE, equal to PAT less dividends paid).
The second period RI growth will be (and similarly for the remaining years in perpetuity):

RI growth = ( gn+2 x PATn+1 ) - ( Kg. x change in BVEn+1 )

[email protected] 3.10

This is then discounted back to the end of the first year and capitalised in perpetuity (no growth).
This can be shown as follows (the equivalent for NOPAT is discussed in Appendix 2 of part 2):

TVn = PATn+1 1 + ROE – Kg x g
Kg Kg. ROE Kg – g
Using our example:

[email protected] 3.11

If the cost of debt (Kd) is calculated as interest paid / opening debt, ROE can be obtained from the ROIC
as follows (see Appendix):

ROEt = ROIC t 1 + D t-1 ( ROIC t - Kd ( 1- t ) )
E t-1

Method 7 Dividend Discount Model

This well known valuation model values dividends rather than equity cash flows, although in the example
provided here all equity cash flows are paid out as dividends, so method 5 would be sufficient. It is
shown here based on the example in Part 1:

The TV is shown on the right as the value of
profit after tax arising in the first terminal year
remaining constant in perpetuity plus the value
from growth, less the book value of equity at the
terminal date.

[email protected] 3.12

Multiples

Introduction

An enterprise or equity multiple can be determined from acquisition prices (‘Transaction’ multiple) or
quoted prices (‘Trading’ multiple) and used to value a business by applying the multiple to the equivalent
earnings or assets measure. Providing the multiple relates to businesses that are a good proxy for the
business being valued (comparable companies – same sector, size, growth and risk) and has been
adjusted to remove the effects of any abnormality (‘normalised’), they could be treated as a ‘benchmark’
multiple to compare to the business (‘relative’ valuation), and are a useful measure to support a DCF
valuation, particularly when analysing the perpetuity cash flow derived terminal value.

As value and price are forward-looking, the underlying financial measure in an earnings multiple
(revenue, EBIT, EBITDA, FCFF or net income) should ideally be the amount expected over the next 12
months (‘forward multiple’) rather than the last 12 months (‘trailing multiple’). Expected future growth
in the underlying measure will be incorporated in the price, which should change as expectations change
(the growth and the risk associated with the growth).

Types of Multiple

The Enterprise Value (EnV), being the market value of all financial capital (equity, net debt, preferred
etc), relating to a company, quoted or acquired, is used together with operating, pre-financing earnings
(revenue, EBITDA, EBITA, EBIT, NOPAT or FCFF) to calculate the EnV multiple. When applied to the same
earnings for the business being valued, the EntV is estimated and the Equity Value (EqV) calculated after
deducting the value of all non-equity financial capital). The EqV can be estimated directly by applying

[email protected] 3.13

an equity multiple (the P / E, using price and earnings per share EPS, being widely used) to a financial
measure that is after all financing and tax costs have been deducted (FCFE or profit after tax). EqV can
also be based on asset multiples applied to the Equity Book Value (the Price-to-Book multipe).

Adjustments

Issues relating to debt financing, different effective tax rates and capital expenditures, can be ignored
when using EBITDA. Growth in EBITDA requires investment, however, and deducting depreciation allows
for some of the capital expenditure to be considered (depending on the capex / depreciation ratio),
meaning EBIT might be more suitable if the business is more capital intensive (with depreciation being
used as proxy for ‘maintenance’ capex).

Debt financing effects and tax can be factored in when calculating the P / E multiple. An increase in
leverage due to capital investment requirements will increase financial risk, but this would be decreased
by the economic benefits from those investments (if RONIC exceeds WACC). As the P / E is based on
EPS as determined under accounting rules (using weighted average shares), the equivalent measure
based on all the whole firm might be preferred to a per share calculation.

Size, growth and risk should be considered when selecting the sample of proxy companies, as these
should reflect the business being valued. Regression techniques can be used to investigate the
correlation between the multiple and ‘value driver’ financial measure, such as revenue growth and
operating margins, and hence adjust the average (median) multiple from the sample to estimate what
would be more suitable for the financial measure of the business being valued.

In all multiples, earnings and assets need to be adjusted to remove any non-recurring items and correct
any differences in accounting treatment, particularly aggressive practices involving revenue timing /
amount and / or expense classification (such as R&D). Non-operating items need to be excluded so the
multiple applies to core operations (these items would not be valued using a multiple, but by using other
fair value estimation techniques),

Multiples also need to be adjusted to take account of the ‘control premium’ incorporated in an
acquisition price (acquirers will pay more when they will have the ability to control the business via
shareholder voting power and extract benefits from synergies that might be available with that level of
control). This would reduce the multiple (‘minority holding discount’). Similarly, a second downwards
adjustment would be required when the multiple reflects trading in a liquid public market that wouldn’t
apply for the business being valued (discount for non-marketability or ‘illiquidity discount’).
__________________________

Copyright © 2025 Christopher F. Agar

The information contained in this article has been prepared for general information and educational purposes only, and should not be
construed in any way as investment, tax, accounting or other professional advice, or any recommendation to buy, sell or hold any
security or other financial instrument. Readers should seek independent financial advice, including advice as to tax consequences,
before making any investment decision.

[email protected] 3.14

While the author has used their best efforts in preparing this article, they make no representations or warranties (express or implied)
with respect to the accuracy, completeness, reliability or suitability of the content. The content reflects the author’s own interpretation
of financial theory, accounting standards and tax requirements. The author accepts no responsibility for any loss which may arise,
directly or indirectly, from reliance on information contained in the article.

All content is the copyright of the author except where stated and a source is acknowledged. The whole or any part of this article may
not be directly or indirectly reproduced, copied, modified, published, posted or transmitted without the author’s express written
consent.

Suggested reading

Books:
Arzac, E.R. (2008) Valuation for Mergers, Buyouts and Restructurings (2
nd
ed.) Wiley.
Damadoran, A. (2015) Applied Corporate Finance. (4
th
ed.) Wiley
Damodaran, A. (2025) Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (4
th
ed.) Wiley
Greenwald, B.C. & Kahn, J. (2021) Value Investing: from Graham to Buffett and Beyond (2
nd
edn.) Wiley
Holthausen, Robert.W & Zmijewski, Mark.E. (2020) Corporate Valuation: Theory, Evidence & Practice (2
nd
ed.). Cambridge.
Koller, T.,Goedhart, D.,Wesells, D., McKinsey & Co. (2025) Valuation: Measuring and Managing the Value of Companies (8
th
ed.). Wiley.
Leibowitz, M.L. (2004) Franchise Value: A Modern Approach to Security Analysis Wiley
Penman, S. & Pope, P. (2025) Financial Statement Analysis for Value Investing, Columbia University Press

Papers:
Booth, L. (2007) “Capital Cash Flows, APV and Valuation”, European Financial Management, Vol. 13, No. 1, 2007, 29–48
Cooper, I.A. & Nyborg, K.G. (2006) “Consistent methods of valuing companies by DCF: Methods and assumptions”
https://www.ssrn.com/abstract=925186
Cooper, I.A. & Nyborg, K.G. (2017) “Consistent valuation of project finance and LBO's using the flows-to-equity method”,
http://ssrn.com/abstract=1724593
Fernandez, P. (1995) Equivalence Of The APV, WACC and Flows To Equity Approaches To Firm Valuation, IESE Research Paper no.292 (April
1995) https://www.iese.edu/media/research/pdfs/DI-0292-E.pdf
Fernandez, P. (2003) “Three Residual Income Valuation Methods And Discounted Cash Flow Valuation”,
https://www.iese.edu/media/research/pdfs/DI-0487-E.pdf
Harris, R.S., and J.J. Pringle (1985), "Risk-Adjusted Discount Rates: Extensions from the Average-Risk Case", Journal of Financial Research,
8, 1985, 237-244.
Kaplan, S.N. & Ruback, R.S. (1994) “The Valuation of Cash Flow Forecasts: An Empirical Analysis” NBER Working Paper No.4724 (April
1994)
Massari, M., Roncaglio, F. & Zanetti, L. (2007) “On the Equivalence between the APV and the wacc Approach in a Growing Leveraged Firm”,
European Financial Management, Vol. 14, No. 1, 2007, 152–162
Mauboussin, M.J. & Callahan, D. 2024) “Valuation Multiples: What They Miss, Why They Differ, and the Link to Fundamentals”, Morgan
Stanley 23 April 2024
Mian, M.A. & Vélez-Pareja, I (2007) “Applicability of the Classic WACC Concept in Practice” https://ssrn.com/abstract=804764
Myers, S.C. (1974), "Interactions of Corporate Financing and Investment Decisions - Implications for Capital Budgeting", Journal of Finance,
29, 1974, 1-25.
Nissim, D. & Penman, S.H. (2001) “Ratio Analysis and Equity Valuation: From Research to Practice” Review of Accounting Studies, 6,
109–154, 2001
Oded, J. & Michel, A. “Reconciling DCF Valuation Methodologies” https://www.researchgate.net/profile/Allen-
Michel/publication/265572808_Reconciling_DCF_Valuation_Methodologies/links/54b7b0ba0cf2bd04be33bbac/Reconciling-
DCF-Valuation-Methodologies.pdf
Ohlson, J.A. (1995) “Earnings, Book Values, and Dividends in Equity Valuation”, Contemporary Accounting Research Vol 11 issue 2 Spring
1995 pp 661-687
Ruback, R.S. (2000) “Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows”
https://www.hbs.edu/faculty/Pages/item.aspx?num=1437 (published in Financial Management Vol. 31, No. 2 (Summer, 2002), pp.
85-103)
Schauten, M.B.J. (2011) “Three discount methods for valuing projects and the required return on equity”
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1565470
Stanton, R. & Seasholes, M.S. (2005) “The Assumptions and Math Behind WACC and APV Calculations”
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=837384
Suozzo, P., Cooper, S., Sutherland, G. & Deng, Z (2001) “Valuation Multiples: A Primer”, UBS Warburg November 2001

[email protected] 3.15

Appendix : Multiples Perpetuity Formulae

Growth and Returns

We can break down the P/E (price / earnings per share) to extract key value drivers for growth, returns
and risk, starting with the simplest of valuation models: the Dividend Discount Model (DDM). If we
assume a dividend of D1 is received in 1 year and thereafter in perpetuity from a company which is all
equity financed, assuming a dividend growth rate of g, the present value of those dividends (using the
growing perpetuity formula introduced in Part 1 of this series) should be a fair value for the share price,
assuming for now that all distributable net income is paid out. As the company is debt free, the discount
rate is the ungeared cost of equity used in the Gordon Growth formula:

Price = D1
Ku - g

The dividend paid per share will depend on the proportion of net income (EPS on a per share basis) that
the company decides to retain and reinvest (‘Retention Ratio’ / ‘RR’) rather than payout (‘Payout Ratio’
/ ‘PR’, where RR + PR = 100%). In a growing perpetuity model, we can replace the dividend at time 1
with EPS x PR or EPS x (1- RR):

Price = EPS1 (1 – RR)
Ku - g

⸫ P / E = 1 - RR
Ku - g

PR is similar to the NOPAT reinvestment rate (RR):

Growth NOPAT t = RONIC t x RR t-1

⸫ Growth NOPAT t = RR t-1
RONIC t

So it is for the P/E RR:

EPS growth = RR
ROE

Return on Equity is Net Income per Share / Book Value of Equity per Share, so

⸫ P / E = 1 -

Ku - g

g

ROE

[email protected] 3.16

= ROE – g
ROE (Ku – g)

This can be decomposed into the following after 1/Ku is added and subtracted:

P / E = 1 + ROE – Ku g
Ku ROE x Ku K - g

Franchise Factor Growth Factor
(see Arzac 2008 p.77, Leibowitz 2004)

In terms of Ku, this can be re-arranged into:

Ku = 1 1 - + g
P / E

The Residual Income model growing perpetuity formula (discussed above under method 6) is:

P = BVE ROE – g
Ku – g

where BVE = book value of equity per share
EPS = ROE x BVE (replacing BVE with EPS / ROE)

This can be derived from the above P / E multiple formula

P = 1 ROE – g Since ROE = EPS
EPS ROE (Ku – g) BVE

In a finite period we use the PV formula mentioned in Part 1 of this series:

PV = C x 1 x 1 - (1 + g)
n

r - g (1 + r)
n

where
C = BVE x (ROE – g) = (EPS / ROE) x (ROE – g)

In a ‘steady state’ scenario (see Part 2 of this series), BVE grows at a constant rate g in perpetuity, if
ROE and the reinvestment rate RR grow at this same g. Over one period this is:

g = BVE1 - BVE0 - 1
BVE0

= ( BVE0 + EPS x RR ) - BVE0 - 1
BVE0
g

ROE
(see Koller et al. (McKinsey) 2025 p.307)

[email protected] 3.17

= ROE x RR (as EPS = ROE x BVE0)

This assumes BVE changes only due to net income less dividends paid out (‘clean surplus’), where EPS
x RR equals EPS less dividend per share (EPS x (1 – RR)). The Price / Book ratio (price / BVE) can be
calculated as ROE x P/E ratio

Returns and Risk

ROE increases because of the effects of leverage, but with this higher return there is greater risk, as
measured in the geared cost of equity (Kg) as D/E increases (see Part 2):

Kg = Rf + a 1 + D (1 – t) ) ERP (ignore 1 – t if leverage is constant)
E

ROE can be analysed further in terms of ROIC and leverage. Assuming there are no non-operating items
or another adjustments, we can reconcile NOPAT to profit after tax as:

NOPAT x
Less: net interest expense x (1 – tax rate) x
Profit after tax x

ROIC t = PATt + i (1 – t )
BVEt-1 + + Debtt-1

= ROEt + i (1 – t )
BVEt-1

1 + Debtt-1
BVEt-1

∴ ROEt = ROIC t + ROIC t D t-1 - i (1 – t )
E t-1

ROEt = ROIC t 1 + D t-1 ( ROIC t - Kd ( 1- t ) )
E t-1

Where Kd = Pre-tax cost of borrowing %

And ROIC t = NOPAT margin
see Part 1 Net PP&E t-1 + Working Capital t-1
Revenues t Revenues t

After dividing top
and bottom by
BVEt-1
After dividing top
and bottom by Dt-1

[email protected] 3.18

see Part 2 but with = Prior year ROIC t-1 1 + gNOPAT t
t = n + 1 1 + gICt-1

Multiples based on return measures

If we replace ICn with an expression for EBITDA, we can derive the forward TV EBITDA multiple version:

ICn = NOPATn+1
ROIC n+1

= EBITDAn+1 x ( 1 – tax rate t ) x (1 – Depreciation / EBITDA)
ROIC n+1

TVn = 1 ( 1 – t ) x (1 – Depreciation / EBITDA) x ROIC n+1 - g*
EBITDAn+1 ROIC n+1 r – g*

Taking the example from Part 1 of this series and referred to in this paper, for the terminal value:

Terminal value multiple:

This is the enterprise value equivalent version of the price-book multiple, which can be written as
follows:

[email protected] 4.1

BUSINESS VALUATION
Part 4: The Value Bridge – Part I

Introduction

The market value of debt (or net debt) and debt and equity equivalents must be be deducted from
Enterprise Value (operating Enterprise Value plus the market value of non-operating assets)(‘EntV’) to
calculate Equity Value (‘EqV’), and form the ‘Bridge’ between the two. This paper discusses some
components of non-operating assets (cash, deferred tax assets) and debt and debt-equivalents (straight
debt, leases, pension deficits), as well as related IFRS financial reporting and UK tax issues. Part 5
discusses option-embedded bridge items (convertibles and employee stock options).

Non-Operating Assets

Cash

In Part 2, the treatment of cash in a DCF valuation was briefly discussed. Cash (whether it be just ‘excess
cash’ or total cash) can be netted off gross debt or kept separate and treated as a non-operating asset.
If cash is netted off debt, then income on cash balances should be included in the cost of debt (or rather
cost of net debt). If cash is added as a non-operating asset, any related income should be ignored as it
is non-operating.

Deferred Tax Assets

A fundamental principle of accruals based financial reporting (‘Generally Accepted Accounting Practice’
/ ‘GAAP’, such as IAS and IFRS financial reporting standards issued by the International Accounting
Standards Board) is that expenditure is matched with related income and both are accrued for in the
same period (booked according to the period they relate to rather than when the cash effect arises). For
example, the upfront cost of acquiring an asset should be matched over time in the income statement
against the periodic revenue and profits arising from the use of the asset (including its sale). This is
achieved via depreciation (tangible assets) and amortisation (intangible assets). The deduction for tax
purposes in respect of the cost of the asset may not equal the expense for accounting purposes due to
permanent differences (amounts that are disallowed for tax purposes, just as some income might be
exempt) and ‘temporary’ differences (mainly due to timing differences that arise when the expense is
included in the accounting profit in one period but in the taxable profit in another, but can arise in other
cases, such as when assets are revalued for accounting purposes but not for tax purposes). Such
differences also arise for income and gains.

In the UK, a tax deduction for the cost of a tangible asset might be accelerated and arise in full in the
year of acquisition or be allocated on a reducing balancing basis. Depreciation in the income statement
is usually based on a straight-line allocation of the ‘Depreciable Amount’ (qualifying cost less ‘residual
value’ at the end of its useful life – IAS 16 para.6) over the period during which the asset is available
for use by the business (‘Useful Life’). This difference is only temporary, however, as whilst in early years
‘tax depreciation’ is greater than accounting depreciation (taxable profit is less than accounting profit)
C.F. Agar 23 Sept. 2025

[email protected] 4.2

a reversal occurs later on (taxable profit is more than accounting profit). Over the life of the asset, tax
depreciation will equal accounting depreciation.

For these assets, the carrying amount in the balance sheet equals cost less accumulated depreciation,
whilst the ‘tax base’ (on which capital allowances are based) equals cost less accumulated tax
allowances. If the carrying amount exceeds the tax base, the accumulated deductions for tax purposes
given so far have been greater than those for accounting purposes. When the temporary difference
reverses, more tax will be payable and this should be provided for via a deferred tax liability. Under IFRS,
a liability is a present obligation arising from past ‘obligating’ events that will, in all probability, lead to
an outflow of economic benefits and is provided for (non-current) if it can be measured reliably (IAS 37).
Discounting is not permitted under IAS 12 (para.53).

A deferred tax liability on ‘taxable temporary differences’ will arise on the excess of the carrying amount
of an asset over its ‘tax base’ (tax rate applicable for the period x (AIFRS - ATAX)) and vice versa for a liability
(tax rate x (LTAX - LIFRS)). The deferred tax charge is the increase in the liability over the period. When
calculating NOPAT or FCFF, deferred tax needs to be determined for operating assets and liabilities and
only the increase in operating deferred tax liabilities is deducted from the statutory tax that applies to
taxable operating EBITA (Koller at al. (McKinsey) (2025) p.220 and ch.20). Deferred tax liabilities are
otherwise ignored in the valuation (Holthausen & Zmijewski (2020) p.117).

A deferred tax asset arises where there are ‘deductible temporary differences’ (ATAX - AIFRS for assets and
LIFRS - LTAX for liabilities) and where tax losses carried forward from prior periods are available to reduce
taxable profits (s45 - s45D Corporation Tax Act 2010 in the UK, subject to carry forward restrictions under
part 7ZA of that Act). A deferred tax asset can only be recognised if its recovery is probable and
sufficient taxable profits will be available in the future to utilise the deductible temporary differences
[para. 25, 27 IAS 12]. Deferred tax assets should be treated as non-operating assets and valued
separately (Koller at al. (McKinsey) (2025) p.216).

Debt and Debt-Equivalents

Straight Debt

Valuation

Debt is measured in the Weighted Average Cost of Capital (WACC) at market value (via the leverage
ratio – see Part 2 of this series), and so the amount to be deducted from the EntV to calculate EqV
should also be the market value. The fair price of a debt instrument (without any embedded option,
such as a straight bond) is the present value of its future cash flows (interest or coupons plus
redemption or maturity amount), discounted at a risk adjusted rate. Basic, traditional bond pricing
uses a single discount rate: the current required 'Yield to Maturity' (YTM) or ‘Gross Redemption Yield’
(the Internal Rate of Return, IRR, for a given market price), which, at the date of issue, may be set with
reference to some benchmark issue.

[email protected] 4.3

If coupons are paid annually, the fair price at the start of a coupon period ('Clean Price' excluding
accrued interest) will be as follows:

Price = c + c + ….... + c + P
(1+ r)
1
(1+ r)
2
(1+ r)
n

= c 1 1 - 1 + P 1 .
r (1 + r)
n
(1 + r)
n

where c Equal annual coupon, starting in 1 year
P Redemption amount (principal)
r Yield to Maturity (IRR) % per annum
n Number of complete years until maturity

If coupons are paid more than once during the year, each coupon equals the annual coupon divided by
the number of coupon periods, which, together with the redemption amount, would be discounted at
the nominal Yield to Maturity:

Price = c/m + c/m + ….. + c/m + P
(1+ r/m)
1
(1+ r/m)
2
(1+ r/m)
nm

= c/m 1 1 - 1 + P 1
r/m (1+r/m)
nm
(1+r/m)
nm

where c Equal annual coupon (coupon % x bond face value)
m Number of equal length coupon periods per year
(n x m is the number of time periods)

Daily interest is accrued on a bond up until the date the coupon is paid, so that, if a bond is purchased
during a coupon period, the purchase price (‘Dirty Price’) includes accrued interest from the last
coupon date to the day before the purchase or ‘settlement’ date (inclusive): accrued interest = coupon
p.a. x days accrued / days in coupon period (if the ‘actual / actual’ convention is used, as is the case
for accrued interest on UK bonds and some US bonds – otherwise, the days in the year are used). The
price can be calculated using an Excel function or from the past or next coupon date.

IFRS Accounting

Under IAS 32, a financial liability includes a liability (a present legal or constructive obligation arising
from a past ‘obligating’ event that results in an outflow of economic benefits – IAS 37) that is a
contractual obligation to deliver cash to another entity where the company has no unconditional right
to avoid delivery of that cash. Such contractual financial liabilities (which would include many types of
preference share capital) are financial instruments that are measured and recognised by the issuer
under IFRS 9 initially at fair value (the price that would have to be paid to transfer the liability in an

[email protected] 4.4

orderly transaction in the market – IFRS 13) and thereafter, subject to some exceptions, at ‘Amortised
Cost’.

A loan or bond, therefore, would usually be recognised on the issuer’s balance sheet at amortised cost.
The IRR of a bond is the discount rate ( YTM) that discounts future expected cash flows to the price or
fair value of the bond. The YTM changes as the required yield changes in the market, increasing (after
yields fall) or decreasing (after yields rise) the price of the bond. The ‘Effective Interest Rate’ (EIR) is the
IRR of the bond at the date of initial recognition by the issuer, and is not re-calculated unless the
financial liability is substantially modified. The EIR will equal the interest or coupon rate if the instrument
is initially recognised at face value. It represents the effective cost of debt, and may differ to the cash
rate (such as a zero coupon instrument), and the resulting amortisation charge is the interest expense
booked to the income statement.

The EIR is used to calculate the carrying amount (book value) of the financial liability, the amortised
cost:

Fair Value on recognition (FV0) x
Add: EIR % x FV0 (P&L) x
Less: interest or coupon paid (cash flow statement) (x.)
Amortised cost at end of year 1 (FV1) (balance sheet) x
Add: EIR % x FV1 x
Less: interest or coupon paid (x.)
Amortised cost at end of year 2 (FV0) x
Etc

At any date, the book value and fair value (market value) will equal the remaining cash flows discounted
at the EIR and YTM, respectively. Book value and market value will differ, therefore, if the YTM on initial
recognition (the EIR) has changed since recognition. A simple example follows:

A 5.0% p.a. 5 year bond (Face Value
‘FV’ = Redemption Amount ‘RA’ =
100) is issued at 100 (Market Value
‘MV’ or ‘PV’), with a YTM of 5.0%.

EIR = coupon rate:
⸫ BV = FV

YTM is constant:
⸫ BV = MV

Note: to allow for varying discount rates, DFn = 1 /{(1 / DFn-1) x (1 + rn)} = DFn-1 / (1 + rn)

[email protected] 4.5

If the coupon is 1.0% and YTM still
5.0%, the redemption amount will
have to increase to 122.10 for the
price to equal 100.

EIR ≠ coupon rate:
⸫ BV ≠ FV

YTM is constant:
⸫ BV = MV

If at a future date yields change, BV
≠ MV. Assume the YTM ‘spot rate’
increases to 6.0%, at the start of
year 3, the 108.20 price at the end
of year 2 will immediately fall and
years 3 and 4 prices will be lower.
BV will stay the same, whatever
market yields do.

The cash flows in this example are the promised contractual cash flows, that, given the initial price paid
to acquire the loan or bond, provide the investor with their minimum required return (the promised YTM).
If there is a risk of default, such that the expected cash flows will be less than the promised cash flows,
then the true cost of debt will be less (Cooper & Davydenko (2001)). In practice, if the market expected
yields to rise in year 3, the bond price would be calculated based on these expected future spot rates
rather than the constant YTM.

UK Taxation

In the UK, taxation of debt instruments for companies falls under the Loan Relationship Rules (LRR)
contained in Corporation Tax Act 2009 (CTA 2009), which includes ‘money debts’ arising from the actual
lending of money (settled in cash, in another money debt or shares in any company). All profits and
losses in the form of credits and debits (including interest) under the LRR are taxed as trading or non-
trading income even if they are of a capital nature (i.e. capital gains and losses). Amounts recognised
are those recognised in the profit and loss account under GAAP, unless the tax rules override the
accounting rules (lending between connected companies, for example, has to be recognised using the
amortised cost method and not fair value accounting, which the lender can use depending on its

[email protected] 4.6

business model and other factors). Losses (excess debits over credits, or ‘deficits’) are relieved
differently for trading and non-trading items.

Subject to avoidance arrangements, interest (not defined) is deductible for tax purposes, but may be
restricted under the Corporate Interest Restriction (‘CIR’) provisions under Taxation (International and
Other Provisions) Act 2010. These aim to restrict tax deduction for UK tax resident companies in a
worldwide group (or single companies) in respect of net interest payable in excess of £2 million, so as
to ensure deductions are commensurate with business activity subject to UK tax (OECD based rules
designed to remove the advantage of shifting group debt to higher tax rate jurisdictions to maximise
dedutions). The amount restricted (‘Interest Capacity’) is based on a percentage (‘fixed ratio’ 30%) of tax
adjusted Earnings Before Interest Tax Depreciation & Amortisation (‘tax-EBITDA) for the UK companies,
subject to a cap. If the worldwide group’s net finance cost (making adjustments to align with UK tax
rules and other adjustments) as a percentage of its EBITDA is higher than 30%, the UK companies in
the group may elect to use this higher ‘group ratio’ in instead of the 30% fixed ratio (again subject to a
cap). The group decides how to allocated the Interest Allowance to its UK group companies. The
disallowed amount may be carried forward for deduction in future years (‘reactivation’), subject to rules.

Interest deductions on a corporation tax return will be challenged if it is suspected one of the main
purposes of the loan relationship is the avoidance of tax. These would include loans for an ‘unallowable
purpose’ (not amongst the purposes of the company)[s441 CTA 2009], loan transactions not at arm’s
length [s444 CTA 2009] and interest which treated as a non-tax deductible distribution [s1000 CTA 2010].

As for a loss making company (where LRR deficits, including interest expense, would be carried forward
for relief), restricting interest deductions under the CIR reduces the value of the tax shield (see Part 2)
by delaying the tax benefits (until used in a future period), and hence increases the after-tax cost of
debt in the affected years.

Leases

Features of a lease

Under a lease agreement, one party (the ‘lessor’) grants another (the ‘lessee’) full use of an asset for a
period (‘primary lease term’) in return for a rental, subject to certain terms and conditions. The lessor
may have legal title to the asset, or lease it from its legal owner (the ‘head lessor’); the lessee may be
entitled to ‘sub-lease’ the asset to a ‘sub-lessee’. There may, therefore, be more than one lease
agreement relating to a single asset. The lessee would normally return the asset to the lessor at the end
of the primary lease term, having maintained it and restored it to the minimum condition stated in the
lease agreement; however, it may be granted the right to extend the lease into a ‘Secondary’ term at a
stipulated rent (‘Renewal Option’) or to purchase the asset (‘Purchase option’). A significant risk for the
lessor is the uncertainty associated with the value of the asset at the end of the lease term (‘Residual
Value’).

If the lessor can earn its required rate of return from cash flows that the lessee has contracted to pay
or guarantee over a non-cancellable term (‘Minimum Lease Payments’ / ‘MLP,’ being rentals and any

[email protected] 4.7

guaranteed payments for all or part of the Residual Value), the lease would be termed a ‘Full Payout’
lease. The lessor has effectively sold its economic interest in the asset to the lessee, and its required
return would be achieved whatever the Residual Value: any proceeds from the sale of the asset at the
end of the lease could be returned to the lessee as a rebate of rentals (if the asset had a nil Residual
Value, the lease term would represent 100% of the asset’s remaining economic life at the start of the
lease). The PV of the MLP, as a percentage of the asset fair value is an indication of how much effective
economic ownership has been transferred to the lessee.

IFRS Accounting

Prior to the introduction of IFRS 16 (effective from 2019), under IAS 17 leases classified as Finance
Leases (‘FL’) (substantially all the risks and rewards associated with ownership transferred to the lessee)
were capitalised by lessees at the PV of MLP. By contrast, where the lessor retained enough risk, the
lease was classified as an Operating Lease (‘OL’) with lessee rentals charged to the P&L and no
requirement for lessee to capitalise lease payments (a form of off-balance sheet financing).

The PV of future lease payments under a FL effectively represent debt servicing (payments of principal
and interest added into the lease rental) on borrowings used to purchase the asset, which would be
treated separately (a liability for future rentals, a depreciated asset and interest and depreciation
expenses in the P&L). An OL required only the rental charge to be shown as an expense.

If an agreement conveys the right to the lessee to control the use of an identified asset for a period of
time in return for consideration, it should be classified as a lease under IFRS 16 (there are detailed rules
on the identification and definition of a lease, which will not be discussed here) and the lessee will be
required to capitalise the underlying ‘right-of-use’ asset (‘ROUA’), even if it would have been classified
as an OL under the old rules (the lessee can opt out if the lease is for 12 months or less and does not
contain a purchase option, or if the lease is deemed to be of low value).

On initial recognition, the cost of the ROUA is recognised as an asset and the PV of the Lease Payments
(‘LP’) as a liability discounted at the interest rate implicit in the lease. LP are the enforceable payments
over the lease term (actual and ‘in-substance’ fixed payments, variable payments that depend on an
index or rate, the exercise price of any purchase option that the lessee is reasonably certain to exercise
and amounts payable by the lessee under any RV guarantees).

The term starts on the date the asset is made available for use by the lessee and ends when the lease
is no longer enforceable. This includes the non-cancellable period and any period covered by an option
granted to the lessee to extend the lease (where it is reasonably certain the extension option will be
exercised) or terminate the lease (where it is reasonably certain the termination option will not be
exercised). If the lessee has the right to purchase the ROUA, and exercising the right was reasonably
certain, that would be considered as well. When the lessor and lessee can terminate the lease for an
insignificant penalty and without permission from the other party, the lease is no longer enforceable
and has come to an end.

[email protected] 4.8

The interest rate implicit in the lease is the IRR that discounts the lessee’s LP and any unguaranteed RV
that the lessor expects to receive to the asset fair value (plus any ‘initial direct costs’). If the lessee
cannot readily determine this rate (if it does not know what unguaranteed RV the lessor is expecting),
it may use its ‘incremental borrowing rate’ (the rate the lessee would expect to pay to borrow funds to
obtain an asset of similar value to the ROUA, based on a similar term, security and economic
environment).

UK Taxation

For some leases a lessee is able to claim capital allowances in the UK, and thereby accelerate tax
deductions compared to relief available for rental payments on other leases. Prior to 2006, the
availability of allowances was restricted to legal ownership (and assets under Hire Purchase
agreements). Since that date, lessees under Long Funding Leases (LFL) can claim allowances as if they
owned the asset (Capital Allowances Act 2001). A LFL is a Funding Lease that is neither a Short Lease
(7 years or less) nor an Excluded Lease (including Hire Purchase agreements), and is a lease of qualifying
plant and machinery (‘P&M’) where one of the following tests applies at the inception date (the date
the contract is agreed and all conditions have been met):
 The lease qualifies as finance lease (or loan) under GAAP in the lessee’s accounts; or
 The PV of the MLP is at least 80% of the fair value of the leased P&M, discounted at the implicit
rate or, if that cannot be determined, the incremental borrowing rate (as defined under GAAP); or
 The lease term is more than 65% of the remaining useful economic life of the leased P&M

Capitalised leases that do not meet these tests will be eligible for relief on the rental expense (no
accelerated allowances are given), if the lease gross rental charge is consistent with the accruals
concept under GAAP. The rental charge will represent the finance charge and depreciation.

An example of a lease is given in the Appendix. This is a leveraged lease, where the lessor has financed
the asset with debt, and a short funding lease under UK tax rules (capital allowances remain with the
lessor, as in a leveraged lease the lessor would want to maximise tax deductions for the asset in order
to obtain its target post-tax return). The implicit rate in the lease is 6.54%, which is used to capitalise
the lessee’s rentals.

Pension Deficits (Defined Benefit)

In a funded Defined Benefit Plan the company agrees to provide future benefits from a fund of
investments built up over the years with contributions by the employer (and possibly the employees). The
present value of the Defined Benefit obligations (DBO) may be more than the market value of the fund
assets, meaning a shortfall (‘deficit’), for which the company is liable, has arisen (a ‘surplus’ arises if
plan assets are valued in excess of the obligations). The fund accumulates from ongoing contributions
and a return on investment (dividends, interest) which are reinvested. Whilst the plan assets are easily
measured, the liability requires actuarial techniques to forecast future benefit payments. In simplistic
terms:

 the fair value of the fund assets will change over the period n to n + 1 as follows:

[email protected] 4.9

Assetsn+1 = Assetsn + contributions paid in + interest income - benefits paid out + AG/L

 the PV of the DBO will change as follows:

DBOn+1 = DBOn + service cost + interest costs - benefits paid out + DBOG/L

Where:
- Service cost (P&L operating profits) = increase in PV of DBO from employee service in the current
period (‘current service cost’) + prior periods (amendments and curtailments)
- Net Interest income and costs (P&L non-operating) = the discount rate applied to the opening value
of plan assets and DBO (the difference between the discount rate and actual return on assets is
included in AG/L). The discount rate must reflect the end of period yield on high quality corporate
bonds.
- AG/L and DBOG/L (Other Comprehensive Income) = the gain / loss on re-measurement of plan assets
at year end market prices and obligations at revised actuarial assumptions.
A surplus is recognised on the balance sheet as an asset subject to an ‘asset ceiling’ that reflects the
surplus recoverable amount (the PV of future refunds and reductions in future contributions resulting
from there being a surplus).

Operating EBITA should include the service cost and no adjustment is made for valuation purposes (it is
part of NOPAT). If FCFF or NOPAT is calculated from net income, the defined benefit cost excluding the
service cost needs to be added back, net of tax.

A DBO net liability for valuation purposes should be treated as a debt equivalent and deducted off the
enterprise value. If contributions required to eliminate the deficit are fully tax deductible, the amount
deducted is DBO x (1 – marginal tax rate). Any related interest costs (net of tax) should be excluded
from FCFF (and included in the WACC along with the deficit as a debt-equivalent). Adjustments may also
be made when de-levering and levering betas under CAPM for the cost of equity estimate, to factor in
additional risk borne by shareholders if appropriate (betas would need to be estimated for pension
liabilities and assets)

(See Koller at al. (McKinsey) (2025) p.455-464, 881; Jin, Merton & Bodie 2006;
https://www.footnotesanalyst.com/dcf-and-pensions-enterprise-or-equity-cash-flow/)
___________________________________

Copyright © 2025 Christopher F. Agar

The information contained in this article has been prepared for general information and educational purposes only, and should not be
construed in any way as investment, tax, accounting or other professional advice, or any recommendation to buy, sell or hold any
security or other financial instrument. Readers should seek independent financial advice, including advice as to tax consequences,
before making any investment decision.

While the author has used their best efforts in preparing this article, they make no representations or warranties (express or implied)
with respect to the accuracy, completeness, reliability or suitability of the content. The content reflects the author’s own interpretation
of financial theory, accounting standards and tax requirements. The author accepts no responsibility for any loss which may arise,
directly or indirectly, from reliance on information contained in the article.

[email protected] 4.10

All content is the copyright of the author except where stated and a source is acknowledged. The whole or any part of this article may
not be directly or indirectly reproduced, copied, modified, published, posted or transmitted without the author’s express written
consent.

Suggested reading

Books:
Choudry, M., Moskovic, D.,Wong, M. & Zhuoshi, S.B, (2014) Fixed Income Markets: Management, Trading, Hedging (2
nd
ed.) Wiley
Damodaran, A. (2025) Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (4
th
ed.) Wiley
Ernst & Young (2025) Internatonal GAAP 2025 https://www.ey.com/en_gl/technical/ifrs-technical-resources/international-gaap-2025-
the-global-perspective-on-ifrs
Fabozzi, F. (2021) The Handbook of Fixed Income Securities (9
th
ed.). McGraw-Hill.
Holthausen, Robert.W & Zmijewski, Mark.E. (2020) Corporate Valuation. (2
nd
ed.). Cambridge.
Koller, T.,Goedhart, D.,Wesells, D., McKinsey & Co. (2025) Valuation: Measuring and Managing the Value
of Companies (8
th
ed.). Wiley
Stafford Johnson, R. (2004) Bond Evaluation, Selection, and Management. Oxford: Blackwell Publishing Ltd.
Tan, P., Lim, C.Y., & Kuah, E.W.(2020) Advanced Financial Accounting: An IFRS

Standards Approach (4
th
ed.) McGraw-Hill
Tuckman, B. (2022) Fixed Income Securities: Tools for Today's Markets. (4
th
ed.) Wiley

Papers
Caness, J.L. & Jarrell, G.A (2022) “The Proper Treatment of Cash Holdings in DCF Valuation Theory and Practice” Journal of Business
Valuation and Economic Loss Analysis 2022: 17(1) pp.39-64
Cooper, I.A. & Davydenko, S. (2001) “The Cost of Debt”, SSRN: https://ssrn.com/abstract=254974
Jin, L., Merton, R.C. & Bodie, Z. (2006) “Do a firm's equity returns reflect the risk of its pension plan?” Journal of Financial Economics
Vol,81/1, July 2006, Pages 1-26

[email protected] 4.11

Appendix : Lease

[email protected] 4.12

[email protected] 4.13

[email protected] 4.14

[email protected] 5.1

BUSINESS VALUATION
Part 5: The Value Bridge – Part II

Introduction

This is the second part of the section on the Enterprise - Equity Value ‘Bridge’. Part I discussed non-operating
assets and some debt and debt-equivalent items; this Part focuses on debt and equity equivalent items that
require the use of option pricing techniques to estimate their fair value, namely convertible bonds and
employee stock options (Appendix 1 discusses option pricing models, parts of which can be used to value
convertible bonds – Appendix 2 gives an example of a convertible bond pricing model).

Debt and Debt-Equivalents

Convertible Debt

Introduction

A convertible bond or note is a debt instrument that can be converted at the investor’s option into shares
of the issuing company, subject to agreed terms and conditions. On conversion, investors effectively pay
an exercise price by surrendering the bonds in exchange for a stated number of shares for each bond
(‘Conversion Ratio’). The value received from converting (‘Conversion Value’ or ‘Parity’ = Conversion Ratio
x share price) should be greater than that received from any alternative strategy (i.e. the value of the bond
if held to maturity and not converted, its ‘Investment Value’). The possibility of a ‘payoff’ means convertible
investors will accept a lower coupon (or even a zero coupon) compared to an otherwise identical non-
convertible debt.

Early Redemption

Most issuers will have the right to service notice to redeem (‘Call’) the bonds early at pre-agreed dates
and prices, usually after some time has elapsed (‘Non-Call Period”) and at a price that preserves the
economic benefit for the holder (the Investment Value). For the investor, early redemption means the
potential upside gain on conversion is lost and redemption proceeds may have to be reinvested at a lower
yield. The fair price of a callable bond will, therefore, be less than the fair price of an otherwise identical
noncallable bond (similar coupon, maturity and risk), due to this extra risk (the difference being the value
of the issuer’s call option).

For the issuer, early redemption allows an issuer to refinance bonds at a lower cost, following a fall in
market yields. The bonds are unlikely to be called if the call price exceeds the bond trading price
(otherwise it would be cheaper to repurchase them on the market), unless there are clear economic
benefits from refinancing the old bonds at that price (on an after-tax NPV basis, net of all repurchase
costs). For a Convertible, the call provision can be conditional on certain events occurring (‘Soft Call’),
C.F. Agar 26 Sept. 2025

[email protected] 5.2

such as the underlying share price reaching specified levels, or unconditional (‘Hard Call’). The serving of
a notice to call a bond should force investors to convert if the call price is less than the Conversion Value
(‘Forced Conversion’), so that they receive a higher amount, although any accrued interest on the bond
would be foregone on conversion. Forcing conversion allows the issuer to avoid a cash payout on
redemption, and allows the Convertible to be seen as a form of deferred equity financing (but with less
dilution than a straight upfront issue of shares due to the lower number of shares being issued, assuming
share prices have risen).

Valuation

The fair price of a convertible bond can be viewed as its value as a straight bond without any conversion
feature (Investment Value) plus the value of the embedded option to convert to equity, except at maturity
the value will be either its equity value (when a high share price means the Conversion Value exceeds the
Investment Value) or its Investment Value (the opposite at a lower share price).

At any date before maturity, it may be optimal to delay conversion due to the Time Value of the conversion
option (see Appendix 1), in which case the Convertible fair price would exceed the Conversion Value and
would reflect the ‘Continuing Value’ of the Convertible. When the Conversion Value is much greater than
the Investment Value, the Convertible fair price will reflect the value of the underlying equity and its
volatility, and the bond’s value as straight debt will be less relevant (i.e. the impact of changes in market
yields and interest rates will be less); conversely, when the Conversion Value is less than the Investment
Value, the Convertible fair price will equal the Investment Value (the fair price should never fall below its
value as straight debt).

The option embedded nature of a convertible means it can be valued using an option pricing model, such
as the Binomial Model or Black-Scholes Model (see Appendix 1). A simple example is given in Appendix
2, where a Binomial Tree is used to estimate the Convertible fair value and its debt and equity components.

IFRS Accounting

Under IAS 32, the issuer of a convertible bond (a ‘Compound Financial Instrument’) is required to separate
the convertible fair value on initial recognition into a liability component (the PV of debt cashflows without
any conversion feature - ‘host contract’) and a residual equity component (the conversion option, being
the fair value of the convertible less the value as straight debt). If there are other embedded features,
such as a call option or early redemption right, these must be separated out as well. Under IFRS 9, an
investor in a convertible (a ‘hybrid’) is not required to separate the two components, and can recognize
the convertible at fair value if certain conditions are met.

In its balance sheet, the issuer must recognise the debt component at amortised cost (discussed in Part
4) and the equity component relating to the conversion feature as equity (and not subsequently remeasure
it), but only if it meets the definition of equity. If treated as an equity derivative, the ‘fixed-for-fixed’

[email protected] 5.3

criterion would need to be met for equity classification, otherwise it is treated as an embedded derivative,
and, like non-equity derivatives such as a call option, would be included as part of the liability if ‘closely’
related to the host contract under IFRS 9 – a call option to redeem the convertible at par or approximately
amortised cost would be closely related. Conversion is not anticipated until it occurs, when the carrying
amount of the debt component is transferred to equity (the consideration given by the convertible holder
for the shares received on conversion is the present value of future cash flows on the convertible that the
issuer is no longer required to make). Finally, convertibles will affect the diluted Earnings Per Shares as
calculated under IAS 33. (See EY International GAAP (2025) p.3,535, p.3,540, and p.2,888 – 2,894 for
further discussion on these issues).

UK Taxation

In general, the tax treatment will follow the accounting treatment. The amount recognised by the issuer as
equity under IAS 32 and IFRS 9 has no tax effect (there is one exception – see HMRC Corporate Finance
Manual CFM55510). If the call option is not treated as part of the host contract it will be taxed separately
as a derivative (the straight bond component will be taxed under the Loan Relationship Rules discussed in
Part 4, subject to the Corporate Interest Restriction rules for the deductible amortisation charge).

Equity-Equivalents

Employee Stock Options

Valuation

A company which has granted employee stock options (ESOs) that remain unexercised at the valuation date
has created a future claim (or ‘contingent’ claim) over the equity value, triggered when the options are
exercised (assuming exercised at a price below market price). The cost for the company of repurchasing
stock to give as options (number of options x share price) less the proceeds received on exercise (number
of options x exercise price), reflects the loss of value (the Treasury method assumes exercise proceeds are
used to repurchase shares at the share price with the excess shares required to top up to the number of
options being new diluting shares). Similarly, if options are granted after the valuation date, a further claim
on equity will arise via a reduction in expected future cash flows to which existing equity investors are
entitled.

One approach is as follows:

 Options granted before the valuation date (deduct from value) - The Fair Value (‘FV’) of options
outstanding at the valuation date can be estimated using an option pricing model and deducted from
the equity DCF value. The equity value per share should be based on outstanding shares (issued shares
less treasury shares) and not increased to reflect dilution arising on option exercise (the effect is already

[email protected] 5.4

taken into account by reduching equity value). See Appendix 1 for a discussion about option pricing
models.

 Options granted after the valuation date (deduct from cash flows) - Rather that attempt to forecast
future option grants and exercise behaviour, the FV of option grants can be based on a percentage
applied to revenues (Damodaran (2005)) or a growth rate applied to the previous period amount (Li and
Wong (2004)). This would then be deducted this from earnings and cash flows (despite being a non-cash
item). Deducting from Free Cash Flows estimated cash outflows arising from the granting of options
over the forecast period would require a forecast of DCF share prices (equity DCF value per share at
each period), exercise prices (which could be the grant date DCF share price), option grants and exercise
behaviour, making the calculation tricky (see Barenbaum & Schubert (2019)). Using the BSM to measure
the FV charge each period would need more assumptions for the risk free rate, volatility and dividend
yield, adding more complexity.

Estimating the FV of employee stock options using an option pricing model like the Binomial Method (‘BM’)
(or Lattice Method) or Black-Scholes Model (‘BSM’) is made complicated by the following:

 The earliest date an employee can exercise the option may depend on certain ‘vesting’ conditions.

 Options may not be exercised immediately on vesting, so an option model needs to estimate the
expected term of the option based on an assumption about exercise behaviour. Options vested at the
valuation date could be exercised immediately (if in-the-money), evenly between the valuation and
expiry dates (on average at the mid-point), on expiry or according to some other method.

 The stock price input for the valuation model needs to incorporate the option value per share, hence
circularity is involved. This is possible by adjusting the model to allow for option value and dilution, as
for a warrant model, to calculate an equity value per share that includes the option value (by dividing
the combined DCF equity value + option FV by the combined shares outstanding and number of options)
which is then used as the stock price input in the model.

For example, assume a company with an equity DCF value per share of £10.00 (equity DCF £100m
outstanding shares 10m) has 1m options granted with an average exercise price of £8.00, using a
warrant pricing model with the inputs below produces an adjusted equity value per share of £9.09. (
Based on the approach in https://pages.stern.nyu.edu/~adamodar/pc/warrant.xls ).

[email protected] 5.5

IFRS Accounting

Under IFRS 2, the FV of the stock option is measured at the grant date (use of the BM or BSM is permitted)
and is not subsequently re-valued. If the employee is only entitled to the option on a date (‘vesting date’)
after a certain period (‘vesting period’) has elapsed, during which ‘vesting conditions’ have been satisfied,
the option FV is expensed to profit and loss over the vesting period (with a corresponding increase in equity)
depending on the proportion of options granted expected to vest (the allocation is intended to match the
period over which the employee services are provided). If there are no vesting conditions, the option FV is
immediately recognised in full.

Vesting conditions usually involving a minimum length of service at the company (‘Service Conditions’) but
may also involve a condition that certain internal financial metrics are achieved (‘Non-Market Performance
Condition’) or that the company share price reaches a stated level (‘Market Performance Condition’). If these
conditions are not met, the options are forfeited. Only Market Performance Conditions are taken into
account when estimating the option FV (IFRS 2 para. 19), typically using the BM, as the BSM is unlikely to
be able to handle them. Service and Non-Market Performance Conditions are incorporated via an
adjustment to the number of options and do not affect grant date FV (‘modified grant date’ method).

An estimate of the proportion of options expected to vest (some employees may leave, for example so the
options never vest) is made on each reporting date during the vesting period. In the first year the charge will
be the vesting fair value (option FV at grant date x options granted x % expected to vest) divided by the
vesting period in years. If the expected vesting proportion is constant, the annual charge will be constant.
If the second year expectation changes, the second year charge will differ (the first year charge is not

[email protected] 5.6

affected), so a cumulative catch up adjustment is made in that year. In the final year, an adjustment is made
to ensure the actual number of options vesting is accounted for (see examples in EY’s Internatonal GAAP
2025 section 6.2.1.A, p.2589).

Taxation (UK)

In the UK, the granting of an option over shares would, if the qualifying conditions are met, enable the
company to deduct an amount for corporation tax, but only if the option is exercised and the employee
obtains beneficial ownership of the shares. Relief is given on ‘an amount equal to the market value of the
shares when they are acquired, less the total amount or value of any consideration given by any person in
relation to the obtaining of the option or to the acquisition of the shares….’ [s1018 Corporation Tax Act
2009] (although some ‘restricted’ and convertible securities have a different relief provision). ‘The relief is
given for the accounting period in which the shares are acquired...as a deduction in calculating the profits
of the qualifying business for corporation tax purposes….’ [s1021 Corporation Tax Act 2009] ‘The statutory
deduction overrides the accounting treatment.’ (HMRC Business Income Manual BIM44265) For non-
qualifying shares, the deduction would be equal to the amount treated as employment income for the
employee.

The expense charged to the income statement for the fair value of employee stock option grants (allocated
over the vesting period under IFRS 2) differs to the amount deductible for tax purposes, which will arise in
later periods when the options are exercised (the tax deduction being the intrinsic value at the exercise
date: share price less exercise price, as discussed above). There is a mismatch between the accounting and
taxable profits, which requires an adjustment via deferred tax (discussed in Part 4). The tax deduction given
after the reporting date for options granted up to that date (based on estimates) is the tax base; the carrying
amount is nil, so the deferred tax asset equals the tax rate x tax base (see EY International GAAP 2025
p.2491).

___________________________________

Copyright © 2025 Christopher F. Agar

The information contained in this article has been prepared for general information and educational purposes only, and should not be
construed in any way as investment, tax, accounting or other professional advice, or any recommendation to buy, sell or hold any security
or other financial instrument. Readers should seek independent financial advice, including advice as to tax consequences, before making
any investment decision.

While the author has used their best efforts in preparing this article, they make no representations or warranties (express or implied) with
respect to the accuracy, completeness, reliability or suitability of the content. The content reflects the author’s own interpretation of
financial theory, accounting standards and tax requirements. The author accepts no responsibility for any loss which may arise, directly or
indirectly, from reliance on information contained in the article.

All content is the copyright of the author except where stated and a source is acknowledged. The whole or any part of this article may not
be directly or indirectly reproduced, copied, modified, published, posted or transmitted without the author’s express written consent.

[email protected] 5.7

Suggested reading

Books:

Calamos, J. (1998) Convertible Securities. McGraw-Hill.
Choudry, M., Moskovic, D.,Wong, M. & Zhuoshi, S.B, (2014) Fixed Income Markets: Management, Trading, Hedging (2
nd
ed.) Wiley
Chriss, N.A. (1997) Black-Scholes and Beyond: Option Pricing Models. McGraw-Hill.
Clewlow, L. & Strickland, C. (1998) Implementing Derivatives Models, Wiley
Cox, J. C., and M. Rubinstein (1985) Option Markets. New Jersey: Prentice Hall.
Damodaran, A. (2025) Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (4
th
ed.) Wiley
Ernst & Young (2025) Internatonal GAAP 2025 https://www.ey.com/en_gl/technical/ifrs-technical-resources/international-gaap-2025-the-
global-perspective-on-ifrs
Fabozzi, F. (2021) The Handbook of Fixed Income Securities (9
th
ed.). McGraw-Hill.
Holthausen, Robert.W & Zmijewski, Mark.E. (2020) Corporate Valuation. (2
nd
ed.). Cambridge.
Hull, J.C. (2022) Options, Futures, and Other Derivatives (11th Edition). Pearson
James, P. (2003) Option Theory. Chichester, W.Sussex: Wiley
Jarrow, R., and A. Rudd (1983) Option Pricing. Homewood, Il: Richard Irwin, Inc.
Koller, T.,Goedhart, D.,Wesells, D., McKinsey & Co. (2025) Valuation: Measuring and Managing the Value of Companies (8
th
ed.). Wiley
McDonald, R.L (2003) Derivatives Markets. Boston: Addison Wesley.
Philips, G.A. (1997) Convertible Bond Markets. London: Macmillan Press.
Rendleman Jr., R. J. (2002) Applied Derivatives: Options, Futures, and Swaps. Oxford: Blackwell Publishers
Rubinstein, M. (1999) Rubinstein on Derivatives: Futures, Options and Dynamic Strategies. London: Risk Publications.
Sadr, A. (2022) Mathematical Techniques in Finance: An Introduction. Wiley
Stafford Johnson, R. (2004) Bond Evaluation, Selection, and Management. Oxford: Blackwell Publishing
Tan, P., Lim, C.Y., & Kuah, E.W.(2020) Advanced Financial Accounting: An IFRS

Standards Approach (4
th
ed.) McGraw-Hill
Tuckman, B. (2022) Fixed Income Securities: Tools for Today's Markets. (4
th
ed.) Wiley
Woodson, H, (2002) Global Convertible Investing. New York: Wiley

Papers

Barenbaum, L. & Schubert, W. (2019) ‘”Share-based Compensation and Firm Value”, Journal of Accounting and Finance Vol. 19(9) 2019
Black, F., and M. Scholes (1973), "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, 81(3), 1973, 637-659.
Cox, J., S. Ross, and M.Rubinstein (1979), "Option Pricing: A Simplified Approach", Journal of Financial Economics, 7(3), 1979, 229-264.
Damodaran, A (2005) “Employee Stock Options (ESOPs) and Restricted Stock: Valuation Effects and Consequences”
https://pages.stern.nyu.edu/~adamodar/pdfiles/papers/esops.pdf
Galai, D., and M. Schneller (1978), "Pricing Warrants and the Value of the Firm", Journal of Finance, 33, 1978, 1339-42.
Goldman Sachs (1993), "Valuing convertible bonds as derivatives", Quantitative Strategies Research Notes
Hull, J. & White, A. (2002) ‘How to value employee stock options’ https://www-
2.rotman.utoronto.ca/~hull/downloadablepublications/esoppaper.pdf
Latham & Watkins (2024) “Demystifying Modern Convertible Notes” (April 2024)
https://www.lw.com/admin/upload/SiteAttachments/Demystifying-Convertible-Bonds-April-2024.pdf
Li, F. & Wong, M.H.F. (2004) Employee Stock Options, Equity Valuation, and the Valuation of Option Grants using a Warrant-Pricing model”
https://utoronto.scholaris.ca/items/d5e39221-1b95-488c-8d13-f651827cfb1b
Mayer Brown (2025) “Convertible Bonds: An Issuer’s Guide (2025)”
https://www.mayerbrown.com/en/insights/publications/2025/04/convertible-bonds-an-issuers-guide-2025
Merton, R.C. (1973), "The Theory of Rational Option Pricing", Bell Journal of Economics and Management Science, 4(1), 1973, 141-183.
Schueler, A (2021) “Executive Compensation and Company Valuation”, Abacus, ISSN 1467-6281
https://www.econstor.eu/bitstream/10419/230255/1/abac.12199.pdf
Tsiveriotis, K., and C. Fernandes (1998), "Valuing Convertible Bonds with Credit Risk", Journal of Fixed Income, 8(2), 1998, 95-102.
Wever, J.O., Smid, P.P.M. & Koning, R.H. (2003) “Pricing of convertible bonds with hard call features”
https://research.rug.nl/en/publications/pricing-of-convertible-bonds-with-hard-call-features-3

[email protected] 5.8

Appendix 1 : Option Pricing Models

Introduction

An option holder has the right (without any obligation) to buy (‘Call’ Option / ‘CO’) or sell (‘Put’ Option /
‘PO’) an asset at a certain price (‘exercise’ or ‘strike’ price) at some future specified date (‘exercise date’)
before such a right expires (‘expiry date’). The exercise date may be at any specified time before expiry
(‘American’ option) or on expiry (‘European’ option). The price paid to acquire the option (‘option
premium’) is the option’s Fair Value (‘FV’).

The exercise price of an employee stock option (a CO) given or ‘granted’ by the employer would normally
be set equal to the market price of the underlying shares at the grant date (X = Sgrant). The exercise date
might depend on certain ‘vesting’ conditions being met, and once vested the employee (option holder)
would hope that S exceeds X (when the CO is ‘in-the-money’ with a value equal to its ‘Intrinsic Value’
(IV) or Sexercise – X). If at time t1 the share price St1 is expected to increase by a later date t2, then the
potential profit might be greater, measured in present value terms, if the option holder delayed exercising
until that future date ( (St2 – X) / (1 +r)
(t2 - t1)
> St1 – X ). The extra value at t1 from delaying an exercise
until t2 represents the ‘Time Value’ (‘tv’), which depends on the probability of S achieving St2 by t2 and
the discount rate r.

An option pricing model forecasts future asset prices at various dates until the expiry date, assuming
some probability distribution for those prices. The dates can be continuous (‘Black-Scholes Model’ BSM)
or discrete (‘Binomial Model’ BM or ‘Lattice Model’), and as the discrete time intervals becoming smaller
and smaller, the discrete model should converge to the continuous model. As the option price at any date
will be zero if ‘out-of-the-money’ (S < X for a CO) with a zero tv (no value is gained by delaying the
exercise), these dates are ignored in the option valuation. So the probability of the option being in-the-
money at the relevant date is a key component of the model, as is the probability of a greater payoff
being available at a future date due to the time value.

One Period

Binomial Model (BM)

BM Methodology

The BM and BSM calculate prices by discounting at the risk free rate. In the BM it is assumed that, over
a single time step, the current price of an asset (S0) can increase by a factor ‘u’ (S1u = u.S0) or decrease
by a factor ‘d’ (S1d = d.S0) with true probabilities of p* and 1 – p*, respectively (the sum of all probabilities
of possible states at any time must equal 1). S0 will therefore be the expected price at the next step S1
(probability weighted price) discounted at the risk-adjusted rate (i.e. cost of equity). In order to value the

[email protected] 5.9

option payoff using the risk-free rate, an adjustment must be made to the true probabilities to ensure the
up and down states are ‘Certainty Equivalents’ / ‘CE’:

Expected price x true probability = CE price x ‘Risk Neutral’ probability
1 + risk adjusted rate 1 + risk free rate

S0 = u. S0 . p* + d. S0 (1-p*) = u. S0 . p + d. S0 (1-p)
1 + Rfd + risk premium 1 + Rfd

Where:
p* true probability
p risk neutral probability (not a real probability but an adjusted true probability)
Rfd risk free rate (discrete rate)

Taking a simple one step / two state example, assuming the exercise price is the grant date market price
(X = S0 = 150.00), time to expiry 1 year, volatility 40.0%, the discrete risk free rate 5.13%
1
and the risk
premium 2.98% (in CAPM this would equal the geared beta x market equity risk premium), using the
approach of Cox, Ross & Rubinstein (1979) and ignoring dividends for now, the up and down factors u =
1.4918 (= e
(40% x 1.0)
) and d = 0.6703 (=1 / u), would give up and down state asset prices and intrinsic
values of Su1 = 223.77 and Sd1 = 100.55. Assuming these up and down states have an equal true
probability (p* = 0.5), we can compute the risk neutral probability as p* = 0.4637:

150 = (1.4918 x 150 x 0.5 + 0.6703 x 150 x (1 – 0.5)) = (1.4918 x 150 x 0.4637 + 0.6703 x 150 (1 – 0.4637)
1 + 5.13% + 2.98% 1 + 5.13%

150 = 162.16 = 150.68
1 + 8.11% 1 + 5.13%

where

p* = (1 + Rfd + u)
(u – d)

= (1 + 5.13% - 0.6703)
(1.4918 – 0.6703)

= 0.4637

The expected price using risk neutral probabilities (150.68) is the certainty equivalent price.

[email protected] 5.10

The up and down factors depend on how volatile the asset price is expected to be over the period to
expiry (measured as the standard deviation of returns). The more volatile the asset returns, the greater
the likelihood the asset price will increase above the exercise price (for a CO), increasing the option FV.
How this volatility is incorporated in u and d depends on the method chosen (the CRR method is used
above, but there are others such as Jarrow and Rudd (1983)).

1
The relationship between the discrete rate (Rfd) and continuous rate (Rfc,) is Rfd = ( e
Rfc
- 1 ) and Rfc = ln (1 +
Rfd) where ‘e’ is the exponential function (2.71828….) and ‘ln’ the natural logarithm. For example, a 5.0%
nominal rate continuously compounded would give an effective annual rate of 5.1271%

BM Single Step Option Value (no dividends)

The expected price using risk neutral probabilities would suggest a modest IV of 0.68 (=150.68 – 150.00),
however this ignores the fact that the down state price would have zero IV as the call option would be
worthless (out-of-the-money). The asset prices and IV at the up and down states using risk neutral
probabilities are: Su1 = 223.77 (=150.00 x 1.4918), IVu1 = 73.77 (=223.77 – 150.00), Sd1 = 100.55, IVd1 = 0
(= max {0, 100.55 – 150.00}). The down state price is ignored in the valuation, so that the option value
is calculated as:

32.54 = IVu Pu + IVd Pd = 73.77 x 0.4637 + 0.00 x (1 – 0.4637)
1 + Rfd 1 + 5.13%

[email protected] 5.11

Black Scholes Model (BM)

BSM Methodology

The well know BSM (a derivation can be found elsewhere) is the continuous time version of the BM, and
attempts, like the BM, to estimate future probability weighted expected prices and expected positive
payoffs. As the number of time periods in the BM increases, the option value converges to the BSM
(discussed below). The BSM uses logarithmic returns and defines the relationship between the current
price and exercise price in terms of ln (S0 / X), adjusting this to estimate the forward value by the risk
free rate of return:

BSM Single Step Option Value (no dividends)

Using the example for the BM, we can value the option assuming exercising occurs after 1 year. The call
option value is 27.0344, lower than the BM because the BSM assumes continuous compounding over
the 1 year whereas the BM is a discrete version with one compounding:

[email protected] 5.12

To equate the BM to the BSM, the time steps in the BM need to be increased significantly, which requires
the use of a multi-step tree.

Multi-period Binomial Trees

A ‘Binomial Tree’ (or ‘Lattice’) shows expected stock prices, Intrinsic Values and option values for each
period until expiry. At the end of each stock price path (a ‘node’ – for example, the up and down state
nodes in the above single period example), the stock price can increase or decrease at the next time
period, so that nodes multiply geometrically (trinomial models add a third path between the up and down
binomial states). If the option can be exercised at any date before expiry (American option), the value at
each node will be the Intrinsic Value at that node or, if higher because of time value, the present value
of the option at the next period (the ‘Continuing Value’):

Continuing Valuet = p x (Option Valuet+1u) + (1 - p) x (Option Valuet+1d)
1 + risk free rate (Rfd)

At the final time period tn (the expiry), the option value will simply be max {0, Sn – X} i.e. the IV or zero
as for the one period example above.

For a European option, the value at any time period before expiry will be the Continuing Value, since it
cannot be exercised until expiry. Using the same information, but assuming the 1 year period is divided
into 6 time steps, the following tree and an option value (26.0852) is shown:

[email protected] 5.13

A European Call Option on a non-dividend paying stock will have the same value as its American
counterpart, since it would never be optimal to exercise the latter early (this is not the case if dividends
are paid).

BM-BSM Convergence

The call option value calculated above (26.0852) can be calculated using the Binomial distribution, a
discrete probability distribution which measures the number of successes (probability ‘p’) and failures
(probability ‘1-p’) in a sequence of independent trials.
The call option can be valued as:
If the IV = 0 (share price not
above 150.0 exercise price) and
time value is 0, the option value
is zero. These nodes (shaded)
are ignored in the option value
calculation.

[email protected] 5.14

C0 = S0 x A

x

u
n
d
T-n
- X x A
(1+ r)
T
(1+ r)
T

Where:
A = T! p
n
(1-p)
T-n
= possible combinations x probability of success
n! (T-n)!

Each node can be reached via T! / n! (T – n!) possible paths.

PV of expected stock price at each node,
where exercising the option is optimal
(probability weighted).
PV of exercise price at each node
where exercising is optimal
(probability weighted).
T
Σ
n=a
T
Σ
n=a

[email protected] 5.15

The Excel function can also be used:

The number of nodes can be increased to check convergence to the BSM, here up to 1000 time steps:

[email protected] 5.16

Dividends

Dividends reduce the value of a call option since the option holder does not receive the cash payout,
which is perceived to reduce equity value marginally. One method of incorporating dividends into the BM
is by assuming they are paid at a continuous yield (q%) and adjusting downwards the risk neutral
probability to p = (e
(r – q) t
– d) / (u - d). Using the 6 period example, assuming a 6.00% annual dividend
yield (1.00% each time step), the option value reduces from 26.0852 to 22.1798 for a European option
and 22.3702 for an American option. In the latter case, it is optimal to exercise early (the layout has been
rotated 45 degrees for presentation purposes)

European American

A European option cannot be
exercised before expiry, so IV
will be zero until the final node
Shaded nodes are ignored,
as there is payoff

[email protected] 5.17

The BSM incorporates a continuous dividend yield by reducing the risk free rate:

[email protected] 5.18

Appendix 2 : Convertible Bond Pricing

Building the convertible binomial tree would typically involve the following steps:

1. Value the bond as a straight bond without any conversion feature (see Part 4).

2. For each coupon payment period until maturity, forecast share prices using techniques described in
Appendix 1 (applying up and down factors to the prior node ex-dividend share price) and deduct any
dividend assumed (this could be a yield %) to arrive at the ex-dividend share price (the yield can
alternatively be deducted in the risk neutral probability calculation). This gives the Conversion Value
(ex. div.share price x Conversion Ratio).

3. At the last node (maturity date), calculate the Investment Value (the redemption amount plus final
coupon). At the previous node discount this back at the risk adjusted rate and add the coupon to
determine the prior period Investment Value. Carry on backwards until time 0.

4. At the last node, the Convertible fair price will be the greater of the Conversion Value (when conversion
is certain and the bond would be priced as 100% equity) and the Investment Value (when the bond is
priced as 100% debt).

5. At the penultimate node, the convertible price will be the greater of the Conversion Value, the
Investment Value and the present value of the Convertible fair price if conversion occurred at some
future date (the ‘Continuing Value’, ‘V’ or ‘Rollback’ value). V is the present value of the risk-neutral
probability weighted convertible fair price (‘C’) at the next period:

Continuing Value Vt = p . Ct+1u + (1- p). Ct+1d + coupon
1 + r

where t+1u, t+1d up and down states at next node after node t
p risk-neutral probability
r discount rate

The same calculation is then carried out at the previous node and all others, going backwards.

There are two other factors to consider

 As discussed in the main text, issuers will usually require the right to call the bonds. If the convertible
fair price or trading price (if quoted) rises above the call price (as yields fall), the bonds could be
redeemed (‘hard call’) and refinanced at a lower coupon at less cost that buying them back in the
market. In practice, issuers may call the bonds to force bond investors to convert if this is the best action
to take (compared to doing nothing or having the bonds redeemed).

[email protected] 5.19

The convertible fair price should reflect the higher of the Conversion Value and the lower of the
Continuing Value (if not converted or called) and Call Price (a call is only likely if the Call Price is less
than the Continuing Value):

Convertible fair price = MAX ( Conversion Value, MIN {Continuing Value*, Call Price*} )

* plus Coupon

A notice to call the bonds should force the investor to convert and receive the higher cash payout.

 As the Convertible is a hybrid instrument whose value reflects the underlying investment value (which
acts as a floor) and equity value (with upside potential), its fair price could be calculated with suitable
discount rates that reflect these two components. As in the option pricing model, the equity component
can be discounted at the risk free rate; the discount rate for the debt portion should reflect the issuer’s
credit risk and would therefore be the risk free rate plus a credit risk premium. Two approaches that
have been suggested in the past are as follows:

o Discount the next period probability weighted equity and debt components at the risk free and risk
adjusted rates, respectively (this requires working backwards from the final node, when the bond
will be priced 100% debt or equity, and discounting back using these rates to arrive at the equity
and debt values at the prior node etc):

Vt = p . Et+1u) + (1-p). Et+1d + p. Dt+1u + (1 - p) Dt+1d
1 + r 1 + r + CRP

Where:
t+1u, t+1d up and down states at next node after node t
p risk-neutral probability
r risk free rate
CRP credit risk premium
(Tsiveriotis and Fernandes (1998) and Hull (2003))

o Discount the next period probability weighted convertible fair value (equity and debt) at a blended
rate that varies as the equity and debt components change, respectively:

Blended rate = r. w + (r + CRP)(1 – w)

Where:
r risk free rate

CRP Credit Risk Premium

[email protected] 5.20

w a measure of the equity component embedded in the next period convertible fair price, which
can be estimated using the convertible’s ‘delta’ or the probability of conversion:

[1] Delta = Convertible Priceu - Convertible Priced
Conversion Valueu - Conversion Valued

(Woodson (2002), Philips (1997))

[2] Prob. of conversion = Pu . p + P . (1 - p)

Pu, Pd probability of conversion at next period up and down states
p risk neutral probability
(Goldman Sachs (1994))

This simplified example illustrates pricing a convertible using the blended rate approach based on the
probability of conversion discussed above. Assume the following:

A 2.00% p.a. coupon paying bond,
maturing in 6 years at 129.318% of
face value, is issued at Є115 with
an option to convert into 5 shares
at any year end at a Є20.00
Conversion Price (39.74% premium
to the Є14.31 share price on issue).
The issuer has the right to redeem
the bond early (call) at amortised
cost from year 4. The yield for a
similar bond without any
conversion feature is 6.184%
(effective rate), giving a PV of Є100
for the straight bond less 4.15 for
call option = 95.85 + 19.15 for the
conversion option (volatility is
40.0%).

[email protected] 5.21

The first step is to
calculate the straight
bond value
(Investment Value),
assuming no
conversion. As the
valuation date is the
bond issue date,
accrued interest is
zero:

Now the tree:

The share price at each node of the
tree is the ex-div price at the
previous node adjusted up or down
by the u and d factors. The dividend
is calculated as a % yield of the price
(which is assumed to be the cum-div
price, from which the divided is
deducted to get the ex-div price). The
alternative would be to adjust the
risk neutral probability

[email protected] 5.22

At maturity (t6), convertible
holders will convert at level 3
and above, as the Conversion
Value (ConvV) is greater than the
Redemption Amount (RA). At
year 5 (E nodes), the issuer can
call (paying 125.67) but would
only do so if this was less than
the convertible fair value
(without a call), being the
maximum of the ConvV,
Investment Value ((V) and
Continuing Value (ContV) (with
time value). At 1E and 2E, the
investor would convert anyway
(ConvV > ContV > RA). At 3E, the
investor receives more from the
call if made (ContV > RA >
ConvV) but at 2D they receive
more from converting compared
to the call (Cont V > ConvV > RA),
so a call would force them to
convert,
Continued on next page
The call option and
conversion option
have been netted off
(15.0). Ignoring the
call, the option is
19.15.

[email protected] 5.23

Workings for node 1C

[email protected] 6.1

BUSINESS VALUATION
Part 6: Comprehensive DCF Example

C.F. Agar 15 Oct. 2025
DCF VALUATION HIGHLIGHTS
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
FINANCIAL METRICS
Revenues 6,424.7 7,067.2 7,773.9 8,162.6 8,570.7
% change 25.0 % 10.0 % 10.0 % 5.0 % 5.0 %
EBITDA 2,738.8 3,004.3 3,334.7 3,501.4 3,719.3
% revenues 42.6 % 42.5 % 42.9 % 42.9 % 43.4 %
Net Operating Profits after Adjusted Taxes (NOPAT) 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
% revenues 24.6 % 24.7 % 24.9 % 24.9 % 25.2 %
Net New Invested Capital (NNI) (2,586.9) (2,365.1) (765.8) (732.4) (339.9)
% NOPAT (Reinvestment Rate) 163.7 % 135.7 % 39.5 % 36.0 % 15.7 %
Free Cashflows to the Firm (NOPAT - NNI) (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Change in Gross Debt and Debt Equivalents 3,583.7 1,496.5 624.8 897.9 1,105.5
Net Interest (182.3) (321.0) (305.7) (390.8) (547.4)
Tax relief on Net Interest 59.8 101.3 96.1 123.4 172.1
Changes in operating cash (not working capital) (137.6) (19.3) (21.2) (11.7) (12.2)
Other changes in non-operating assets 248.1 - - - -
Free Cashflows to Equity 2,564.6 635.9 1,565.3 1,919.7 2,541.9
add back non-equity cash flows (3,571.7) (1,257.6) (394.0) (618.7) (718.0)
add back NNI 2,586.9 2,365.1 765.8 732.4 339.9
less: finance costs (net of tax) (122.5) (262.0) (291.4) (309.6) (329.9)
Share of Associates profits - - - - -
Profit After Tax 1,457.3 1,481.4 1,645.7 1,723.7 1,834.0
Borrowings (net of surplus cash) 3,350.2 7,094.2 7,956.9 8,545.4 9,165.7 9,742.2
Debt equivalents (pension deficit, long term provisions) 569.3 676.1 690.5 705.7 721.6 738.3
Net Debt and Equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Equity BV 3,890.3 2,626.4 4,114.3 4,276.5 4,372.7 4,119.4
Investor Funds 7,809.8 10,396.7 12,761.8 13,527.6 14,260.0 14,599.9
Invested Capital (pre goodwill) at start 7,705.5 7,705.5 10,292.4 12,657.5 13,423.3 14,155.7
NNI 2,586.9 2,365.1 765.8 732.4 339.9
Invested Capital (pre goodwill) at end 10,292.4 12,657.5 13,423.3 14,155.7 14,495.6
Goodwill (existing previous acquisitions) 104.3 104.3 104.3 104.3 104.3 104.3
Invested Capital at end 7,809.8 10,396.7 12,761.8 13,527.6 14,260.0 14,599.9
VALUATION PARAMETERS
Tax rate 31.06 % 31.06 % 31.06 % 31.06 % 31.06 %
Pre-Tax Cost of Net Debt 5.00 % 5.00 % 5.00 % 5.00 % 5.00 %
Post-Tax Cost of Net Debt 3.45 % 3.45 % 3.45 % 3.45 % 3.45 %
Ungeared Cost of Equity 9.50 % 10.00 % 10.00 % 10.00 % 10.00 %
Geared Cost of Equity (CAPM) 10.07 % 11.25 % 11.25 % 11.25 % 11.25 %
Equity Risk Premium 5.00 % 5.00 % 5.00 % 5.00 % 5.00 %
Ungeared Beta 0.900 1.000 1.000 1.000 1.000
Geared Beta 1.015 1.250 1.250 1.250 1.250
Leverage at start of period 11.32 % 20.00 % 20.00 % 20.00 % 20.00 %
Pre-Tax WACC 9.50 % 10.00 % 10.00 % 10.00 % 10.00 %
Post-Tax WACC 9.32 % 9.69 % 9.69 % 9.69 % 9.69 %

[email protected] 6.2

DCF VALUATION HIGHLIGHTS
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
EQUITY VALUATION METHODS
FREE CASH FLOWS TO THE FIRM
Free Cashflows to the Firm (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Discounted back one period (cumulative) at post-tax WACC [A]1,505.0 2,652.4 3,531.1 2,701.9 1,662.8
Terminal Value 52,402.7
Discounted back one period at post-tax WACC [B] 33,111.5 36,198.9 39,706.3 43,553.6 47,773.7
Enterprise Value at each period
1
34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 -
Add: market value of associates and non-operating assets - - - - - -
Adjusted Enterprise Value at each period 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Net Debt + Debt Equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Discount Rate (post-tax WACC) 9.32 % 9.69 % 9.69 % 9.69 % 9.69 %
Leverage (Net Debt + Debt Equivalents / Adj Enterprise Value)
2
11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Target leverage used in WACC (market values) 11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Actual Leverage (book Invested Capital) 50.19% 74.74% 67.76% 68.39% 69.34% 71.78%
Terminal value as % of EV 95.65% 93.17% 91.83% 94.16% 96.64% 100.00%
Implied Forward EBITDA x 12.6 x 12.8 x 12.9 x 13.1 x 13.2 x 13.2 x
1
Ent Value at each year end = {Ent Value next yr + Cash Flows next yr} / (1 + discount rate)
2
Borrowings are rebalanced each period to ensure Net Debt and Debt equivalents (e.g. pension deficit) are the same percentage of
Enterprise Value using in the WACC calculation]
TERMINAL ENTERPRISE VALUE
Free Cash Flows to the Firm - final forecast year 1,823.9
Growth rate in perpetuity Assumed 6.00 %
Discount rate - post-tax WACC 9.69 %
Free Cash Flows to the Firm - first perpetuity year 1,823.9 x (1 + 6.00%) = 1,933.3
Terminal value (Enterprise Value) 1,933.3 / (9.69% - 6.00%) = 52,402.7
Free Cash Flows to the Firm - final forecast year - no growth 35.9 % 18,823.8
Free Cash Flows to the Firm - final forecast year growth 64.1 % 33,578.92
FREE CASH FLOWS TO EQUITY
Free Cashflows to Equity 2,564.6 635.9 1,565.3 1,919.7 2,541.9
Remove: (Incr)/Decr in Operating Cash (if not treated as working capital)137.6 19.3 21.2 11.7 12.2
Remove: increase/decrease in derivatives, pension liabililty, change in non-op A/L(248.1) - - - -
Notional adjustment for debt rebalancing re. debt and equivalents 254.5 (667.5) (109.6) (313.1) (477.8)
Notional adjustment for debt rebalancing re. non-operating assets - - - - -
Adjusted Free Cash Flows to Equity 2,708.6 (12.3) 1,476.9 1,618.2 2,076.3
Discounted back one period (cumulative) at post-tax WACC [A]5,833.9 3,713.0 4,143.0 3,132.2 1,866.4
Terminal Value 41,922.1
Discounted back one period at post-tax WACC [B] 24,863.2 27,368.0 30,446.9 33,872.2 37,682.8
Enterprise Value at each period
1
30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 -
Add: market value of associates and non-operating assets - - - - - -
Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Discount Rate (geared Cost of Equity) 10.07 % 11.25 % 11.25 % 11.25 % 11.25 %
TERMINAL EQUITY VALUE
Free Cash Flows to the Firm - first perpetuity year 1,933.3
Debt cash flows post-tax 267.6
Free Cash Flows to Equity - first perpetuity year (FCFF) 2,200.9
Growth rate in perpetuity Assumed 6.00 %
Discount rate - geared Cost of Equity 11.25 %
Terminal Value (Equity Value) 2,200.9 / (11.25% - 6.00%) = 41,922.1

[email protected] 6.3

DCF VALUATION HIGHLIGHTS
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
RESIDUAL OPERATING INCOME
NOPAT for period 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
Invested Capital (pre Goodwill) at start of period x post-tax WACC 718.5 997.3 1,226.4 1,300.6 1,371.6
Economic Profits (Residual Operating Income) 861.3 746.2 710.7 732.7 792.3
Discounted back one period (cumulative) at post-tax WACC [A]2,958.8 2,373.4 1,857.2 1,326.4 722.3
Terminal Value 37,907.0
Discounted back one period at post-tax WACC [B] 23,952.2 26,185.5 28,722.7 31,505.8 34,558.5
Value of Economic Profits at each period 26,911.0 28,558.9 30,579.9 32,832.2 35,280.8 37,907.0
Invested Capital (pre Goodwill) at start of period 7,705.5 10,292.4 12,657.5 13,423.3 14,155.7 14,495.6 Add: market value of associates and non-operating assets
- - - - - -
Adjusted Enterprise Value at each period 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Net Debt + Debt Equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Discount Rate (post-tax WACC) 9.32 % 9.69 % 9.69 % 9.69 % 9.69 %
TERMINAL RESIDUAL INCOME VALUE
Invested Capital at start of terminal period 14,495.6
Steady state growth in Invested Capital Assumed 6.00 %
Discount rate - post-tax WACC 9.69 %
NNI in first perpetuity year 6.00% x 14,495.64 = 869.7
Free Cashflows in first year 1,933.3
NOPAT in first year 2,803.1
less: Post-tax WACC x Invested Capital at start of terminal period 9.69% x 14,495.64 = (1,404.5)
Economic Profits 1,398.5
Terminal Value (Residual Income) 1,398.5 / (9.69% - 6.00%) = 37,907.0
ADJUSTED PRESENT VALUE (TAX SHIELD)
Free Cashflows to the Firm (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Discounted back one period (cumulative) at ungeared Cost of Equity1,478.5 2,626.0 3,510.3 2,690.0 1,658.1
Terminal Value 48,333.6
Discounted back one period (cumulative) at ungeared Cost of Equity30,148.4 33,012.5 36,313.8 39,945.1 43,939.6
Add: market value of associates and non-operating assets - - - - - -
less: vaue of tax shield relating to associates and non-operating assets- - - - - -
Enterprise Value excluding Tax Shield31,626.9 35,638.6 39,824.1 42,635.1 45,597.7 48,333.6
Tax cash flows - Free Cash Flows to the Firm 60.9 120.7 134.3 143.7 153.5
Tax cash flows - Associates and Non-Operating Assets - - - - -
Tax cash flows 60.9 120.7 134.3 143.7 153.5
Discounted back one period (cumulative) at ungeared Cost of Equity451.5 433.5 356.2 257.5 139.6
Terminal Value of Tax Shields 4,069.1
Discounted back one period (cumulative) at ungeared Cost of Equity2,538.1 2,779.2 3,057.2 3,362.9 3,699.2
Value of Tax Shield at each period 2,989.6 3,212.7 3,413.3 3,620.4 3,838.7 4,069.1
Adjusted Enterprise Value at each period 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Net Debt + Debt Equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Ungeared Cost of Equity 9.50 % 10.00 % 10.00 % 10.00 % 10.00 %
Value of Tax Shield / Enterprise Value 8.64 % 8.27 % 7.89 % 7.83 % 7.77 % 7.77 %
TERMINAL RESIDUAL INCOME VALUE
Excluding Tax Shield
Free Cash Flows to the Firm - first perpetuity year 1,933.3
Growth rate in perpetuity Assumed 6.00 %
Discount rate - ungeared Cost of Equity 10.00 %
Terminal value (excluding tax) 1,933.3 / (10.00% - 6.00%) = 48,333.6
Tax Shield
Net Debt at start of final forecast year 9,887.3
Pre-tax Cost of Net Debt (Kd) 5.00%
Tax rate (t) 31.06%
Tax Shield in final forecast year 153.5
Tax Shield in first perpetuity year= 153.5 x (1 + 6.00%) 162.8
Terminal value (tax shield) = 162.8 / (10.00% - 6.00%) = 4,069.1
Terminal value (Enterprise Value) 52,402.7

[email protected] 6.4

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
CASHFLOW RECONCILIATIONS
PROFIT AFTER TAX - NET CASH FLOWS
PROFIT AFTER TAX 1,457.3 1,481.4 1,645.7 1,723.7 1,834.0
add back: finance costs (net of of finance income) 175.3 360.7 403.4 429.7 459.1
add back: income tax expense 656.6 667.4 741.4 776.6 826.3
EARNINGS BEFORE INTEREST TAX AMORTISATION (EBITA) 2,289.1 2,509.6 2,790.5 2,930.0 3,119.4
add back: notional Interest on Pension Liability 2.5 19.4 19.4 19.4 19.4
Adjusted EBITA 2,291.6 2,528.9 2,809.9 2,949.4 3,138.8
Operating cash taxes on EBITA (711.8) (785.5) (872.7) (916.1) (974.9)
NET OPERATING PROFIT LESS ADJUSTED TAXES (NOPAT) 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
add back: depreciation on PP&E 449.7 494.7 544.2 571.4 599.9
Gross Cash Flow 2,029.5 2,238.1 2,481.3 2,604.7 2,763.8
(Increase)/Decrease in Operating Working Capital (ignoring cash and tax)(1,109.2) 179.1 (143.9) (79.4) (82.8)
Capex (net of Disposals) (1,927.4) (3,038.9) (1,166.1) (1,224.4) (857.1)
FREE CASHFLOWS TO THE FIRM (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Increase/(decrease) in long term provisions 13.8 14.4 15.2 15.9 16.7
Change in other non-operating assets/liabilities 155.0 - - - -
Notional Interest on Pension Liability (2.5) (19.4) (19.4) (19.4) (19.4)
less: tax on Notional Interest on Pension Liability0.8 6.0 6.0 6.0 6.0
Add back: employee option grant costs 64.2 70.7 77.7 81.6 85.7
Operating and Investing Cash Flows (before tax and interest received)(775.8) (549.9) 1,250.9 1,385.1 1,913.0
Interest received 14.7 7.7 5.2 9.3 9.8
less: tax on Interest received (4.6) (2.4) (1.6) (2.9) (3.0)
Tax on interest paid - excluding debt leverage management 59.0 59.0 59.0 59.0 59.0
Net Post-Tax Cash Flows from Operating and Investing Activities (IFRS)(706.7) (485.6) 1,313.4 1,450.5 1,978.7
Additional tax on interest paid - leverage management- 36.3 31.1 58.4 107.1
Net Post-Tax Cashflows from Operating & Investing (IFRS) - adjusted(706.7) (449.3) 1,344.5 1,508.9 2,085.8
Increase/(decrease) in derivatives (244.6) - - - -
Increase/(decrease) in Pension Net Liability and funding 337.7 - - - -
Cash flows before debt and equity financing (613.6) (449.3) 1,344.5 1,508.9 2,085.8
Debt Cash Flows - capital - without leverage management 792.9 842.2 (939.8) (1,069.8) (1,579.1)
Additional Debt Cash Flows - capital - leverage management2,777.1 639.9 1,549.5 1,951.7 2,667.8
Debt Capital Cashflows 3,570.0 1,482.1 609.7 881.9 1,088.8
Debt Cash Flows - gross interest paid - without leverage management(189.9) (189.9) (189.9) (189.9) (189.9)
Additional Debt Cash Flows - gross interest paid adjustment - leverage management- (117.0) (100.0) (188.0) (344.8)
Gross Interest Cashflows (189.9) (306.9) (289.9) (377.9) (534.8)
Gross Debt Cashflows 3,380.1 1,175.2 319.8 504.0 554.0
(Incr)/Decr in Operating Cash (if not treated as working capital)(137.6) (19.3) (21.2) (11.7) (12.2)
less:: employee option grant costs (64.2) (70.7) (77.7) (81.6) (85.7)
Net Debt and Debt Like Cash Flows (pre-tax) 3,178.2 1,085.2 220.8 410.7 456.0
FREE CASHFLOWS TO EQUITY 2,564.6 635.9 1,565.3 1,919.7 2,541.9
Ordinary Share Dividends to equity owners (163.3) (147.4) (162.5) (179.1) (197.5)
Special Dividends and buybacks (2,777.1) (559.3) (1,480.5) (1,822.1) (2,430.1)
Add back: employee option grant costs (notional cash flows for valuation)64.2 70.7 77.7 81.6 85.7
Net Cash Flows before reinvestment of surplus cash (311.6) - - - -
(Increase)/Decrease in Cash Equivalents (excess cash) 311.6 - - - -
NET CASH FLOWS - - - - -

[email protected] 6.5

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
CASHFLOW RECONCILIATIONS
FREE CASH FLOWS - PROFIT AFTER TAX
FREE CASHFLOWS TO THE FIRM (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Debt - capital cashflows 3,570.0 1,482.1 609.7 881.9 1,088.8
Increase/(decrease) in long term provisions 13.8 14.4 15.2 15.9 16.7
Change in gross debt and equivalents 3,583.7 1,496.5 624.8 897.9 1,105.5
Gross Interest Cashflows (189.9) (306.9) (289.9) (377.9) (534.8)
Tax thereon 59.0 95.3 90.0 117.4 166.1
Debt - interest (net of tax) (130.9) (211.6) (199.9) (260.5) (368.7)
Notional Gross Interest on debt equivalents (2.5) (19.4) (19.4) (19.4) (19.4)
Tax thereon 0.8 6.0 6.0 6.0 6.0
Debt equivalents - notional interest (net of tax) (1.7) (13.4) (13.4) (13.4) (13.4)
Net Interest on Debt and Debt equivalents (132.7) (224.9) (213.2) (273.9) (382.0)
less: Interest received (if Net Debt method used) 10.1 5.3 3.6 6.4 6.8
Interest (net of tax) (122.5) (219.6) (209.7) (267.5) (375.3)
Debt cash flows (post tax) 3,461.2 1,276.9 415.2 630.4 730.2
Free Cash Flows less debt cash flows 2,454.1 655.2 1,586.5 1,931.3 2,554.1
(Incr)/Decr in Operating Cash (if not treated as working capital)(137.6) (19.3) (21.2) (11.7) (12.2)
Dividends received and change in non-operating assets / (liabilities)248.1 - - - -
FREE CASHFLOWS TO EQUITY 2,564.6 635.9 1,565.3 1,919.7 2,541.9
Free Cash Flows to Equity - without target debt management (212.5) 76.7 84.7 97.5 111.8
Additional Free Cash Flows to Equity - with target debt management2,777.1 559.3 1,480.5 1,822.1 2,430.1
Free Cash Flows to Equity 2,564.6 635.9 1,565.3 1,919.7 2,541.9
Remove: (Incr)/Decr in Operating Cash (if not treated as working capital)137.6 19.3 21.2 11.7 12.2
Remove: increase/decrease in derivatives, pension liabililty, change in non-op A/L(248.1) - - - -
Adjusted Free Cash Flows to Equity 2,454.1 655.2 1,586.5 1,931.3 2,554.1
Add back: Net New Investment 2,586.9 2,365.1 765.8 732.4 339.9
Remove: Debt funding and equivalent (3,583.7) (1,496.5) (624.8) (897.9) (1,105.5)
Add back: Gross Interest paid in Valuation 189.9 306.9 289.9 377.9 534.8
less: tax on Gross Interest paid in Valuation (59.0) (95.3) (90.0) (117.4) (166.1)
Less: gross Interest Expense in Profit After Tax (185.4) (366.0) (406.9) (436.1) (465.9)
add: tax on Interest Expense in Profit After Tax 55.2 118.1 131.3 139.5 148.6
Remove: tax on debt equivalents interest (0.8) (6.0) (6.0) (6.0) (6.0)
PROFIT AFTER TAX 1,457.3 1,481.4 1,645.7 1,723.7 1,834.0
Note: Free Cash Flows to Equity are adjusted for valuation purposes to align debt / leverage with that used in WACC:
Adjusted Free Cash Flows to Equity 2,454.1 655.2 1,586.5 1,931.3 2,554.1
Increase / (Decrease) in debt funding implied in WACC leverage assumption267.1 (619.3) (21.2) (261.7) (512.2)
(Increase( / Decrease in debt interrest implied in WACC leverage assumption(12.6) (48.2) (88.4) (51.4) 34.5
Free Cash Flows to Equity used in Equity Valuation 2,708.6 (12.3) 1,476.9 1,618.2 2,076.3

[email protected] 6.6

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
NOPAT & INVESTED CAPITAL
Operating Profit to NOPAT Reconcilation:
Operating profit (excl. associates) 2,289.1 2,509.6 2,790.5 2,930.0 3,119.4
Depreciation, amortisation and impairment 449.7 494.7 544.2 571.4 599.9
EBITDA 2,738.8 3,004.3 3,334.7 3,501.4 3,719.3
less: Depreciation (449.7) (494.7) (544.2) (571.4) (599.9)
Earnings Before Interest Tax Amortisation (EBITA) 2,289.1 2,509.6 2,790.5 2,930.0 3,119.4
add back: notional Interest on Pension Deficit/Surplus
4.1
2.5 19.4 19.4 19.4 19.4
Adjusted EBITA 2,291.6 2,528.9 2,809.9 2,949.4 3,138.8
Operating cash taxes on EBITA (711.8) (785.5) (872.7) (916.1) (974.9)
Net Operating Profit Less Adjusted Taxes (NOPAT) 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
Net Profit to NOPAT Reconcilation:
Profit / (Loss) After Taxation (continuing operations) 1,457.3 1,481.4 1,645.7 1,723.7 1,834.0
add back: notional Interest on Pension Liability (net of tax)
2.8
1.7 13.4 13.4 13.4 13.4
add back: Interest expense (net of tax)
40.3
130.9 254.0 281.6 302.6 323.3
add back: Interest income (net of tax)
(3.7)
(10.1) (5.3) (3.6) (6.4) (6.8)
Net Operating Profit Less Adjusted Taxes (NOPAT) 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
-
- - - - -
Invested Capital
Inventories 704.1 774.5 843.4 885.6 920.5
Trade Receivables 704.1 774.5 851.9 894.5 939.3
Other receivables 704.1 774.5 851.9 894.5 939.3
less: other non-operating items - - - - -
Tax repayable, prepayments and accruals
49.6
161.3 174.7 192.5 202.1 212.7
Operating cash (if treated as working capital) - - - - -
Operating Current Assets 2,273.5 2,498.2 2,739.8 2,876.7 3,011.7
Trade Payables (308.0) (677.7) (738.0) (774.9) (805.4)
Accruals and deferred income (257.0) (282.7) (311.0) (326.5) (342.8)
Income tax payable - - - - -
Other Current Liabilities and provisions (83.5) (91.9) (101.1) (106.1) (111.4)
Operating Current Liabilities (648.5) (1,052.2) (1,150.0) (1,207.5) (1,259.7)
Operating Working Capital 1,625.0 1,445.9 1,589.8 1,669.2 1,752.0
Intangible Assets (excl. goodwill) 19.3 19.3 19.3 19.3 19.3
add back: cumulative amortisation and impairment 30.6 30.6 30.6 30.6 30.6
Property, Plant & Equipment 8,617.5 11,161.7 11,783.6 12,436.6 12,693.7
Long term operating non-current assets - - - - -
Operating Invested Capital (before Goodwill) 10,292.4 12,657.5 13,423.3 14,155.7 14,495.6
Goodwill 97.0 97.0 97.0 97.0 97.0
Cumulative Goodwill Impairments 7.3 7.3 7.3 7.3 7.3
Operating Invested Capital (post- Goodwill) 10,396.7 12,761.8 13,527.6 14,260.0 14,599.9
Investor Funds
Borrowings 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
less: deposits, investments (current assets) - 83.2 - - -
less: operating cash (if not treated as working capital) (192.7) (212.0) (233.2) (244.9) (257.1)
Retirement Benefit Deficit / (Surplus) 387.4 387.4 387.4 387.4 387.4
Long term non-operating liabilities and provisions 288.8 303.2 318.3 334.3 351.0
Net debt equivalents 7,770.3 8,730.6 9,251.1 9,887.3 10,480.5
Equity & Non-Controlling Interests 5,180.1 6,584.8 6,830.2 6,926.4 6,673.1
add back: cumulative amortisation and impairment 37.9 37.9 37.9 37.9 37.9
Deferred Tax Liability / (Asset) 889.7 889.7 889.7 889.7 889.7
Financial Assets (2,480.9) (2,480.9) (2,480.9) (2,480.9) (2,480.9)
Investment in Associates (1,000.4) (1,000.4) (1,000.4) (1,000.4) (1,000.4)
Net equity equivalents 2,626.4 4,031.1 4,276.5 4,372.7 4,119.4
Investor Funds 10,396.7 12,761.8 13,527.6 14,260.0 14,599.9

[email protected] 6.7

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
FINANCING
Cash Flow Summary
Net Cash Flows from Operating and Investing Activities (IFRS) (706.7) (430.2) 1,381.3 1,527.9 2,065.4
Net change in other borrowings and derivative instruments (244.6) - - - -
Pension costs and other financing items 337.7 - - - -
Cash flows before debt and equity financing (613.6) (430.2) 1,381.3 1,527.9 2,065.4
Borrowings 3,965.8 1,961.0 1,711.4 1,925.8 2,371.3
Repayments (395.8) (1,079.0) (1,101.7) (1,293.9) (1,782.5)
Debt Cash Flows - capital 3,570.0 882.1 609.7 631.9 588.8
Debt Cash Flows - gross interest and fees (189.9) (368.4) (408.5) (439.0) (468.9)
Equity dividends and buybacks (2,940.4) (147.4) (1,478.1) (1,709.2) (2,173.0)
Net cash flows (174.0) (63.9) 104.4 11.7 12.2
Opening Cash 366.7 192.7 128.9 233.2 244.9
Closing Cash 192.7 128.9 233.2 244.9 257.1
Operating Cash 192.7 212.0 233.2 244.9 257.1
Excess Cash - (83.2) - - -
Closing Cash 192.7 128.9 233.2 244.9 257.1
- - - - -
Cash Flow Analysis for funding
Cash flows before debt and equity financing (613.6) (430.2) 1,381.3 1,527.9 2,065.4
Opening cash 366.7 192.7 128.9 233.2 244.9
Cash available before financing (246.9) (237.4) 1,510.2 1,761.1 2,310.3
Interest paid and fees (189.9) (368.4) (408.5) (439.0) (468.9)
Mandatory borrowing - Commercial Paper 395.8 395.8 395.8 395.8 395.8
Mandatory debt repayments (395.8) (995.8) (395.8) (645.8) (895.8)
Ordinary dividends (163.3) (147.4) (162.5) (179.1) (197.5)
Cash balance before new funding (600.1) (1,353.2) 939.2 893.0 1,143.9
less: cash minimum required 192.7 212.0 233.2 244.9 257.1
Adjusted cash balance before new funding (792.9) (1,565.2) 705.9 648.1 886.7
Adjusted cash balance before debt funding (792.9) (1,565.2) 705.9 648.1 886.7
Borrowing - funding 792.9 1,565.2 - - -
Borrowing - managing leverage 2,777.1 - 1,315.6 1,530.0 1,975.5
Surplus cash remaining 2,777.1 - 2,021.6 2,178.1 2,862.2
Discretionary debt repayments: - (83.2) (705.9) (648.1) (886.7)
Surplus cash remaining 2,777.1 (83.2) 1,315.6 1,530.0 1,975.5
Excess paid to shareholders as special dividend (2,777.1) - (1,315.6) (1,530.0) (1,975.5)
- (83.2) - - -

[email protected] 6.8

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
FINANCING
FUNDING
Operating and Investing Cash Flows (before tax and interest received)(775.8) (549.9) 1,250.9 1,385.1 1,913.0
Interest received (net of tax) 10.1 5.3 3.6 6.4 6.8
Tax on interest paid 59.0 95.3 90.0 117.4 166.1
Net Post-Tax Cashflows from Operating & Investing (IFRS) - adjusted(706.7) (449.3) 1,344.5 1,508.9 2,085.8
Change in derivatives and pension funding 93.1 - - - -
Contractual debt repayments - (600.0) - (250.0) (500.0)
Interest paid on opening borrowings balance (189.9) (306.9) (289.9) (377.9) (534.8)
Ordinary dividends (163.3) (147.4) (162.5) (179.1) (197.5)
Opening cash 366.7 192.7 212.0 233.2 244.9
Cash available before financing (600.1) (1,310.8) 1,104.1 935.1 1,098.5
less: cash minimum required (192.7) (212.0) (233.2) (244.9) (257.1)
Adjusted cash balance before new funding - see below (792.9) (1,522.8) 870.9 690.2 841.3
Borrowing - funding / (repayments) 792.9 1,442.2 (939.8) (819.8) (1,079.1)
Borrowing - managing leverage 2,777.1 639.9 1,549.5 1,951.7 2,667.8
Equity - funding - - - - -
Equity - special dividends and buybacks (2,777.1) (559.3) (1,480.5) (1,822.1) (2,430.1)
- - - - -
Cash balance before new funding (before interest paid and tax thereon):(661.9) (1,311.2) 1,070.7 950.7 1,210.0
Interest paid on opening borrowings (net of tax) (189.9) (189.9) (189.9) (189.9) (189.9)
Tax relief thereon 59.0 59.0 59.0 59.0 59.0
Interest paid on opening borrowings (net of tax) - for leverage target- (117.0) (100.0) (188.0) (344.8)
Tax relief thereon - 36.3 31.1 58.4 107.1
Cash balance before debt funding (792.9) (1,522.8) 870.9 690.2 841.3
BORROWINGS
DEBT BALANCES
Opening borrowings 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6
Net borrowing/(repayments) - mandatory - (600.0) - (250.0) (500.0)
Balance before new borrowing 3,716.9 6,686.9 8,169.0 8,528.6 8,910.6
Borrowing/(repayments) - cash flow 792.9 1,522.8 (870.9) (690.2) (841.3)
Borrowing before leverage management 4,509.8 8,209.7 7,298.1 7,838.4 8,069.2
Borrowing - managing leverage 2,777.1 (40.7) 1,480.5 1,572.1 1,930.1
Closing borrowings 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
Debt equivalents 676.1 690.5 705.7 721.6 738.3
Gross debt before target leverage borrowing (incl. fair value gains)7,963.0 8,859.5 9,484.3 10,132.2 10,737.7
less: cash if net debt method used (192.7) (212.0) (233.2) (244.9) (257.1)
Net debt and debt equivalents 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Target debt leverage
11. 32%
20.00% 20.00% 20.00% 20.00% 20.00%
DCF Enterprise Value 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Market value of associates and non-operating assets
-
- - - - -
Enterprise Value 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
DCF Enterprise Value x target leverage 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Market value of associates and non-operating assets x target leverage
-
- - - - -
Net debt & debt equivalents = Enterprise Value x target leverage7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
less: debt equivalents (676.1) (690.5) (705.7) (721.6) (738.3)
Target borrowing 7,094.2 7,956.9 8,545.4 9,165.7 9,742.2
Change in borrowings (closing - opening) 4,246.1 1,572.6 1,315.4 1,353.6 1,327.1

[email protected] 6.9

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
FINANCING
INTEREST
Opening borrowings 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6
Average pre-tax borrowing rate 5.11% 4.21% 3.55% 4.30% 5.68%
Interest (189.9) (306.9) (289.9) (377.9) (534.8)
Tax rate 31.06% 31.06% 31.06% 31.06% 31.06%
Tax on interest 59.0 95.3 90.0 117.4 166.1
Tax on other finance costs - - - - -
Tax on finance costs 59.0 95.3 90.0 117.4 166.1
INTEREST RATES AND TAX
Blending interest rate on borrowings and finance leases (opening balance)5.11% 4.21% 3.55% 4.30% 5.68%
Interest rate on notional capitalised operating leases (opening balance)- - - - -
Interest rate on pension deficit (opening balance) 5.00% 5.00% 5.00% 5.00% 5.00%
Deposit interest rate on opening cash 4.00% 4.00% 4.00% 4.00% 4.00%
Statutory tax rate (marginal rate) 31.06% 31.06% 31.06% 31.06% 31.06%
Operating cash taxes rate 31.06% 31.06% 31.06% 31.06% 31.06%
BORROWINGS
DEBT BALANCE
Net Debt
Current debt 995.8 395.8 645.8 895.8 395.8
Non-current debt (incl. fair value gains) 6,291.1 7,773.2 8,132.8 8,514.8 9,603.5
Gross debt 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
less: cash (192.7) (212.0) (233.2) (244.9) (257.1)
Net debt 7,094.2 7,956.9 8,545.4 9,165.7 9,742.2
Gross debt carrying amounts
Commercial Paper 395.8 395.8 395.8 395.8 395.8
Revolving Facilities
-
3,570.0 5,052.1 5,661.7 6,543.7 7,632.4
Senior Term Loan A
8.0
8.0 8.0 8.0 8.0 8.0
Senior Notes A 3,350.0 2,750.0 2,750.0 2,500.0 2,000.0
7,323.8 8,205.9 8,815.5 9,447.5 10,036.2
Unamortised debt costs and swap gains
(36.9)
(36.9) (36.9) (36.9) (36.9) (36.9)
7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
Gross Debt 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
Opening Gross Debt 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6
Mandatory borrowing - Commercial Paper 395.8 395.8 395.8 395.8 395.8
Repayments (395.8) (1,079.0) (1,101.7) (1,293.9) (1,782.5)
Debt balance before debt borrowing 3,716.9 6,603.7 7,463.0 7,880.5 8,023.8
Borrowing - funding 792.9 1,565.2 - - -
Borrowing - managing leverage 2,777.1 - 1,315.6 1,530.0 1,975.5
Closing Gross Debt 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
CALCULATION OF TARGET DEBT BALANCE
DCF Enterprise Value at each year end 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Target Leverage used in WACC calculation 20.00% 20.00% 20.00% 20.00% 20.00%
7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Target Net Debt + Debt Equivalents 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
less: Debt Equivalents (676.1) (690.5) (705.7) (721.6) (738.3)
Target Net Debt (borrowings) 7,094.2 7,956.9 8,545.4 9,165.7 9,742.2
Cash 192.7 212.0 233.2 244.9 257.1
Target Gross Debt 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3

[email protected] 6.10

TARGET FORECASTS
FORECAST
2025
2026 2027 2028 2029 2030
FINANCING
FACILITY ANALYSIS
Revolving Facilities
Term Remaining (months) at start 120 mths108 mths96 mths84 mths72 mths
Carrying amount at start - 3,570.0 5,052.1 5,661.7 6,543.7
Borrowing 3,570.0 1,565.2 1,315.6 1,530.0 1,975.5
Repayment - - (705.9) (648.1) (886.7)
Repayment (manual) (83.2)
Carrying amount at end 3,570.0 5,052.1 5,661.7 6,543.7 7,632.4
Interest rate (in loan currency) - Floating Rate ref. (LIBOR)5.000% 5.000% 5.000% 5.000% 5.000%
Interest Paid - 178.5 252.6 283.1 327.2
Senior Term Loan A
Carrying amount at end
8.0
8.0 8.0 8.0 8.0 8.0
Senior Notes A
Term Remaining (months) at start 324 mths312 mths300 mths288 mths276 mths
Carrying amount at start 3,350.0 3,350.0 2,750.0 2,750.0 2,500.0
Repayment (amortisation/redemption) - (600.0) - (250.0) (500.0)
Carrying amount at end 3,350.0 2,750.0 2,750.0 2,500.0 2,000.0
Nominal Cash Interest Rate 5.670% 5.670% 5.670% 5.670% 5.670%
Interest Paid 189.9 189.9 155.9 155.9 141.7
SHARE CAPITAL
Opening shares 296,581,476 297,322,501 298,053,822 298,759,614 299,418,542
Options - on exercise 960,565 1,027,731 1,032,845 973,365 932,165
Repurchases and reorganisations (219,539) (296,410) (327,054) (314,437) (316,608)
Closing shares 297,322,501 298,053,822 298,759,614 299,418,542 300,034,099
Average basic shares in issue 296,951,989 297,688,162 298,406,718 299,089,078 299,726,321
In-the-money options (issued on exercise less repurchased with proceeds)5,297,306 1,133,334 1,206,972 637,549 477,802
Average diluted shares 302,249,295 298,821,496 299,613,690 299,726,627 300,204,123
DIVIDENDS
Dividends per share
0.20
0.45 0.50 0.54 0.60 0.66
Average shares 296,951,989 297,688,162 298,406,718 299,089,078 299,726,321
Ordinary dividends
59.3
133.6 147.4 162.5 179.1 197.5
Change in dividends payable 29.7 - - - -
Ordinary dividends paid
(59.3)
(163.3) (147.4) (162.5) (179.1) (197.5)
Ordinary dividend Growth p.a. rate 10.00% 10.00% 10.00% 10.00%
Special Dividend (full payout of surplus cash) (2,777.1) - (1,315.6) (1,530.0) (1,975.5)

[email protected] 6.11

DCF VALUATION
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
FREE CASH FLOWS • POST-TAX WACC
FUTURE ENTERPRISE VALUE
Terminal Value - - - - 52,402.7
Discounted back one period 33,111.5 36,198.9 39,706.3 43,553.6 47,773.7 -
Free Cash Flows to the Firm (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Discounted back one period (cumulative) 1,505.0 2,652.4 3,531.1 2,701.9 1,662.8 -
DCF Enterprise Value
1
34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Market value of associates and non-operating assets - - - - - -
Add cash balances (gross debt method only)(incl. Operating Cash)- - - - - -
Enterprise Value at each year end (Net Debt Method) 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Discount Rate (Post-Tax WACC)- see Discount Rate Analysis 9.32% 9.69% 9.69% 9.69% 9.69%
One year discount factor 0.91471 0.91167 0.91167 0.91167 0.91167
Market value of associates and non-operating assetsDon't use 8,249.8 9,019.8 9,861.6 10,782.0 11,788.4 12,888.6
1
Ent Value at each year end = {Ent Value next yr + Cash Flows next yr} / (1 + discount rate)
CURRENT ENTERPRISE VALUE
Present Value of Free Cash Flows + TV 34,616.5 (921.2) (518.4) 890.5 901.7 34,264.0
Market value of associates and non-operating assets -
Add cash balances (gross debt method only)(incl. Operating Cash)-
Enterprise Value at each year end (Net Debt Method) 34,616.5
Discount Rate (Post-Tax WACC)- see Discount Rate Analysis 9.32% 9.69% 9.69% 9.69% 9.69%
Cumulative discount factor to valuation date 0.91471 0.83391 0.76025 0.69309 0.63187
Terminal Value
Perpetuity Leverage (D / D+E) at start 20.00%
Terminal Post-Tax WACC 9.69% 9.69%
Growth (2.91% real) 6.00% 6.00%
Inflation 3.00%
Free Cash Flows 1st terminal year1,823.9 x (1 +6.00%) =1,933.3
Terminal Value (TV) 1,933.3 / (9.69% - 6.00%) =52,402.7
EQUITY VALUE PER SHARE
DCF Equity Value - including options 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
less: fair value of outstainding options (709.2) (675.9) (721.0) (740.7) (760.8) (776.1)
DCF Equity Value - excluding options 29,987.9 30,405.1 33,869.0 36,263.7 38,788.4 41,146.0
Shares in issued - basic 296,581,476.0 297,322,501.2 298,053,821.9 298,759,613.8 299,418,542.1 300,034,099.1
DCF Equity Value per Share - minority quoted holding 101.11 102.26 113.63 121.38 129.55 137.14
DCF Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Shares in issued - diluted 308,734,331.7 308,792,504.9 309,057,071.9 309,273,095.5 309,476,144.3 309,654,688.7
DCF Equity Value per Share - diluted 99.43 100.65 111.92 119.65 127.79 135.38
LEVERAGE
Borrowings and finance leases 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
Pension Deficit 49.7 387.4 387.4 387.4 387.4 387.4
Gross debt and debt equivalents 3,766.6 7,674.2 8,556.3 9,166.0 9,797.9 10,386.7
less: cash if Net Debt Method used (excluding cash treated as working capital)(366.7) (192.7) (212.0) (233.2) (244.9) (257.1)
Net Interest bearing debt 3,399.9 7,481.5 8,344.3 8,932.8 9,553.0 10,129.6
Non-interest bearing debt equivalents - long term provisions 519.6 288.8 303.2 318.3 334.3 351.0
Net debt & debt equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Net Debt and debt equivalents / Enterprise Value11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
DCF equity value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Value of non-operating investmens - - - - - -
Equity 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Enterprise Value at each year end (Net Debt Method) 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Implied Forward EBITDA x 12.6 x 12.8 x 12.9 x 13.1 x 13.2 x 13.2 x
Target leverage used in WACC (market values) 11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Actual Leverage (market values i.e. DCF value) 11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Actual Leverage (book Invested Capital) 50.19% 74.74% 67.76% 68.39% 69.34% 71.78%
Terminal value as % of EV 95.65% 93.17% 91.83% 94.16% 96.64% 100.00%
DCF Enteprise Value 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
x target leverage = net debt 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5

[email protected] 6.12

DCF VALUATION
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
FREE CASH FLOWS + TAX SHIELD
FREE CASH FLOWS (UNGEARED COST OF EQUITY)
Free Cash Flows (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
Cumulative PV of Free Cashflows at each period 1,478.5 2,626.0 3,510.3 2,690.0 1,658.1 -
PV of Terminal Value at each period 30,148.4 33,012.5 36,313.8 39,945.1 43,939.6 48,333.6
Value of free cash flows (excluding tax shield) 31,626.9 35,638.6 39,824.1 42,635.1 45,597.7 48,333.6
Market value of associates and non-operating assets - - - - - -
Add cash balances (gross debt method only)(incl. Operating Cash) - - - - - -
less: value of tax shield (shown below) - - - - - -
Enterprise Value (excluding tax shield)A 31,626.9 35,638.6 39,824.1 42,635.1 45,597.7 48,333.6
Discount Rate (Ungeared Cost of Equity) 9.50% 10.00% 10.00% 10.00% 10.00%
One year discount factor 0.91324 0.90909 0.90909 0.90909 0.90909
Terminal Value
Terminal Ungeared Cost of Equity 10.00% 10.00%
Free Cash Flow 1st terminal year1,823.9 x (1 +6.00%) =1,933.3
Terminal Value (TV) 1,933.3 / (10.00% - 6.00%) =48,333.6
TAX SHIELDS (UNGEARED COST OF EQUITY)
Tax shield on debt relating to free cash flows value 60.9 120.7 134.3 143.7 153.5
Tax shield on debt relating to cash (Gross Debt only) and Associates and Non-operating assets- - - - -
60.9 120.7 134.3 143.7 153.5
Value of Tax Shield (debt relating to free cash flows) 451.5 433.5 356.2 257.5 139.6 -
Value of Tax Shield (debt relating to cash, associates etc) - - - - - -
PV of Tax shield at each period 451.5 433.5 356.2 257.5 139.6 -
PV of Terminal Value of tax shields at each period 2,538.1 2,779.2 3,057.2 3,362.9 3,699.2 4,069.1
PV of Tax shield cashflows at each periodB 2,989.6 3,212.7 3,413.3 3,620.4 3,838.7 4,069.1
Enterprise Value at each year end A + B 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Tax Shield as % of EV 8.6% 8.3% 7.9% 7.8% 7.8% 7.8%
Discount Rate (Ungeared Cost of Equity) 9.50% 10.00% 10.00% 10.00% 10.00%
One year discount factor 0.91324 0.90909 0.90909 0.90909 0.90909
Terminal Value
Terminal Ungeared Cost of Equity 10.00%
Tax Shield in first year of terminal period (see note A)162.8
TV - Tax Shield of debt 162.8 / (10.00% - 6.00%) =4,069.1
NOTES:
Tax Shield on debt - "Debt" below is Net Debt if that method used and Gross Debt is used
[A] Debt rebalanced: target WACC leverage = actual leverage (debt / enterprise value at each period)
Tax shield on net debt Opening Debt x Kd x t Use 60.9 120.7 134.3 143.7 153.5
Tax Shield on cash balances (Gross Debt method only):Opening Cash x opening Leverage x Kd x tUse - - - - -
Opening Net Debt 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3
Pre-tax Cost of Debt (Kd) 5.00% 5.00% 5.00% 5.00% 5.00%
Tax rate (t) 31.06% 31.06% 31.06% 31.06% 31.06%
Tax Shield 60.9 120.7 134.3 143.7 153.5
Terminal Value 153.5 x (1 + 6.00%) 162.8

[email protected] 6.13

DCF VALUATION
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
ECONOMIC PROFITS
Opening Invested Capital (excl. Associates and Non-Operating items) - pre-Goodwill7,705.5 10,292.4 12,657.5 13,423.3 14,155.7
NOPAT 1,579.8 1,743.4 1,937.1 2,033.3 2,163.9
Average Return On Invested Capital (ROIC
av = NOPAT / Opening IC) 12.43%20.50% 16.94% 15.30% 15.15% 15.29%
WACC 9.32% 9.69% 9.69% 9.69% 9.69%
Economic Profits (=Opening IC x (ROIC
av-WACC
n) ) 861.3 746.2 710.7 732.7 792.3
Free Cash Flows to the Firm (1,007.1) (621.7) 1,171.3 1,300.9 1,823.9
less: opening Invested Capital (pre-goodwill) x ( WACC
n - InvCap Growth g
ICn ) 1,868.4 1,367.8 (460.6) (568.2) (1,031.7)
Economic Profits 861.3 746.2 710.7 732.7 792.3
Enterprise Valuation at each year end
Discount Rate (Post-Tax WACC) 9.32% 9.69% 9.69% 9.69% 9.69%
One year discount factor 0.91471 0.91167 0.91167 0.91167 0.91167
Market value of associates and non-operating assets
Cumulative EVA PV at year end 26,911.0 28,558.9 30,579.9 32,832.2 35,280.8 37,907.0
Invested Capital 7,705.5 10,292.4 12,657.5 13,423.3 14,155.7 14,495.6
Enterprise Value 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Terminal Value
Free Cash Flows to the Firm 1,933.3
Net New Investment = Invested Capital yr5 x Growth14,495.6
x 6.00% 869.7
NOPAT 2,803.1
Chargee on Capital = Invested Capital yr5 x WACC14,495.6
x 9.69% 1,404.5
Economic Profits 1,398.5
Terminal Economic Profits 1,398.5 / (9.69% - 6.00%) =37,907.0
Also computed as:
NOPAT in first year = NOPATyr.5 x (1 + g) 2,293.7
Invested Capital see below 6,005.8
Terminal Post-Tax WACC 9.69%
Charge on Capital (581.9)
Economic Profits in first year 1,711.8
Economic Profit Component of TV1,711.8 / (9.69% - 6.00%) =46,396.9
add: Terminal Invested Capital
1
6,005.8
Economic Profits Value + Invested Capital 52,402.68
less: actual Invested Capital (14,495.64)
37,907.0
1
Terminal Invested Capital
Net New Investment
yr5 (339.95)
NOPATyr5 2,163.9
Reinvestment Rateyr5 = NNI5 / NOPAT5RR 15.71%
Av Return on Inv Capital = growth / RRROICav 38.19%
Invested Capital = NOPATyr.5 x (1 + g) / ROICav 6,005.8
Enterprise Valuation Today
Nominal Discount Factor 1 0.91471 0.83391 0.76025 0.69309 0.63187
PV of EVA 26,911.0 787.9 622.2 540.3 507.8 24,452.8
Invested Capital 7,705.5
Market value of associates and non-operating assets -
Add cash balances (gross debt method only)(incl. Operating Cash) -
34,616.5

[email protected] 6.14

DCF VALUATION
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
EQUITY CASH FLOWS
ADJUSTED FREE CASH FLOWS TO EQUITY 2,454.1 655.2 1,586.5 1,931.3 2,554.1
Notional adjustment to align debt cash flows to those implied in WACC leverage 254.5 (667.5) (109.6) (313.1) (477.8)
ADJUSTED FREE CASH FLOWS TO EQUITY 2,708.6 (12.3) 1,476.9 1,618.2 2,076.3
Enterprise Valuation at each year end
Discount Rate (Geared Cost of Equity) 10.07% 11.25% 11.25% 11.25% 11.25%
One year discount factor 0.90848 0.89888 0.89888 0.89888 0.89888
Equity Value at each year end (includes cash if Gross Debt method used)30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Market value of associates and non-operating assets - - - - - -
Add cash balances (gross debt method only)(incl. Operating Cash) - - - - - -
Equity Value 30,697.1 31,081.0 34,589.9 37,004.4 39,549.2 41,922.1
Net debt and debt equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Enterprise Value 34,616.5 38,851.3 43,237.4 46,255.5 49,436.5 52,402.7
Terminal Value
Terminal Geared Cost of Equity 11.25% 11.25%
Free Cash Flows to the Firm 1st terminal year 1,933.3
less: interest10,480.5 adj debt x 3.45% post-tax cost of debt =(361.3)
Debt funding 10,480.5 adj. debt x 6.00% growth =628.8
Adj. Cash Flows to Equity 1st terminal year2,076.33 x (1 + 6.00%) =2,200.9
Equity Terminal Value (TV) 2,200.9 / (11.25% - 6.00%) =41,922.1
Enterprise Valuation Today
Nominal Discount Factor 0.90848 0.81661 0.73403 0.65980 0.59308
Present Value of Free Cash Flows + TV 30,697.1 2,460.7 (10.0) 1,084.1 1,067.7 26,094.6
Market value of associates and non-operating assets -
Add cash balances (gross debt method only)(incl. Operating Cash) -
Debt 3,919.5
34,616.5
Adjustment to match actual debt cash flows to those implied in WACC leverage:
Leverage (Net Debt and Debt Equivalents / DCF Enterprise Value) used in WACC11.32% 20.00% 20.00% 20.00% 20.00%
Implied opening Net Debt and Debt Equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3
Implied closing Net Debt and Debt Equivalents 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
Change in Net Debt and Debt Equivalents - used in WACC calculation 3,850.8 877.2 603.6 636.2 593.2
Change in Net Debt and Debt Equivalents - actual 3,583.7 1,496.5 624.8 897.9 1,105.5
Debt Capital Cashflow adjustment 267.1 (619.3) (21.2) (261.7) (512.2)
Post-tax Cost of Net Debt - assumed in WACC 3.45% 3.45% 3.45% 3.45% 3.45%
Implied opening Gross Debt 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3
Interest expense (post tax) - used in WACC calculation (135.1) (267.8) (298.1) (318.9) (340.8)
Post-tax Cost of Net Debt - actual blended rate 3.61% 2.91% 2.44% 2.97% 3.95%
Interest Expense (189.9) (306.9) (289.9) (377.9) (534.8)
Interest on Debt Equivalents (notional) (2.5) (19.4) (19.4) (19.4) (19.4)
Tax relief on interest expense 59.8 101.3 96.1 123.4 172.1
Interest Received 14.7 7.7 5.2 9.3 9.8
Tax payable on interest incom (4.6) (2.4) (1.6) (2.9) (3.0)
Actual and notional interest paid (less interest received if Net Debt method used) (net of tax)(122.5) (219.6) (209.7) (267.5) (375.3)
Debt Interest Cashflow adjustment (12.6) (48.2) (88.4) (51.4) 34.5
Debt Cashflow adjustment 254.5 (667.5) (109.6) (313.1) (477.8)

[email protected] 6.15

DCF VALUATION
VALUATION FORECAST (y/e 30 Sept)
30 Sep 20252026 2027 2028 2029 2030
VALUATION DISCOUNT RATES
SUMMARY
Pre-tax Cost of Net Debt 5.00% 5.00% 5.00% 5.00% 5.00%
Post-tax Cost of Debt 3.45% 3.45% 3.45% 3.45% 3.45%
Ungeared Cost of Equity 9.50%10.00%10.00%10.00%10.00%
Geared Cost of Equity 10.07%11.25%11.25%11.25%11.25%
Leverage at start of period 11.32%20.00%20.00%20.00%20.00%
Post-tax WACC 9.32% 9.69% 9.69% 9.69% 9.69%
Pre-tax WACC 9.50%10.00%10.00%10.00%10.00%
LEVERAGE
Override and use target leverage for WACC? 11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Assumed Constant Leverage Used
Tax Shield discounted at ungeared Cost of Equity
Leverage Ratios
Borrowings and finance leases 10.74% 18.76% 18.89% 18.98% 19.04% 19.08%
Pension Deficit 0.14% 1.00% 0.90% 0.84% 0.78% 0.74%
Less cash balances (if Net Debt method used) (incl. Operating Cash)(1.06%) (0.50%) (0.49%) (0.50%) (0.50%) (0.49%)
Interest bearing net debt equivalents 9.82% 19.26% 19.30% 19.31% 19.32% 19.33%
Non-interest bearing debt equivalents 1.50% 0.74% 0.70% 0.69% 0.68% 0.67%
Net debt as % of DCF Enterprise Value 11.32% 20.00% 20.00% 20.00% 20.00% 20.00%
Market Values
Borrowings and finance leases 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6 9,999.3
Pension Deficit 49.7 387.4 387.4 387.4 387.4 387.4
Less cash not treated as working capital (if Net Debt method used) (incl. Operating Cash)(366.7) (192.7) (212.0) (233.2) (244.9) (257.1)
Interest bearing net debt equivalents 3,399.9 7,481.5 8,344.3 8,932.8 9,553.0 10,129.6
Non-interest bearing debt equivalents 519.6 288.8 303.2 318.3 334.3 351.0
Net debt and equivalents 3,919.5 7,770.3 8,647.5 9,251.1 9,887.3 10,480.5
COST OF DEBT
Pre-Tax Cost of Net Debt (marginal) Kd 5.00% 5.00% 5.00% 5.00% 5.00%
Post-Tax Cost of Net Debt Kd(1-t) 3.45% 3.45% 3.45% 3.45% 3.45%
Tax Rate t 31.06% 31.06% 31.06% 31.06% 31.06%
Actual blended rate for borrowings and finance leases:
Pre-tax cost of gross borrowings 5.11% 4.21% 3.55% 4.30% 5.68%
Opening gross borrowings 3,716.9 7,286.9 8,169.0 8,778.6 9,410.6
Pre-tax cash deposit rate (ignored if gross debt used) 4.00% 4.00% 4.00% 4.00% 4.00%
Opening cash balances not treated as working capital (incl. operating cash)(ignored if gross debt used)366.7 192.7 212.0 233.2 244.9
Pre-tax cost of net debt 5.23%4.22%3.54%4.31%5.73%
Post-tax cost of net debt 3.61%2.91%2.44%2.97%3.95%
1
= (Cost of Gross Debt x Gross Debt - Interest Income Rate x Cash) - (Gross Debt - Cash)
COST OF EQUITY (CAPM)
Real Risk Free Rate Rfr 1.94% 1.94% 1.94% 1.94% 1.94%
Inflation I 3.00% 3.00% 3.00% 3.00% 3.00%
Nominal Risk Free Rate Rf 5.00% 5.00% 5.00% 5.00% 5.00%
Equity Risk Premium ERP 5.00% 5.00% 5.00% 5.00% 5.00%
Ungeared, Assets Beta ba 0.900 1.000 1.000 1.000 1.000
Implied Debt Beta : Kd = Rf + bdi (ERP) bdi 0.000 0.000 0.000 0.000 0.000
Actual Leverage (D / D+E) at start L 11.32%20.00%20.00%20.00%20.00%
Actual Gearing (D/E) D/E = L / (1-L) 12.77%25.00%25.00%25.00%25.00%
Size Premium (Fama & French) SP - - - - -
Ungeared Cost Equity Ku = Rf + ba ERP + SP 9.50%10.00%10.00%10.00%10.00%
Geared Equity Beta be = ba + (ba - bd)D/E 1.015 1.250 1.250 1.250 1.250
Geared Cost of Equity Kg = Rf + be ERP + SP"= Ku + (Ku - Kd)D/E(1-t)" 10.07%11.25%11.25%11.25%11.25%
(1) if debt is based on an assumed leverage ratio using market values (i.e. a % of the Enterprise Value): be = ba + (ba - bd)D/E
(2) if debt is a known amount and does not depend on the risk of the business: be = ba + (ba - bd)D(1-t)/E
WEIGHTED AVERAGE COST OF CAPITAL (WACC)
Post-Tax WACC Kg(1 - L) + Kd(1-t).L"= Ku - Ku.t.L" 9.32% 9.69% 9.69% 9.69% 9.69%
Pre-Tax WACC Kg(1 - L) + Kd.L 9.50%10.00%10.00%10.00%10.00%

[email protected] 6.16

TERMINAL VALUE ANALYSIS
FREE CASH FLOWS - PERPETUITY - CONSTANT GROWTH
FREE CASH FLOWS TO THE FIRM
See WORKINGS 1
Free Cash Flows in first year FCFt+1 1,933.3
➗ ➗
Perpetuity Factor (WACC
n -
GN
n
) = 9.69% - 6.00% 3.69%
Terminal Enterprise Value 52,402.7
FREE CASH FLOWS TO EQUITY
Free Cash Flows to Equity in first year 2,200.9
➗
Perpetuity Factor (Ke
n -
GN
n
) = 11.25% - 6.00% 5.25%
Terminal Equity Value 41,922.1
Net Debt 10,480.5
Terminal Enterprise Value 52,402.7
WORKINGS 1 FREE CASH FLOWS - PERPETUITY - CONSTANT GROWTH
Final Year1st Yr Terminal
NOPAT growth (nominal) GN
n
6.42% 6.00%
NOPAT NOPATt+1 = 2,163.86 x (1 + 6.00%)2,163.9 2,293.7
Net New Investment NNIt+1 = 2,293.7 x 15.71% (339.9) (360.3)
Free Cash Flow to the Firm = NOPAT
t - NNI
t FCFF
t+1 = 2,293.7 - 360.3 1,823.9 1,933.3
Net Interest (= net debt x post-tax cost of debt) (340.8) (361.3)
Debt funding (= net debt x NOPAT growth) = 10,480.5 x 6.00% 593.2 628.8
Free Cash Flows to Equity FCFE
t+1 2,076.3 2,200.9
less: equity investment (= NNI see above - debt funding)Equity NNIt+1 = 360.3 NNI - 628.8 (253.3) (268.5)
less: difference in net interest (after tax) 10.9
Profit After Tax PAT
t+1 = 1,834.0 x 6.00% = 1,834.0 1,932.4
Net Debt (leverage x DCF EntValue) at start of period - excluding debt equivalents 9,887.3 10,480.5
Post-tax cost of debt 3.45% 3.45%
Post-tax interest 340.82 361.26
Invested Capital at end of period (incl. goodwill) 14,599.9
less: net debt (excluding amount relating to non-operating assets) 10,480.5
Adjusted Equity book value at end of period E
BVt 4,119.4
ECONOMIC PROFIT GROWTH & RETURNS - PERPETUITY - CONSTANT GROWTH
NOPAT GROWTH
See WORKINGS 2
No Growth Value
NOPAT in first year NOPATt+1 2,293.7
➗ ➗
Perpetuity factor WACC
r
(1 + i) = 6.49% x (1 + 3.0%) ] 6.69%
34,288.4
Growth Value
NOPAT in first year NOPATt+1 2,293.7
x x
Growth Factor GN
r
2.91%
➗ ➗ 0.8131
WACC
r
- GN
r
= 6.49% - 2.91% 3.58%
x 1,865.1
x
Franchise Factor RONICr - WACCr = 18.54% - 6.49% 12.04%
➗ ➗ 9.7122
RONICr x WACCr (1 + i)= 18.54% x 6.49% x (1 + 3.0%)1.24%
18,114.2
Terminal Enterprise Value = 34,288.4 + 18,114.2 52,402.7

[email protected] 6.17

TERMINAL VALUE ANALYSIS
VALUE FROM AVERAGE RETURNS ON EXISTING INVESTED CAPITAL
Invested Capital at start of terminal period 14,495.6
Economic Profits on total invested capital at start of terminal periodICt+1 = 14,495.6
x x
ROICavt+1 - WACC
r
(1 + i)= 15.82% - [ 6.49% x (1 + 3.0%) ]9.13%=1,324.0
➗ ➗
Perpetuity factor WACC
r
(1 + i) = 6.49% x (1 + 3.0%) ] } 6.69%
Value of Economic Profits in perpetuity (no growth) = 1,324.0 / 6.69% 19,792.8
Value from existing invested capital = 14,495.6 + 19,792.80 34,288.4
VALUE FROM MARGINAL RETURNS ON NEW INVESTED CAPITAL
Economic Profits on new investments during terminal periodNNIt+1 360.3
x X
RONICr - WACCr 18.54% - 6.49% 12.04%
➗ ➗
(WACC
r -
GN
r
) 6.49% - 2.91% 3.58% 1,211.7
➗ ➗
Perpetuity factor WACC
r
(1 + i) = 6.49% x (1 + 3.0%) ] 6.69%
18,114.2
Terminal Enterprise Value = 34,288.4 + 18,114.2 52,402.7
WORKINGS 2 ECONOMIC PROFIT GROWTH & RETURNS - PERPETUITY - CONSTANT GROWTH
Final Year1st Yr Terminal
Inflation i 3.00%
NOPAT growth (real) GN
r
= (1 + 6.00%) / (1 + 3.00%) - 1 2.91%
NOPAT NOPATt 2,163.9
NOPAT NOPATt+1 = 2,163.86 x (1 + 6.00%) 2,293.7
Invested Capital (excl. goodwill) IC (ex Gw)t 14,495.6
Reinvestment Rate (option 1) = NNIt / NOPATt RR 15.71% 15.71%
Net new Investment (change in Invested Capital) NNI = 2,163.9 x 15.71% 339.9
RONIC(real) = GN
r
/ RR RONICr = 2.91% / 15.71% 18.54%
RONIC (nominal) RONICn = (1 + 18.54%) x (1 + 3.00%) - 1 22.10%
ROIC (nominal) =NOPATt+1 / ICt ROICavt+1 = 2,293.7 / 14,495.6 15.82%
WACC (nominal) WACC
n
9.69%
WACC (real) Note: WACC
r
(1 + i) = WACC
n
- i WACC
r
= (1 + 9.69%)/(1 + 3.00%) - 1 6.49%
NOPATt+1 (for the first year in the terminal period, grows thereafter due to inflation and a return on capital) =
= NOPATt x (1 + i) x (1 + GN
r
)
= NOPATt x (1 + i) + NNIt x RONICrt+1 x (1 + i) **
= NOPATt x (1 + i) + [ RRt x NOPATt ] x [ RONICnt+1 - i )/(1 + i) ] x (1 + i)
= NOPATt x { 1 + i + RRt x ( RONICnt+1 - i ) }
RONICnt+1 = i + (g - i) / RRt= 3.00% + (6.00% - 3.00%) / prior period RR 15.71%= 22.10%
** = 2,163.9 x (1 + 3.00%) + 339.9 x 18.54% x (1 + 3.00%) = 2,293.7 where 2,163.9 is the final forecast year NOPAT and 339.9 the final year NNI
Final ROICav
n
= GN
n
/ RR = 6.00% / 15.71% = 38.19%
= ( RONICn - i ) x [ GNn / (GNn - i ) ]= (22.10% - 3.00%) / [ 6.00% / ( 6.00% - 3.00%) ] = 38.19%

[email protected] 6.18

TERMINAL VALUE ANALYSIS
RESIDUAL INCOME GROWTH & RETURNS - PERPETUITY - CONSTANT GROWTH
RESIDUAL INCOME & GROWTH See WORKINGS 3
Value from RESIDUAL INCOME in the first year received in perpetuity
Net profit in perpetuity (no growth) = PATt+1 1,932.4
➗ ➗
Perpetuity factor Ke
r
(1 + i) 8.25%
23,423.4
Value from growth in Residual Income
Profit after tax in first year PATt+1 1,932.4
x
Growth Factor GFCFE
r
2.91%
➗ ➗ 0.5714
Ke
r
- GFCFE
r
= 8.01% - 2.91% 5.10%
x x
Franchise Factor ROEm
r
- Ke
r
=- -20.96% - 8.01% -28.97%
➗ ➗ 16.7524
ROEm
r
x Ke
r
(1 + i) = -20.96% x 8.25% -1.73%
18,498.8
Terminal Equity Value = 23,423.4 + 18,498.8 41,922.1
Net Debt 10,480.5
Terminal Enterprise Value 52,402.7
RESIDUAL INCOME & RETURNS
Value from average returns on existing Equity Capital
Invested Capital at start of terminal period (incl. goodwill) 14,599.9
Net debt EBVt 10,480.5
Book value of equity equivalents at start of period 4,119.4
Residual Income on total equity capital at start of terminal periodEBVt 4,119.4
x x
ROEavt+1 - Ke
r
(1 + i) = 46.91% - 8.25% 38.66%=1,592.6
➗ ➗
Perpetuity factor Ke
r
(1 + i) 8.25%
Value of residual Income in perpetuity (no growth) 19,304.0
Value from existing equity capital = 4,119.4 + 19,304.0 23,423.4
Value from marginal returns on new Equity Capital
Residual income on new investments in terminal periodEquity NNIt+1 = 360.3 - 628.8 (268.5)
X x
ROEm
r
- Ke
r
= -20.96% - 8.01% -28.97%
➗ ➗
Ke
r
-

GN
r
= 8.01% - 2.91% 5.10%
1,526.2
➗ ➗
Perpetuity factor Ke
r
(1 + i) 8.25%
18,498.8
Terminal Equity Value = 23,423.4 + 18,498.8 41,922.1
Net Debt 10,480.5
Terminal Enterprise Value 52,402.7

[email protected] 6.19

TERMINAL VALUE ANALYSIS
WORKINGS 3 RESIDUAL INCOME GROWTH & RETURNS - PERPETUITY - CONSTANT GROWTH
1st Yr Terminal
Profit after tax 1,932.4
Equity book value at start of period 4,119.4
Average Return on Equity = PATt+1 / EBVt ROEavt+1 = 1,932.4 / 4,119.4 46.91%
Geared cost of equity (nominal) Ke
n
11.25%
Equity reinvestment rate = Equity NNIt+1 / PATt+1 RRE = -268.5 / 1,932.4 -13.89%
Marginal ROE (nominal) ROEm
n
= 3.0% inf +(6.00% - 3.00%) / -13.89% -18.59%
Marginal ROE (real) ROEm
r
= (1 + -18.59%)/(1 + 3.00%) - 1 -20.96%
Inflation i 3.00%
Geared cost of equity (real) Ke
r
= (1 + 11.25%)/(1 + 3.00%) - 1 8.01%

Business Valuation Parts 1 - 5 plus Example.pdf

About This Presentation

Slide Content

Tags

Categories

Download

Quick Actions

Statistics

Related Slideshows

Business Valuation Parts 1 - 5 plus Example.pdf

About This Presentation

Slide Content

Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77