Pike Robert, Neal Bill. Corporate finance and investment: decisions and strategy

Подождите немного. Документ загружается.

same market value as West. Lancelot is all-equity-financed with a Beta of 1.06. The overall return on the FT

All-Share Index is 25 per cent, with a standard deviation of 16 per cent.

Recently, South has been under-performing and Lancelot’s management plan to sell it and use the entire

proceeds to purchase East Ltd, an unquoted company. East is all-equity-financed and Lancelot’s financial

strategists reckon that while East is operating in broadly similar markets and industries to South, East has a

revenue sensitivity of 1.4 times that of South, and an operating gearing ratio of 1.6 compared to the current

operating gearing in South of 2.0.

Assume: no synergistic benefits from the divestment and acquisition. You may ignore taxation.

Required

(a) Calculate the asset Betas for the North, South and West divisions of Lancelot. Specify any assumptions

that you make.

(b) Calculate the asset Beta for East.

(d) What discount rate should be applied to any new investment projects in East division?

(e) Indicate the problems in obtaining a ‘tailor-made’ project discount rate such as that calculated in sec-

tion (d).

Note: More questions on required rates of return can be found in Chapter 19, where the additional complexi-

ties of gearing are discussed.

Chapter 11 The required rate of return on investment and Shareholder Value Analysis 295

CFAI_C11.QXD 10/26/05 11:38 AM Page 295

Identifying and valuing options

Learning objectives

By the end of this chapter, you should possess a clear understanding of the following:

■ The basic types of option and how they are employed.

■ The main factors determining option values.

■ How options can be used to reduce risk.

■ How option values can be estimated.

■ The various applications of option theory to investment and corporate finance.

■ Why conventional net present value analysis is not sufficient for appraising projects.

The marriage (option) contract

‘Wilt thou have this woman to be thy lawful wedded

wife?’ As the minister posed this question, the groom,

a highly trained financial analyst, reflected that mar-

riage bore many characteristics of the investment

decisions he faced every day. It was clearly a long-

term commitment, involving uncertain costs and

benefits. What is more, it was largely irreversible; and

the abandonment option of divorce was too costly

and painful to contemplate. The follow-on option was

interesting. How many kids had she mentioned?

But what about the options he would be sacrific-

ing? The option to remain an independent bachelor,

or the option to wait another six months to be better

informed as to whether the couple were really right

for each other. Just how valuable was the marriage

option contract, and was now the right expiry date?

After a moment’s hesitation, the groom turned

and looked into his bride’s adoring eyes. All thoughts

of rational economic analysis and option theory

evaporated as he found himself saying, ‘I will’.

*The authors are grateful for the contribution to this chapter by Andrew Marshall.

CFAI_C12.QXD 3/15/07 7:21 AM Page 296

Chapter 12 Identifying and valuing options 297

12.1 INTRODUCTION

Business managers like to ‘keep their options open’. Options convey the right, but not

the obligation, to do something in the future. Like getting married, most business deci-

sions involve closing off certain options while opening up others. Managers should

seek to create capital projects or financial instruments with valuable options embedded

in them. For example, an investment proposal will be worth more if it contains the flex-

ibility to exit relatively cheaply should things go wrong. This is because the ‘downside’

risk is minimised. Often it is not possible, or too costly, to build in such options.

However, the financial manager can achieve much the same effect by creating options

in financial markets.

Options are derivative assets. A ‘derivative’ is an asset which derives its value from

another asset. The primary asset is referred to as the ‘underlying’ asset. Option-like fea-

tures occur in various aspects of finance, and option theory provides a powerful tool

for understanding the value of such options.

This chapter concludes Part III of this book, on handling risk in investment deci-

sions, by examining the nature and types of options available and how they can reduce

risk or add value. It also explains why the conventional net present value approach

may not tell the whole story in appraising capital projects.

’underlying’ asset

The asset from which option

value is derived

12.2 SHARE OPTIONS

In finance, options are contractual arrangements giving the owner the right, but not the obli-

gation, to buy or sell something, at a given price, at some time in the future. Note the two key

elements in options: (1) the right to choose whether or not to take up the option, and

(2) at an agreed price. It is not a true option if I am free to buy in the future at the pre-

vailing market price, or if I am compelled to buy at an agreed price. Many securities have

option features: for example, convertible bonds and share warrants, where options to

convert to, or acquire, equity are given to the owner.

■ Share options in Enigma Drugs plc

The simplest form of share option is when a company issues them as a way of reward-

ing employees. If the current share price of Enigma Drugs plc is it might award

share options to some of its employees at, say, the same price. If, over the period in

which the shares can be exercised, the shares go up, employees could then purchase

shares at a price below market price either to sell at a profit or gain an equity interest.

Most options relate to assets which already exist. These are termed pure options. To

begin with, we will consider pure share options, although much of our analysis could

apply equally to interest rates, currency, oil and commodity markets. But first we need

to go back to basics. Figure 12.1(a) depicts the payoff line for investing in ordinary

shares in Enigma Drugs plc. If the shares are bought today at 400p, the payoff, or gain,

from selling at the same price is zero. If, say, three months later, the share price has

risen to 450p, the payoff is but if it has dropped to 350p, the payoff is The

line is drawn at 45 degrees because a 50p increase in share price from its current level

of 400p gives a 50p payoff.

We have all seen the warnings accompanying advertisements for financial prod-

ucts, reminding us that share prices can go up or down. But wouldn’t it be nice if,

whichever way prices moved, you ended up a winner? This can be done if you also

acquire share options. With options you can create a ‘no lose’ option strategy provid-

ing protection from a drop in share price, as shown in Figure 12.1(b). The arrowed line

represents the payoff from the option to buy shares. If share price increases, so does

50p.50p;

£4,

CFAI_C12.QXD 3/15/07 7:21 AM Page 297

298 Part III Investment risk and return

350 400 450

(a)

Share price

movements over

time

. The underlying share price

can move up or down

(b)

Option to buy shares

. By

entering into an option contract,

any downward risk below current

price can be protected

(c)

Option to buy and sell

. With this option strategy

the payoff is positive whichever

way the share price moves

Share price

(pence)

Payoff (pence)

+ 50

− 50

350 400 450

Payoff (pence)

+50

350 400 450 Share price

(pence)

Share price

(pence)

Payoff (pence)

+ 50

−

Figure 12.1

Payoff lines for shares

and share options in

Enigma Drugs plc

(underlying share price

is blue, option contract

is red)

the option payoff. But if the share price falls below 400p, to say 350p, the option pay-

off remains at zero.

By combining different types of option you can even create a ‘win–win’ situation.

For example, Figure 12.1(c) shows the effects of combining options to buy and sell

shares at a fixed price. Here, either a rise or a fall in share price gives you a positive

payoff. At this stage, however, you do not need to know how this is achieved, simply

that it can be done. Of course, few things in life are free and a share option is not one

of them (unless they form part of a remuneration package). Later we will show how

to value such options.

■ Issuing options

Options on shares are not issued by the companies on whose shares they are written

but by large financial institutions, such as insurance companies. The companies play no

role in the issuing process. For the institutions issuing options the primary motivation

is the fee income that their sale generates, but some also use options in their portfolio

of management activities to limit their risk exposure.

CFAI_C12.QXD 3/15/07 7:21 AM Page 298

Chapter 12 Identifying and valuing options 299

There are two parties to an option contract, the buyer (or option holder) and seller (or

option writer). The buyer has the right, but not the obligation, to exercise the option.

One feature of an option is that, if the share price does not move as expected, it can

become completely worthless, regardless of the solvency of the company to which it

relates. However, if it does move in line with expectations, very considerable gains can

be achieved for very little outlay. Such volatility gives share options a reputation as a

highly speculative investment. But, as will be seen later, options can also be used to

reduce risk.

In return for the option, the purchaser pays a fee or premium. The premium is a

small fraction of the share price, and offers holders the opportunity to gain significant

benefits while limiting their risk to a known amount. The size of the premium depends

on the exercise price and expected volatility of shares, which, in turn, is a function of

the state of the market and the underlying risk of the share. The premium might range

from as little as 3 per cent for a well-known share in a ‘quiet’ market to over 20 per cent

for shares of smaller companies in a more volatile market. During past stock market

collapses, or where there is substantial volatility, option premiums have shot up dra-

matically to reflect such uncertainty.

Considerable interest has developed in recent years in share options, and there is a

highly active market on the Stock Exchange for traditional and traded options.

Traditional options are available on most leading shares and last for three months. A

problem with these is that they are not particularly flexible or negotiable: investors

must either exercise their option (i.e. buy or sell the underlying share) or allow it to

lapse; they cannot trade their option.

To overcome these difficulties, Traded options markets were established, first in

Chicago, then in Amsterdam (the European Options Exchange). In 1978 the London

Traded Options Market was established for major companies, now part of the London

International Financial Futures and Options Exchange (LIFFE) (see www.liffe.com).

An exchange traded contract is characterised by certain standardised features, par-

ticularly the exercise date and the exercise price. This makes it far easier to develop a

continuous market in options than was the case for traditional options that were

developed and traded on an ad hoc basis.

traditional options

An option available on any

security agreed between buyer

and seller. It typically lasts for

three months

traded options

An option traded on a market

option contract

A contract giving one party

the right, but not the obliga-

tion, to buy or sell a financial

instrument or commodity at

an agreed price at or before a

specified date

exercise price

Price at which an option can

be taken up

Options terminology

This topic has more than its fair share of esoteric jargon, some of the more essential of which

are defined below.

■ A call option gives its owner the right to buy specific shares at a fixed price – the exercise

price or strike price.

■ A put option gives its owner the right to sell (put up for sale) shares at a fixed price.

■ A European option can be exercised only on a particular day (i.e. the end of its life), while

an American option may be exercised at any time up to the date of expiry. These terms are

a little confusing because most options traded in the UK and the rest of Europe are actually

American options!

■ The premium is the price paid for the option. Option prices are quoted for shares and trad-

ed in contracts (or units) each containing 1,000 shares.

■ In the money is where the exercise price for a call option is below the current share price.

In other words, it makes sense to take up the option.

■ Out of the money is where the exercise price for a call option is above the current share

price and it is not profitable to take up the option.

CFAI_C12.QXD 3/15/07 7:21 AM Page 299

300 Part III Investment risk and return

A call option gives the purchaser the right to buy a share at a given price within a

set period, usually three months; a put option gives the right to sell. Payment for the

option is not immediate, but takes place when the option is exercised (i.e. taken up) or

on expiry, if it is not exercised. The seller of an option must meet his or her obligation

to buy or sell shares if the right of the purchaser is so exercised. The reward is, of

course, the premium received.

Table 12.1 shows the prices (or premiums) at which options on BP are traded on a

particular day on the traded options market of the Stock Exchange. The options are

traded over a nine-month period with expiry dates every three months. Two exercise

prices are given; the first, at 390p, is below the current share price of 397p (‘in the

money’) and the second, at 420p, is above the current price (‘out of the money’). Notice

that option prices vary both with the agreed exercise price (the lower the exercise price

for a call option, the higher the premium) and the exercise date (the longer the period,

the higher the premium). To buy a call option on BP shares, at an exercise price of 390p,

costs 17p for expiry in April, but for expiry six months later in October.31



put option

The right to sell an asset at a

specified price on or before

expiry date

Table 12.1

Option on BP shares

(current price 397p)

Call option prices (p) Put option prices (p)

Exercise price April July Oct April July Oct

390 17 12 17

420 12 28 33



call option

The right to buy an asset at a

specified price on or before

expiry date

■ Speculative use of options: Kate Casino

Kate Casino thinks that oil prices will rise in the coming months and that the share

price will move up sharply from its current level of 397p to a level in April suffi-

ciently above the exercise price of 390p to justify the option price of 17p. Kate

instructs her broker to purchase a contract for 1,000 April call options at a cost of

This is termed a naked option, held on its own rather than as a

hedge against loss.

The current share price of 397p is above the 390p exercise price, so the option is

already ‘in the money’, since Kate could immediately exercise her option to buy shares

at 390p to gain 7p, before transaction costs. Of course, she would not do this because

the premium to be paid for the option is 17p.

117p  1,0002  £170.

Self-assessment activity 12.1

By now your head may be spinning with all the terms and concepts introduced. It is there-

fore a good time to take stock of what you should know.

1 Define a call option and a put option.

2 What is the basic difference between European and American call options?

3 Options are available on what types of asset?

4 In relation to the information on traded options in Table 12.1 explain why the following

features were observed:

(a) the lower the exercise price, the higher the value of a call;

(b) the greater the time to maturity, the higher the price of a call; and

exercising the call.

(Answer in Appendix A at the back of the book)

exercise date

Final date on which an option

is exercised or expires

CFAI_C12.QXD 3/15/07 7:21 AM Page 300

Chapter 12 Identifying and valuing options 301

Kate would obviously not exercise her option if the price fell to 380p, so the loss in

this case would be restricted to the 17p premium paid. The premium is the maximum

loss on the contract. If BP’s price on expiry is 415p, the contract profit is a modest

But if the share price shoots up to 460p, a large gain of is made on the contract.

It is interesting to compare the option returns with those from investing directly in

BP shares. Table 12.2 shows that buying a call option has very different effects from

buying the underlying share:

1 The capital outlay for the option contract for 1000 shares is much smaller ( com-

pared with for the underlying shares).

2 The downside risk on the option contract is far greater in relative terms, but not in

absolute terms. Kate Casino loses all her initial investment on the option contract

while the share value declines by only 4 per cent. However, in money terms, the loss

is the same for both, Of course, the shareholder does not have to sell at the

option expiry date.

3 The return achieved, if the shares reach 460p, is a phenomenal 312 per cent on the

options contract compared with 16 per cent on the underlying shares (ignoring

dividends).

Figure 12.2 shows that, if the share price does not rise above the exercise price of

390p, the option is worthless. The option breaks even at 407p

and the potential profit to be made thereafter is unlimited.

1390p  17p premium2

£170.

£3,970

£170

£530

£80.

Table 12.2

Returns on BP shares

and options

Expiry share price 460p 380p

Buy 1,000 shares ££

Cost 397p each (3,970) (3,970)

Proceeds from sale 4,600 3,800

Profit (loss) 630 (170)

Return over 3 months on original cost

Call option on 1,000 shares ££

Cost of option (170) (170)

Cost of exercise at 390p (3,900) –

(4,070)

Proceeds on sale 4,600 –

Profit (loss) 530 (170)

Return over 3 months

100%312%

4.3%15.9%

Kate Casino’s profit on the call option (pence)

Best Likely Worst

Share price in April 460 415 380

Exercise price 390 390 390

Profit on exercise 70 25 Not exercised

Option premium paid (17) (17) (17)

Profit (loss) before transaction costs 53 8 (17)

Profit on contract of 1,000 shares £530 £80 (£170)

Let us look at three possible share prices arising in April when the option ends:

Best – if the takeover attempt is made, BP’s share price will rise to 460p by April.

Likely – it will do no better than 415p.

Worst – it falls as low as 380p.

Her profit in each case would be:

CFAI_C12.QXD 3/15/07 7:21 AM Page 301

302 Part III Investment risk and return

380

390

400 410 420 430 440 450 460

Share price (p)

Potential profit

Loss

53p

17p

Exercise

price 390p

Profit of 53p

when share

price is 460p

Break-even

price 407p

Figure 12.2

BP call option

In general, the value of a call option at expiry with a share price and exer-

cise price (E) is:

At a share price of 460p, therefore, the option value is

■ Options as a hedge: Rick Aversion

While options offer an excellent opportunity to speculate, they are equally useful as a

means of risk reduction, insurance or hedging. Rick Aversion is concerned that the cur-

rent share price on his BP shareholding will fall over the next two months. Because he

wants to keep his shares as a long-term investment, he buys a put option (see Table 12.1),

giving the right to sell shares in April at the strike price of 390p. This option costs

him

By late April, the shares have fallen to 350p, and the option has increased in value

to 40p (i.e. ). So Rick sells the option and retains the shares, using the profit

on the option to offset the loss on the shares. This is administratively cheaper and more

convenient than selling his shares and then buying them back. In this way, investors

can capture any profits from a rise in share price and hedge against any price fall.

Figure 12.3 shows that when share prices are above the exercise price, the option

value of the put is worthless. It should be exercised when prices fall below the 390p

exercise price and breaks even at (exercise price less premium).

In general, the value of a put option is:

At a 370p share price, the value of the put option is therefore 20p:

This is because the holder could buy the shares in the market at 370p and exercise

the option to sell at 390p. The profit on this transaction is 120p  6



p2  13



 20p

 390p  370p

 E  S

, if S

6 E

383



390  350



 70p, giving a profit of 53p per share after paying the premium.

 460p  390p

 S

 E, if S

7 E

21C

CFAI_C12.QXD 3/15/07 7:21 AM Page 302

Chapter 12 Identifying and valuing options 303

■

Option strategies

Combinations of investments in options and the underlying shares are both of practi-

cal and analytical interest. From a practical standpoint a combination can provide a

means of reducing exposure to the risks associated with substantial changes in the price

of the underlying asset, or, from a speculative perspective, can provide some interest-

ing payoff patterns. The analytical interest stems from the insights provided by such

portfolios for the valuation of options.

Straddles or doubles

Combining investments in a put and a call, written on a share at the same exercise

price and expiry date, produces what is referred to as a straddle (long straddle is

where you buy both the call and put option and the opposite is true: a short straddle

is where you sell both the call and put option). Why should anyone wish to invest in

calls and puts simultaneously (short straddle)? This strategy will be employed by an

investor who believes that the price of the underlying share is going to change quite

significantly, but is unable to predict the direction of the change. Such an expectation

will arise, for example, whenever an investor knows that a company is expected to

make an important announcement, but has no knowledge of the content of the

announcement.

This is a strategy to adopt whenever there is considerable short-term uncertainty

about the price of a share, and it is anticipated that this uncertainty will be resolved

before the expiry of the options. A straddle will lose an investor money if there is little

change in the share price, but large price changes in either direction will produce gains.

Protective put

A protective put protects investment in the underlying asset by restricting the possi-

ble losses on the asset. Suppose an investor holds shares in British Airways. She may

buy put options to help protect the value of her investment. The put options guaran-

tee a minimum value for the shares up to the expiration date of the options. Whatever

happens the shares can be sold at the option exercise price.

For example: buy British Airways shares at 579p

Protect the investment with April out of the money puts

Exercise Premium

No matter how far the share price falls the investor can sell for 550p up to the expiration

date. This is portfolio insurance, and the cost of the insurance is the put premium of 33p.

cost  33pprice  550p

350 360 370 380 390 400

Gain

Exercise

price

Break-even price

383

6 p premium

Share price (p)

383

Loss

Figure 12.3

BP put option

CFAI_C12.QXD 3/15/07 7:21 AM Page 303

304 Part III Investment risk and return

Alternatively, the investor might choose to protect the investment with in the money

puts, e.g. April 600. Obviously this guarantees a higher minimum selling price up to

expiration, but the premium cost is higher.

Covered call

The writing of calls is a risky business. One way of limiting the risk exposure is to buy

the share on which the call is being written. When an investor simultaneously writes a

call and purchases the underlying asset the resulting combination is known as a covered

call. The returns on the written call and the share are negatively correlated as the liabil-

ity implicit in the written call increases with rises in the value of the share. Covered calls

may appeal to risk-averse investors who are mildly pessimistic about the future price

performance of a share. The fee income from writing calls is attractive and holding the

share implies the risk from an unanticipated rise in the share price is neutralised.

(Covered calls are of no interest to really pessimistic investors. They will not wish to pur-

chase the share even if the writing of calls is attractive, and if they already hold the share

they will consider its sale or the purchase of puts rather than the writing of calls.)

Covered calls are the combination most frequently employed by financial institu-

tions that regularly write calls. Let us recap on the value of the two main forms of

option, the call and put.

Consider the implications of buying a call option and selling a put option, where

the exercise price is the same for both.

12.3 OPTION PRICING

Option Share price at expiry date Option value at expiry

Call above exercise price

below exercise price zero

Put above exercise price zero

below exercise price exercise price  share price

share price  exercise price

We can now focus on what determines the value of options. Option prices comprise

two elements: intrinsic value and time-value. Intrinsic value is what the option would

be worth were it about to expire; it reflects the degree to which an option is ‘in the

money’ – in the case of a call option, the extent to which the exercise price is below the

current share price. The time-value element depends on the length of time the option has

to run – the longer the period, the better the chance of making a gain on the contract.

■ Put–call parity

We showed in the previous section how the combination of buying a call option and

selling a put option gave the same payoff as the underlying share price. To find a com-

bination that yields a riskless return, we reverse the options.

When a call and a put are written on the same asset with the same exercise price and

expiry date a relationship, referred to as the put–call parity, can be expected to hold

between their market values.

Put-call parity

Value of share + Value of put - Value of call = Present value of exercise price

S + P - C = E/(1 + R

)

It follows from the above that, given four of the five factors, the fifth can be estimated.

CFAI_C12.QXD 3/15/07 7:21 AM Page 304