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Guided Tour
Understanding and Application
The best way to understand corporate finance is to
explain it via situations and scenarios you can relate
to.
• Example boxes in every chapter to provide
hypothetical examples to illustrate theoretical
concepts.
• Opening chapter vignettes illustrate topical
discussions that will be covered in the chapter.
• Real World Insight boxes use real companies
to show how they have applied corporate
finance theories and concepts to their
businesses and business decisions.
• Practical case studies, mini cases and
additional reading further aid your
understanding of concepts and to practise
applying them.
Mastery of Mathematics
Many find the hardest part of learning finance
is mastering the jargon, maths, data and
standardized notation. Corporate Finance helps
you by:
• Making extensive use of figures and
tables that use real data throughout the
text
• Listing in key notation boxes at the start
of the chapter the variables and acronyms
you will encounter as you read the chapter.
• Numbering maths equations the first time
they appear in full, for ease of reference
and understanding.
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KEY NOTATIONS
# Number of shares
outstanding
#
W
Number of warrants
c
w
Value of a call option
written on the equity of a
firm without warrants
S Current share price
E Exercise price of option
R Annual risk-free rate
of return, continuously
compounded
σ
2
Variance (per year) of the
continuous share price
return
t Time (in years) to
expiration date
N(d) Probability that a
standardized, normally
distributed, random
variable will be less than
or equal to d
d
1
= [ln(S/E ) + (R + σ
2
/2)t]/ √
___
σ
2
t
d
2
= d
1
−
___
σ
2
t
CHAPTER
24
In the last few years, there has been a major paradigm shift in the way in which corporate finance is practised.
We have come through a sustained period of deregulation and globalization in the world’s markets.
Financial innovation and the introduction of new securities have been commonplace as a result of the free
markets that have spread throughout the world. However, things are very much different going into the second
decade of the twenty-first century.
The financial world has seen a glut of corporate insolvencies. Governments of the major developed
economies have all reduced interest rates to near zero and pumped cash into their ailing firms. Whole industries
have effectively been nationalized and purchased by governments. Corporate strategies that were successful
because of the availability of cheap debt are no longer possible.
Finally, financial instruments that may have been viable and
popular in a vibrant economy have become obsolete.
Conver tible bonds are par t of many companies’ capital
structure. They allow bondholders to conver t the debt instruments
into equity during a specified window in the future. The conversion
feature is an embedded option that holders will exercise if the
conver tible is in the money. At the turn of the century, these
became exceptionally popular investment targets of hedge funds
that looked for a quick return from conversion and although we
have seen much market volatility in recent times, conver tible
bonds are more popular than ever.
Warrants and
Convertibles
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More about the Binomial Model
new terms, u and d. We define u as 1 + 0.37 = 1.37 and d as 1 − 0.27 = 0.73.
2
Using the methodology of the previous
chapter, we value the contract in the following two steps.
Step 1: Determining the Risk-Neutral Probabilities
We determine the probability of a price rise such that the expected return on oil exactly equals the risk-free rate.
Assuming an 8 per cent annual interest rate, which implies a 2 per cent rate over the next 3 months, we can solve
for the probability of a rise as follows:
3
2 % = Probability of rise × 0.37 + ( 1 − Probability of rise ) × ( −0.27 )
Solving this equation, we find that the probability of a rise is approximately 45 per cent, implying that the
probability of a fall is 55 per cent. In other words, if the probability of a price rise is 45 per cent, the expected return
on heating oil is 2 per cent. In accordance with what we said in the previous chapter, these are the probabilities that
are consistent with a world of risk neutrality. That is, under risk neutrality, the expected return on any asset would
equal the riskless rate of interest. No one would demand an expected return above this riskless rate, because risk-
neutral individuals do not need to be compensated for bearing risk.
Step 2: Valuing the Contract
If the price of oil rises to €2.74 on 1 December, CECO will want to buy oil from Mr Meyer at €2.10 per litre.
Mr Meyer will lose €0.64 per litre because he buys oil in the open market at €2.74 per litre, only to resell it to
CECO at €2.10 per litre. This loss of €0.64 is shown in parentheses in Figure 23.2. Conversely, if the market price of
heating oil falls to €1.46 per litre, CECO will not buy any oil from Mr Meyer. That is, CECO would not want to pay
€2.10 per litre to him when the utility could buy heating oil in the open market at €1.46 per litre. Thus, we can say
that Mr Meyer neither gains nor loses if the price drops to €1.46. The gain or loss of zero is placed in parentheses
under the price of €1.46 in Figure 23.2. In addition, as mentioned earlier, Mr Meyer receives €1,000,000 up front.
Given these numbers, the value of the contract to Mr Meyer can be calculated as:
[0.45 × (€2.10 - €2.74) × 6 million + 0.55 × 0]/1.02 + €1,000,000,000 =-€694,118
Value of the call option
(23.1)
As in the previous chapter, we are valuing an option using risk-neutral pricing. The cash flows of –€0.64
(= €2.10 − €2.74) and €0 per litre are multiplied by their risk-neutral probabilities. The entire first term in Equation 23.1
is then discounted at €1.02 because the cash flows in that term occur on 1 December. The €1,000,000 is not
discounted because Mr Meyer receives it today, 1 September. Because the present value of the contract is negative,
Mr Meyer would be wise to reject the contract.
As stated before, the distributor has sold a call option to CECO. The first term in the preceding equation, which
equals –€1,694,118, can be viewed as the value of this call option. It is a negative number because the equation
looks at the option from Mr Meyer’s point of view. Therefore, the value of the call option would be +€1,694,118 to
CECO. On a per-litre basis, the value of the option to CECO is:
[ 0.45 ( €2.74 − €2.10 ) + 0.55 × 0 ] /1.02 = €0.282 (23.2)
Equation 23.2 shows that CECO will gain €0.64 (= €2.74 − €2.10) per litre in the up state because CECO can buy
heating oil wor th €2.74 for only €2.10 under the contract. By contrast, the contract is wor th nothing to CECO in the
down state because the utility will not pay €2.10 for oil selling for only €1.46 in the open market. Using risk-neutral
pricing, the formula tells us that the value of the call option on one litre of heating oil is €0.282.
Three-date Example
Although the preceding example captures a number of aspects of the real world, it has one deficiency. It assumes
that the price of heating oil can take on only two values on 1 December. This is clearly not plausible: oil can take
on essentially any value in reality. Although this deficiency seems glaring at first glance, it is easily correctable.
All we have to do is to introduce more intervals over the 3-month period of our example.
For example, consider Figure 23.3, which shows the price movement of heating oil over two intervals of
1½ months each.
4
As shown in the figure, the price will be either €2.50 or €1.60 on 15 October. We refer to €2.50 as
the price in the up state and €1.60 as the price in the down state. Thus, heating oil has returns of 25 per cent
(= €2.50/€2.00) and –20 per cent (= €1.60/€2) in the two states.
We assume the same variability as we move forward from 15 October to 1 December. That is, given a price
of €2.50 on 15 October, the price on 1 December will be either €3.12 (= €2.50 × 1.25) or €2 (= €2.50 × 0.80).
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Chapter 15 Equity Financing
1 ‘In a public share issue, the probability of receiving an allocation of an underpriced security is less than
or equal to the probability of receiving an allocation of an overpriced issue.’ Discuss this statement in the
context of initial public offerings. (25 marks)
Ai Due Fanali SA has decided to undertake a rights issue that will raise €288 million. The current share price is
€4.50 and there are 160 million shares in circulation. They have to make a decision on whether to underwrite
the rights issue. The underwriting fee will be 2 per cent of proceeds if the shares are offered at a 20 per
cent discount. Ai Due Fanali’s finance director believes that a discount of 40 per cent will avoid the need for
underwriting altogether.
2 Set out the terms of the issue under each of the two alternatives referred to above. Calculate the theoretical
ex-rights price and the value of a right. (25 marks)
3 Demonstrate that, in principle, a wealth-maximizing shareholder owning six shares will be indifferent
between the two alternative methods of raising the funds. (25 marks)
4 Discuss the benefits of using an underwriter in a rights issue. Review the factors that determine an
underwriter’s fee. (25 marks)
Exam Question (45 minutes)
West Coast Yachts Goes Public
Larissa Warren and Dan Ervin have been discussing the future of West Coast Yachts. The company has been
experiencing fast growth, and the future looks like clear sailing. However, the fast growth means that the
company’s growth can no longer be funded by internal sources, so Larissa and Dan have decided the time
is right to take the company public. To this end, they have entered into discussions with the bank of Crowe
& Mallard. The company has a working relationship with Robin Perry, the underwriter who assisted with
the company’s previous bond offering. Crowe & Mallard have helped numerous small companies in the IPO
process, so Larissa and Dan feel confident with this choice.
Robin begins by telling Larissa and Dan about the process. Although Crowe & Mallard charged an
underwriter fee of 4 per cent on the bond offering, the underwriter fee is 7 per cent on all initial equity
offerings of the size of West Coast Yachts’ initial offering. Robin tells Larissa and Dan that the company can
expect to pay about £1,200,000 in legal fees and expenses, £12,000 in registration fees, and £15,000 in other
filing fees. Additionally, to be listed on the London Stock Exchange, the company must pay £100,000. There
are also transfer agent fees of £6,500 and engraving expenses of £450,000. The company should also expect
to pay £75,000 for other expenses associated with the IPO.
Finally, Robin tells Larissa and Dan that, to file with the London Stock Exchange, the company must
provide three years’ worth of audited financial statements. She is unsure of the costs of the audit. Dan
tells Robin that the company provides audited financial statements as part of its bond indenture, and the
company pays £300,000 per year for the outside auditor.
1 At the end of the discussion Dan asks Robin about the Dutch auction IPO process. What are the
differences in the expenses to West Coast Yachts if it uses a Dutch auction IPO versus a traditional IPO?
Should the company go public with a Dutch auction or use a traditional underwritten offering?
2 During the discussion of the potential IPO and West Coast Yachts’ future, Dan states that he feels the
company should raise £50 million. However, Larissa points out that, if the company needs more cash
soon, a secondary offering close to the IPO would be potentially problematic. Instead she suggests that
the company should raise £80 million in the IPO. How can we calculate the optimal size of the IPO?
What are the advantages and disadvantage of increasing the size of the IPO to £80 million?
3 After deliberation, Larissa and Dan have decided that the company should use a firm commitment
offering with Crowe & Mallard as the lead underwriter. The IPO will be for £60 million. Ignoring
underpricing, how much will the IPO cost the company as a percentage of the funds received?
Mini Case
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Chapter 15 Equity Financing
5 Third-round financing: Financing for a company that is at least breaking even and is contemplating an
expansion. This is also known as mezzanine financing.
6 Fourth-round financing: Money provided for firms that are likely to go public within half a year. This round is
also known as bridge financing.
Although these categories may seem vague to the reader, we have found that the terms are well accepted within the
industry. For example, the venture capital firms listed in Pratt’s Guide to Venture Capital indicate which of these
stages they are interested in financing. Figure 15.2 also presents a breakdown of where private equity funding was
made in Europe in 2017. The use of venture capital varied considerably across countries and, whereas in the UK
and Ireland it was used to fund new growth, in continental Europe it was more associated with start-up funding.
The penultimate stage in venture capital finance is the initial public offering.
12
Venture capitalists are important
participants in initial public offerings. Venture capitalists rarely sell all of the shares they own at the time of the
initial public offering. Instead they usually sell out in subsequent public offerings.
Real World Insight 15.1
What do Business Angels look for in an Investment?
(Excerpts taken from ‘How to Find and Pitch your Business to an Angel Investor’ from growthbusiness.co.uk)
Jenny Tooth, CEO of the UK Business Angels Association, explains what angel investors look for if they
are thinking of investing in your growth business.
Where do I find an angel investor?
The best way to approach an angel investor is often through a warm introduction – one from a friend,
contact, company or entrepreneur. Investors get a lot of inbound pitches, so it’s hard to qualify what’s a cold
lead or not. There is a lack of infrastructure, which means that neither angels nor entrepreneurs are visible
to one another.
What do angel investors want to know?
We want to know the challenge that you’re addressing in the market or society, whether you have done your
market research to show why your project meets a real need and can bring something new or disruptive to
the market. We also want to know how you plan to make money and that your business model can be scaled.
We will ask if you have tested it out on any potential customers – not necessarily having sold anything, but
you have to prove interest and whether you have checked out your competitors. International scalability
is growing ever more important, so to be able to think about how you would like your business to fit on an
international stage is always a huge bonus.
How much can a UK angel investor invest?
While business angels can invest on their own, more frequently angels invest alongside other angel investors
through syndication. This enables you to pool your funds and share the risks, as well as share the due
diligence and experience of other investors. The average individual angel investment is around £25,000, with
syndicates providing – on average – around £190,000. How much an angel investor invests depends on the
individual needs of both the business and the investor. Larger SMEs expanding internationally may require
more funding than a small business looking to grow nationally. This is one of the ways in which angel
investors can tailor their support in ways that may be unavailable from traditional bank lenders. It also
benefits the investor with an increased flexibility to the amount invested, especially as part of a syndicate.
How long do angel investors stay on as investors?
Angel investing is generally regarded as ‘patient capital’ and you may not see an exit or a return for up to
8–10 years. Entrepreneurs often rely on the guidance of people who have experience in running and building
a business. This guidance is of just as much importance as investment and funding. How long angels remain
part of the business again varies on a case-by-case basis, depending on the amount of guidance needed in
the life of the business. It is often beneficial to the business to retain the expertise and experience of angels,
and what is good for the business is by extension good for the investors themselves.