Financial Management ; Chapter- 6, Capital budgeting.ppt

Course material for the course Financial Management

1. Department of FinanceDepartment of Finance
Course Course Code: FCC - 209 FCC - 209
Course Title : Financial ManagementCourse Title : Financial Management
Dr. Ismat Ara Huq
Professor, Finance, Faculty of Business
Administration, University of Chittagong
Contact : Mobile: [phone]
E-mail : [email protected]
1

2. CHAPTER - 5: CHAPTER - 5:
Basics of Basics of Capital Capital
BudgetingBudgeting
Should we
build this
plant?

3. Chapter OutlineChapter Outline
• Understanding Capital Budgeting
• Steps to capital budgeting
• Types of project
• Capital Budgeting Techniques:
 1. Traditional methods:
a) - Pay Back Period
b) Average Rate of Returns (ARR)

4. Contd.Contd.
2. Discounted cash Flow methods:
a) Net Present Value (NPV)
b) IRR (Internal Rate of Return)
c) MIRR (Modified Internal Rate of Return)
d) Profitability Index ((PI)

e) Comparing the NPV and IRR methods Exercises
•Capital Rationing;
•Uncertainty in Capital Budgeting.

5. Capital Budgeting Capital Budgeting
•Definition:
•The term capital refers to long-term assets used
in production,
•while a budget is a plan that details projected
inflows and outflows during some future period.
•Thus, the capital budget is an outline of planned
investments in fixed assets, and
•capital budgeting is the whole process of
analyzing projects and deciding which ones to
include in the capital budget.
55

6. C/B – Definition (contd.)C/B – Definition (contd.)
•Capital Budgeting is the process of planning
expenditures on assets whose cash flows are
expected to extend beyond one year.
•Capital budgeting is a long term planning for
commitment of funds to fixed assets.
•It involves the whole process of capital
expenditure planning which includes: (i) planning
of capital exp. (ii) evaluation of capital
investment projects & (iii) Control of capital
expenditures
66

7. Administrative Aspect of Capital
Investment Decision:
•The successful administration of capital
investment decision of a firm involves the
following aspect:
• Generation of ideas of proposal.
•Formulation of investment projects.
•Principles and process of investment decision.
•Elements of capital investment decision.
• 
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8. Significance / Importance of C/BSignificance / Importance of C/B
•Capital budgeting is significant because:
•(i) Such decision has long term effect &
affects the firm’s cost structure by
committing a sizeable amount of fixed
assets.
•(ii) It entails a huge amount of fixed capital
which is limited & subject to rationing.
•(iii) It is not easy to make since it requires
technical know how.
88

9. •(iv) Fixed Assets’ acquision & expansion
are related to future sales which is always
uncertain.
•(v) It involves greater risk & uncertainty.
•(vi) Such decision once taken &
implemented can not easily be changed
without considerable financial loss to the
firm.
Significance / Importance of C/BSignificance / Importance of C/B
99

10. Feature of Capital Investment Feature of Capital Investment
DecisionDecision
The following are the main feature of capital
investment decision:
•The exchange of current funds for future
benefits.
•The funds are invested in long term assets.
•The future benefits will occur to the firm over a
series of years.
•It involves commitment of large amount of funds.

11. PROJECT CLASSIFICATIONSPROJECT CLASSIFICATIONS
•Analyzing capital expenditure proposals is not a
costless operation—benefits can be gained, but
analysis does have a cost. For certain types of
projects, a relatively detailed analysis may be
warranted; for others, simpler procedures should
be used.
•Accordingly, firms generally categorize projects
and then analyze those in each category
somewhat differently:
1111

12. Types of Capital investment Decision:
•There are many ways to classify investment
decision. One classification is as follows:
• Expansion project: - expansion of existing product
or market
•Diversification: - expansion of new business
•Replacement project.
•Research and development.
• Yet another useful way to classify investment
project is as follows:
•Independent Investment.
•Mutually Exclusive Investment.
1212

13. •1. Replacement: maintenance of business.
One category consists of expenditures to
replace worn-out or damaged equipment used in
the production of profitable products.
Replacement projects are necessary if the firm is
to continue in business. The only issues here
are
•(a) should this operation be continued and
•(b) should we continue to use the same
production processes?
PROJECT CLASSIFICATIONSPROJECT CLASSIFICATIONS
1313

14. (Contd.)(Contd.)
•The answers are usually yes, so maintenance
decisions are normally made without going
through an elaborate decision process.
•2. Replacement: cost reduction. This category
includes expenditures to replace serviceable but
obsolete equipment. The purpose here is to
lower the costs of labor, materials, and other
inputs such as electricity. These decisions are
discretionary, and a fairly detailed analysis is
generally required.
1414

15. (Contd.)(Contd.)
•3. Expansion of existing products or
markets. Expenditures to increase output of
existing products, or to expand retail outlets or
distribution facilities in markets now being
served, are included here. These decisions are
more complex because they require an explicit
forecast of growth in demand. Mistakes are
more likely, so a more detailed analysis is
required.
1515

16. (Contd.)(Contd.)
•4. Expansion into new products or markets.
These are investments to produce a new
product or to expand into a geographic area not
currently being served. These projects involve
strategic decisions that could change
•the fundamental nature of the business, and
they normally require the expenditure of large
sums of money with delayed paybacks.
1616

17. •5. Safety and/or environmental projects.
Expenditures necessary to comply with
government orders, labor agreements, or
insurance policy terms fall into this category.
These expenditures are called mandatory
investments, and they often involve nonrevenue-
producing projects. How they are handled
depends on their size,
•6. Other. This catch-all includes office buildings,
parking lots, executive aircraft, and so on. How
they are handled varies among companies.
(Contd.)(Contd.)
1717

18. STEPS IN THE PROCESS of capital STEPS IN THE PROCESS of capital
BudgetingBudgeting
•The capital budgeting process consists of five
distinct but interrelated steps:
•1. Proposal generation. Proposals for new
investment projects are made at all levels within a
business organization and are reviewed by finance
personnel. Proposals that require large outlays are
more carefully scrutinized than less costly ones.
•2. Review and analysis. Financial managers
perform formal review and analysis to assess the
merits of investment proposals.
1818

19. STEPS IN THE PROCESS of capital STEPS IN THE PROCESS of capital
BudgetingBudgeting
•3. Decision making. Firms typically delegate capital
expenditure decision making on the basis of dollar
limits. Generally, the board of directors must
authorize expenditures beyond a certain amount.
Often plant managers are given authority to make
decisions necessary to keep the production line
moving.
•4. Implementation. Following approval, expenditures
are made and projects implemented. Expenditures
for a large project often occur in phases.
1919

20. STEPS IN THE PROCESS of capital STEPS IN THE PROCESS of capital
BudgetingBudgeting
•5. Follow-up. Results are monitored, and actual
costs and benefits are compared with those that
were expected. Action may be required if actual
outcomes differ from projected ones.
•Each step in the process is important. Review and
analysis and decision making (Steps 2 and 3)
consume the majority of time and effort, however.
•Follow-up (Step 5) is an important but often ignored
step aimed at allowing the firm to improve the
accuracy of its cash flow estimates continuously.
2020

21. Steps to Capital BudgetingSteps to Capital Budgeting
1.Estimate CFs (inflows & outflows).
2.Assess riskiness of CFs.
3.Determine the appropriate cost of capital.
4.Find NPV and/or IRR.
5.Accept if NPV > 0 and/or IRR > WACC.

22. What is the difference between normal What is the difference between normal
and non normal cash flow streams?and non normal cash flow streams?
•Normal cash flow stream – Cost
(negative CF) followed by a series of
positive cash inflows. One change of
signs.
•Non normal cash flow stream – Two or
more changes of signs. Most common:
Cost (negative CF), then string of positive
CFs, then cost to close project. Nuclear
power plant, strip mine, etc.

23. Cash Flows
Cash flow refers to the actual cash, as
opposed to accounting net income that a firm
receives or pays during certain specified period.
What the firm receives is known as cash
inflows, but what the firm pays is known as cash
outflow. The difference between cash inflows and
cash outflows are considered as net cash flows.
23

24. Cash Flows
Relevant cash flows are the specific cash flows
that should be considered in a capital
investment decision. There are some cash flows
known as irrelevant for a specific investment.
24
Relevant Cash Flows Irrelevant Cash Flows
i. Variable labor expenses
ii. Variable material costs
iii. Cost of the investment
iv. Marginal taxes
i. Fixed overhead costs
ii. Sunk costs
Relevant and Irrelevant Cash Flow

25. Cash Flows
Differences between Concepts of Cash Flow
and Profit:
Accounting profit is the difference between a
company’s revenues, cost of goods sold and
expenses. The first item represents money coming
in, while the latter two items represent money going
out of the business. This figure, called "operating
profit," is fictitious number since it has no physical
representation in the company’s business
operations. Non-operating items can increase or
decrease accounting profit. These include the sale
or disposal of assets and other one-time items.
25

26. Cash Flows
Differences between Concepts of Cash Flow and
Profit:
Cash Flows
Cash flows represent the different sources and uses
of cash in a business. Cash is a physical asset
companies track through bank accounts, statements
and reconciliations. Companies use the income
statement and balance sheet to prepare the
statement of cash flows. Three main activities --
operating, investing and financing -- represent the
sources or uses of cash. Revenues and operating
expenses are part of the first section, derived from
the company’s current income statement. 26

27. Cash Flows
Components of Cash Flow
A typical investment will have three components
of cash flow:
Initial investment
Annual net cash flow
Terminal cash flow
Initial Investment
Initial investment is the net cash outlay in the
period in which an asset is acquired.
27

28. Cash Flows
Initial Investment
Initial investment is the net cash outlay in the
period in which an asset is acquired. A major
element of the initial investment is original value
of the asset which comprises of its costs and
installation charges. When an asset is acquired
for expanding revenues it may require a lump
sum investment in working capital. Thus, initial
investment will equal to gross investment plus
increase in net working capital.
28

29. Cash Flows
Annual Net Cash Flows
An investment is expected to generate annual cash
flows from operations after the initial cash outlay
has been made. Cash flows should always be
estimated on an after tax basis. The net cash flows
(NCF) are simply the difference between cash
receipts and cash payment including taxes. NCF
will mostly consist of annual cash flows occurring
from the operation of an investment. But it may also
be affected by changes in net working capital and
capital expenditure during the life time of the
investment. NCF will be found out as follows:
NCF = Revenues – Expenses – Taxes .
29

30. Cash Flows
Terminal Cash Flow
Terminal Cash flows are the net cash flows that
occur at the end of the life of a project, including
the cash flows associated with : (i) the final
disposal of the project and (ii) returning the firm’s
operations to where they were before the project
was accepted. Consequently, the terminal cash
flows include the salvage value and the tax impact
of the disposition of the project. Any working capital
accounts changes that occurred at the beginning of
the project’s life will be reversed at the end of its
life.
30

31. Determination of cash flow involves three main
steps : namely i) estimating cash flow, ii)
determining incremental cash flow and iii)
determining relevant cash flow.
Estimating Cash Flow: For capital budgeting cash
flows have to be estimated. There are certain
elements of cash flow stream namely tax effect,
effect on other project, effect of indirect expenses,
effect of working capital and effect of depreciation.
Determining Incremental Cash Flow: Incremental
cash flows are those that results directly from the
decision to accept the project. These cash flows,
called incremental cash flows, represent the
31

32. Determination of Cash Flows
changes in a firm’s total cash flows that occur as a
direct result of accepting the project. Cash flows
that will change because the project is purchased
are incremental cash flows. While calculating
incremental cash flows sunk costs, opportunity
costs, externalities etc. need to be considered.
Determining Relevant Cash Flow: In case of
single proposal, relevant cash flows will be : i) cost
of new project, ii) + installation costs, iii) +- working
capital requirement.
The following format shows the determination of
cash inflows:
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33. Determination of Cash Flows
  Years
  123----N
Cash sales revenues
Less Cash Operating cost
Cash inflow before taxes (CFBT)
Less Depreciation
Taxable income
Less Tax
Earning after taxes
Plus Depreciation
Cash inflow after taxes (CFAT)
Plus salvage value (in nth year)
Plus Recovery of working capital (in nth
year)
33

34. Techniques of Capital Budgeting

Capital Budgeting
Technique
Discounting
Criteria
Non-discounting
Criteria
Net present
value (NPV)
Internal rate of
return (IRR)
Profitability
index (PI)
Payback period
(PB)
Accounting rate of
return
(ARR)
Discounted
payback period
Net Terminal
Value (NTL)
3434

35. Discounted Cash Flow (DCF)Discounted Cash Flow (DCF)
Methods for ranking investment proposals that
employ time value of money concepts.
•Discounted Cash Flow (DCF) Techniques: Is
the methods for ranking investment proposals
that employ time value of money concepts.

36. Project Evaluation under Net Present Project Evaluation under Net Present
Value Method:Value Method:
The net present value of a project is the difference
between the present value of all cash inflows and
the present value of all cash outflows.
The present value or recognize that cash inflow in
different time periods differ in value and can be
compared only when they are expressed in terms
of a common denominator, that is, present values.
It, thus, take into account the time value of money.

37. (Contd.)(Contd.)
•Net Present Value Technique
•The net present value (NPV) method is the
discounted cash flow (DCF) techniques
explicitly, recognizing the time value of money.
•So, this is a method of ranking investment
proposals using the NPV, which is equal to the
present value of future net cash flows,
discounted at the marginal cost of capital.
3737

38. •The following steps are involved in the
calculation of NPV:
•1. Find the present value of each cash flow,
including both inflows and outflows, discounted
at the project’s cost of capital.
•2. Sum these discounted cash flows; this sum is
defined as the project’s NPV.
•3. If the NPV is positive, the project should be
accepted, while if the NPV is negative, it should
be rejected.
• If two projects with positive NPVs are mutually
exclusive, the one with the higher NPV should
be chosen.
(Contd.)(Contd.)
3838

39. (Contd.)(Contd.)
The formula of the NPV can be written as follows:
0
1
03
3
2
21
)1(
)1(
.............
)1()1(1(
C
k
C
NPV
C
k
C
k
C
k
C
k
C
NPV
n
t
t
t
n
n





















or
where C
1
, C
2
, …. represent net cash inflows in year 1, 2,
…., k is the opportunity cost of capital, C
0
is the
investment and n is the expected life of the investment.
3939

40. •It should be clear that the acceptance rule using the NPV
method is to accept the investment project if its net present
value is positive (NPV > 0) and to reject it if the net present
value is negative (NPV < 0). Positive NPVs contribute to the
net wealth of the shareholders which should result in the
increased price of a firm's share. The positive net present
value will result only if the project generates cash inflows at
a rate higher than the opportunity cost of capital. A project
may be accepted if NPV =0. A zero NPV implies that project
generates cash flows at a rate just equal to the opportunity
cost of capital. Thus, the NPV acceptance rules are :
•Accept if NPV > 0
•Reject if NPV < 0
•May accept if NPV = 0
• 
Acceptance rule:Acceptance rule:
4040

41. 10-41
Decision Rule for NPV -MethodDecision Rule for NPV -Method

42. RATIONALE FOR THE NPV METHODRATIONALE FOR THE NPV METHOD
•An NPV of zero signifies that the project’s cash
flows are exactly sufficient to repay the invested
capital
•and to provide the required rate of return on that
capital.
•If a project has a positive NPV, then it is
generating more cash than is needed to service
its debt
•and to provide the required return to
shareholders, and this excess cash accrues
•solely to the firm’s stockholders.
4242

43. (Contd.)(Contd.)
•There is also a direct relationship between NPV
and EVA (economic value added)—NPV is equal
to the present value of the project’s future EVAs.
•Therefore, accepting positive NPV projects
should result in a positive EVA and a positive
•MVA (market value added, or the excess of the
firm’s market value over its book value).
• So, a reward system that compensates
managers for producing positive EVA will lead to
the use of NPV for making capital budgeting
decisions.
4343

44. The Internal Rate of Return MethodThe Internal Rate of Return Method
The internal rate of return method is an
alternative to the net present value
method. It too uses the time value of
money. Specifically, the internal rate of
return (IRR) is the rate of return that
equates the present value of future cash
flows to the investment outlay.

45. Internal Rate of Return Technique
•The internal rate of return (IRR) of a project is the
discount rate which makes its NPV equal to zero. That
is, it is the discount rate which equates the present
value of future cash flows with the initial investment. It
is the value of r in the following equation:
IRR = A +
C
X [B - A]

C - D

Where:
A = Discount Rate at Low Trial
B = Discount Rate at high Trial Rate
C = Present Value of Cash Inflow between Low Trial

Rate and Actual Rate
D = Present Value of Cash Inflows between High Trial
Rate and Low Trial rate.
4545

46. (Contd.)(Contd.)
•Acceptance Rule:
•The accept or reject rule, using the IRR method,
is to accept the project it its IRR is higher than
the opportunity cost of capital. The IRR
acceptance rules are as follows:
Situation Decision
IRR > Cost of Capital Accept the project
IRR < Cost of Capital Reject the project
IRR = Cost of Capital Indifference

4646

47. RATIONALE FOR THE IRR METHODRATIONALE FOR THE IRR METHOD
•Why is the particular discount rate that equates
a project’s cost with the present value of its
receipts (the IRR) so special? The reason is
based on this logic:
•(1) The IRR on a project is its expected rate of
return. (2) If the internal rate of return exceeds
the cost of the funds used to finance the project,
a surplus remains after paying for the capital,
and this surplus accrues to the firm’s
stockholders.
4747

48. (contd.)(contd.)
•(3) Therefore, taking on a project whose
IRR exceeds its cost of capital increases
shareholders’ wealth.
•On the other hand, if the internal rate of
return is less than the cost of capital, then
taking on the project imposes a cost on
current stockholders. It is this “breakeven”
characteristic that makes the IRR useful in
evaluating capital projects.
4848

49. Profitability Index TechniqueProfitability Index Technique
•Profitability index (PI) also known as
Benefit Costs Ratio measures the present
value of returns (cash inflows) per taka
invested. It is a relative measure which is
obtained by dividing the present value of
future cash inflows by the present of cash
out flows. Symbolically –
•PI = PV of cash inflows/PV of cash out
flows
4949

50. Profitability Index TechniqueProfitability Index Technique
5050

51. (Contd.)(Contd.)
•Acceptance Rule:
•A project will qualify for acceptance if its PI
exceeds 1, the rules are as follows:
•Accept if PI > 1,
•Reject if PI < 1, and
•May accept if PI = 1
5151

52. Discounted Payback PeriodDiscounted Payback Period
•The discounted payback period (DPP) is the length of
time until the sum of the discounted cash flows becomes
equal to the initial investment.
•So, DPP IS the length of time required for an
investment’s cash flows, discounted at the investment’s
cost of capital, to cover its cost.
•The DPP rule is as follows: An investment is acceptable
if its DPP < some pre-specified number of years. DPP
will be always higher than the PBP since the former the
considers discounted cash flows ; while the later
considers conventional cash inflows.
•If DPP lies within the project’s life the project will produce
positive NPV.
5252

53. Project Evaluation under Accounting Project Evaluation under Accounting
Rate of Return / Average Rate of ReturnRate of Return / Average Rate of Return
Return on Investment is based upon
accounting information rather than cash
flows. There are no unanimity regarding the
definition of the rate of return. There are a
number of alternative methods for
calculating the ARR.

54. Contd.Contd.
Simple rate of return is based on incremental net
income, which is the difference between
incremental revenues and incremental expenses.
• Remember that revenues are not the same
thing as cash inflows and that expense is not the
same thing as cash outflows. One big difference
is depreciation, which is an expense but not a
cash flow. The biggest problem with the simple
rate of return is that it ignores the time value of
money.

55. Contd.Contd.
The most common usages of the average
rate of return expresses is as follows:
ARR = (Average annual profits after
taxes/ Average investment over the life of
the project ) X 100
Average annual profits= Total annual
Profits/ no. of years
Average investment = Net working capital
+ salvage value + ½ of ( initial cost –
salvage value).

56. Accounting Rate of Return TechniqueAccounting Rate of Return Technique
•Accounting rate of return (ARR) refers to
average rate of return on investment. So, ARR is
found out by dividing return on investment by its
investment and multiplying the result by 100.
ARR =
Average annual profits after taxes
X 100
Average investment over the life of the project
Average investment = Net working capital + salvage value +
½ of (initial cost – salvage value).
5656

57. Contd.Contd.
Decision Rule:
The decision rule regarding Accounting
Rate of Return (ARR) is as follows:
In case of independent project ARR >
expected rate of return Accepted
In case of mutually exclusive project,
project with higher ARR Accepted
•In a Nutshell: Acceptance Rule:
•Accept if ARR > minimum rate
•Reject if ARR< minimum rate

58. Contd. (Example) Contd. (Example)
Given the information: initial investment is
Tk. 11,000; salvage value Tk. 1,000;
working capital Tk. 2,000; service life 5
years; and that the straight line method of
depreciation is adopted,
The average investment is: 1,000 + 2,000 +
½ of (11,000-1,000) = Tk. 8,000

59. Project Evaluation under Pay Back PeriodProject Evaluation under Pay Back Period
The payback period is defined as the length of
time that it takes for an investment project to get
back its initial cost out of the cash flows that it
generates.
• There are two ways of calculating the Pay Back
period.
•The first methods can be applied when the cash flow
stream is in the nature of annuity for each year of the
project’s life that is cash flow after tax is uniform. In
such a situation the initial cost of investment is divided
by the constant annual cash flow.

60. Pay Back PeriodPay Back Period
•Pay back period (PBP) refers to the number of years
required to recover the initial outlay of the investment by
the returns derive from the investment. Symbolically
PBP = Initial investment / Annual return (cash inflow).
•The second method is used when projects cash flows
are not uniform:
•The second method is used when projects cash
flows are not uniform. i.e. mixed stream but vary
from year to year. In such a situation, Pay Back
Period is calculated by the process of cumulating
cash flows till the year when cumulative cash flows
become equal to the original investment outlay.
6060

61. The formula for calculating pay back period in
this regard is as follows:
•Payback Period = Year before full recovery +
Unrecovered cost at start of year
Cash flow during year
Pay Back Period = A + NCO - C
D

62. Contd.Contd.
Where:
A = Number of year immediately preceding
the year of final recovery.
NCO = Net Cash Outlay
C = The cumulative Cash flow from the year A
D = Cash flow from the following year of the
year A

63. (Contd.)(Contd.)
Pay Back Period = A +
NCO - C
D
Where:
A = Number of year immediately preceding the year
of final recovery.
NCO = Net Cash Outlay
C = The cumulative Cash from the year A
D = Cash from the following year of the year A
6363

64. (contd.)(contd.)
•Decision Rule:
• The decision rule regarding Pay back
Period is as follows:
•SituationDecision
•PBP < Project Life Accept the project
•PBP = Project Life May Accept the project
•PBP > Project Life Reject the project
•The shorter the payback period, the better.
6464

65. (contd.)(contd.)
•Mutually Exclusive Projects
•A set of projects where only one can be
accepted.
•Independent Projects
•Projects whose cash flows are not affected
by the acceptance or non-acceptance of
other projects
6565

66. Example 1:Example 1:
An investment of Tk. 48,000 in a machine
is expected to produce cash flow of Tk.
8,000 for 10 years. Calculate the Pay Back
Period of the project.
Pay Back Period =Net Cash Outlay/ Net
Cash Benefits for each period.
= 48, 000/ 8000= 6 years

67. Example 2Example 2
Suppose a sum of Tk 10,00,000 has to be invested in a project
whose expected net cash flows after tax are as follows:
.
Year Cash Flows
1 2,00,000
2 3,00,000
3 4,00,000
4 5,00,000
5 6,00,000

68. Contd.Contd.
Calculate the pay back period of the project.
We know that formula for calculating pay back period in
case of unequal cash inflows is as follows:
Pay Back Period = A + NCO – C
D
Table for calculation of Pay Back Period
Year Cash flow after tax Cumulative cash flow after tax
1 2,00,000 2,00, 000
2 3,00,000 5,00,000
3 4,00,000 9,00,000
4 5,00,000 14,00,000
5 6,00,000 20,00,000

69. ContdContd
Now putting the values in the formula we
get,

Pay Back Period =
3+ (10,00,000 - 9,00,000)
5,00,000
= 3+0.2 = 3.2 years

70. Some Important TermsSome Important Terms
NPV ProfilesNPV Profiles
•A graphical representation of project NPVs at
various different costs of capital.
k NPV
L
NPV
S
0 $50 $40
5 33 29
10 19 20
15 7 12
20 (4) 5

71. Drawing NPV profilesDrawing NPV profiles
-10
0
10
20
30
40
50
60
5 10 15 2023.6
NPV
($)
Discount Rate (%)
IRR
L
= 18.1%
IRR
S
= 23.6%
Crossover Point = 8.7%
S
L
.
.
.
.
.
.
.
.
.
.
.

72. Finding the crossover pointFinding the crossover point
•Crossover Rate
•The cost of capital at which the NPV profiles of two
projects cross and, thus, at which the projects’ NPVs
are equal.
•To Find the Crossover Rate
1.Find cash flow differences between the projects for
each year.
2.Enter these differences in CFLO register, then press
IRR. Crossover rate = 8.68%, rounded to 8.7%.
3.Can subtract S from L or vice versa, but better to
have first CF negative.
4.If profiles don’t cross, one project dominates the
other.

73. Reasons why NPV profiles crossReasons why NPV profiles cross
•Size (scale) differences – the smaller project
frees up funds at t = 0 for investment. The
higher the opportunity cost, the more valuable
these funds, so high k favors small projects.
•Timing differences – the project with faster
payback provides more CF in early years for
reinvestment. If k is high, early CF especially
good, NPV
S
> NPV
L
.

74. Reinvestment rate assumptionsReinvestment rate assumptions
•NPV method assumes CFs are reinvested at k,
the opportunity cost of capital.
•IRR method assumes CFs are reinvested at IRR.
•Assuming CFs are reinvested at the opportunity
cost of capital is more realistic, so NPV method is
the best. NPV method should be used to choose
between mutually exclusive projects.
•Perhaps a hybrid of the IRR that assumes cost of
capital reinvestment is needed.

75. Since managers prefer the IRR to the NPV Since managers prefer the IRR to the NPV
method, is there a better IRR measure?method, is there a better IRR measure?
•Yes, Modified IRR (MIRR) is the discount
rate that causes the PV of a project’s
terminal value (TV) to equal the PV of
costs. TV is found by compounding
inflows at WACC.
•MIRR assumes cash flows are reinvested
at the WACC.

76. Modified IRR(Modified IRR(MIRR) MIRR)
•The discount rate at which the present
value of a project’s cost is equal to the
present value of its terminal value, where
the terminal value is found as the sum of
the future values of the cash inflows,
compounded at the firm’s cost of capital.

77. Some Important TermsSome Important Terms
•So,
•Modified IRR (MIRR) method corrects
some of the problems with the regular
IRR. MIRR involves finding the terminal
value (TV) of the cash inflows,
compounded at the firm’s cost of capital,
and then determining the discount rate
that forces the present value of the TV to
equal the present value of the outflows.
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78. Modified IRRModified IRR
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79. •Here COF refers to cash outflows (negative
numbers), or the cost of the project, and CIF
refers to cash inflows (positive numbers).
•Multiple IRRs
•The situation where a project has two or more
IRRs
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80. Why use MIRRWhy use MIRR
•There is a situation in which the IRR approach
may not be usable— this is when projects with
non-normal cash flows are involved.
•A project has normal cash flows if it has one or
more cash outflows (costs) followed by a series
of cash inflows.
•If, however, a project calls for a large cash
outflow sometime duringor at the end of its life,
then the project has nonnormal cash flows.

81. Why use MIRRWhy use MIRR
•Projects with non-normal cash flows can
present unique difficulties when they are
evaluated by the IRR method, with the most
common problem being the existence of
multiple IRRs.

82. Review QuestionsReview Questions
•What are the various steps followed in
capital budgeting decision?
• What are the various data used for
evaluating any capital investment project?
•Define Discounted Cash Flow Method.
Distinguish between the NPV and IRR
methods in case of long-term investment
evaluation.
•What are the Rationale for the IRR method?

83. Contd.Contd.
•What is the difference between
independent and mutually exclusive
projects?
•Why are there multiple IRRs in capital
investment projects?
•Why use MIRR versus IRR?
•When to use the MIRR instead of the IRR?

84. Example: (BUB)Example: (BUB)
•A company is considering an investment
proposal to install new milling controls. The
project will cost Tk. 50,000. The facility has a
life expectancy of 5 years and no salvage
value. The company’s tax rate is 55% and no
investment allowance is allowed. The firm
uses straight line depreciation. The estimated
cash flows before tax (CBT) from the
proposed investment proposal are as follows:
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85. Example: (BUB)Example: (BUB)
YearCFBT
(Tk.)
1
2
3
4
5
10,000
11,000
14,000
15,000
25,000
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Compute the following:
1. Payback period,
2. Average rate of return,
3. Internal rate of return,
4. Net present value at 10%
discount rate,
5. Discounted payback period
6. Profitability index at 10%
discount rate,
Comment on the results computed
as above

86. Example –(NK)Example –(NK)
•Baishakhi Ltd. is considering the purchase of a
new machine at a cost of Tk. 4,00,000. The
Machine will cost an expected years life and
the end of it’s the salvage value will be Tk.
15,000. The machine will require an additional
working capital of Tk. 1, 00,000. The
company employs straight-line method for
charging depreciation. The pre tax cash flows
are as follows:
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87. Example –(NK)Example –(NK)
• Year Cash Inflows
• 1 1,00,000
• 2 1,00,000
• 3 1,40,000
• 4 1,30,000
• 5 1,10,000
• 6 1,20,000
• 7 1,00,000
•The target return on capital of the company is 15% and
using that rate determines the NPV and Profitability
index of the machine. Assume a 50% tax rate.
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88. Starter Problem: Houston & Brigham)Starter Problem: Houston & Brigham)
•ST- 2: You are a financial analyst for
Damon Electronics Company. The director
of capital budgeting has asked you to
analyze two proposed capital investments,
Projects A and B. Each project has a cost
of $10,000, and the cost of capital for each
project is 12 percent. The projects’
expected net cash flows are as follows:
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89. Starter Problem:Starter Problem:
•YearEXPECTED NET CASH FLOWS
• PROJECT A PROJECT B
•0 ($10,000) ($10,000)
•1 6500 3500
•2 3000 3500
•3 3000 3500
•4 1000 3500
•
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90. Starter Problem:Starter Problem:
•i.Calculate each project’s payback
period, net present value (NPV), internal
rate of return (IRR), MIRR.
•ii.Which project or projects should be
accepted if they are independent?
•iii.Which project should be accepted if
they are mutually exclusive?
9090

91. Starter Problem:Starter Problem:
•11.6: Your division is considering two
investment projects, each of which requires
an up-front expenditure of $15 million. You
estimate that the investments will produce the
following net cash flows:
•YEAR PROJECT A PROJECT B
• 1 $ 5,000,000 $20,000,000
• 2 10,000,000 10,000,000
• 3 20,000,000 6,000,000
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92. Starter Problem:Starter Problem:
•What are the two projects’ net present values,
assuming the cost of capital is 10 percent? 5 percent?
15 percent?
•11.7: Northwest Utility Corporation has a cost of capital
of 11.5 percent, and it has a project
•with the following net cash flows:
•YEAR NET CASH FLOW
• 0 -$200
• 1 235
• 2 - 65
• 3 300
•What is the project’s NPV?
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93. Starter Problem:Starter Problem:
•11.8 : Edelman Engineering is considering
including two pieces of equipment, a truck
and an overhead pulley system, in this
year’s capital budget. The projects are
independent. The cash outlay for the truck
is $17,100, and that for the pulley system is
$22,430. The firm’s cost of capital is 14
percent. After-tax cash flows, including
depreciation, are as follows:
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94. Starter Problem:Starter Problem:
•YEAR TRUCK PULLEY
• 1 $5,100 $7,500
• 2 5,100 7,500
• 3 5,100 7,500
• 4 5,100 7,500
• 5 5,100 7,500
•Calculate the IRR, the NPV, and the MIRR
for each project, and indicate the correct
accept/reject decision for each.
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95. GitmenGitmen
•ST-10.1: Fitch Industries is in the process of
choosing the better of two equal-risk, mutually
exclusive capital expenditure projects—M and
N. The relevant cash flows for each project are
shown in the following table. The firm’s cost of
capital is 14%.
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96. •a. Calculate each project’s payback period.
•b. Calculate the net present value (NPV) for each
project.
•c. Calculate the internal rate of return (IRR) for each
project.
•d. Summarize the preferences dictated by each
measure you calculated, and indicate which project
you would recommend. Explain why.
•e. Draw the net present value profiles for these
projects on the same set of axes, and explain the
circumstances under which a conflict in rankings
•might exist.
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