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**preview**shows pages 1-3. to view the full**14 pages of the document.**CHAPTER 25

OPTIONS AND CORPORATE SECURITIES

Learning Objectives

LO1 The basics of call and put options and how to calculate their payoffs and profits.

LO2 The factors that affect option values and how to price call and put options using

no arbitrage conditions.

LO3 How to value a firm’s equity as an option on the firm’s assets and use of option

valuation to evaluate capital budgeting projects.

LO4 The basics of employee stock options and their benefits and disadvantages.

LO5 The basics of convertible bonds and warrants and how to value them.

Answers to Concepts Review and Critical Thinking Questions

1. (LO1) A call option confers the right, without the obligation, to buy an asset at a given price on or before a

given date. A put option confers the right, without the obligation, to sell an asset at a given price on or before a

given date. You would buy a call option if you expect the price of the asset to increase. You would buy a put

option if you expect the price of the asset to decrease. A call option has unlimited potential profit, while a put

option has limited potential profit; the underlying asset’s price cannot be less than zer .

2. (LO1)

a. The buyer of a call option pays money for the right to buy....

b. The buyer of a put option pays money for the right to sell....

c. The seller of a call option receives money for the obligation to sell....

d. The seller of a put option receives money for the obligation to buy....

3. (LO1) The intrinsic value of a call option is Max [S – E,0]. It is the value of the option at expiration.

4. (LO1) The value of a put option at expiration is Max[E – S,0]. By definition, the intrinsic value of an option is

its value at expiration, so Max[E – S,0] is the intrinsic value of a put option.

5. (LO2) The call is selling for less than its intrinsic value; an arbitrage opportunity exists. Buy the call for $10,

exercise the call by paying $35 in return for a share of stock, and sell the stock for $50. You’ve made a riskless

$5 profit.

6. (LO2) The prices of both the call and the put option should increase. The higher level of downside risk still

results in an option price of zero, but the upside potential is greater since there is a higher probability that the

asset will finish in the money.

7. (LO2) False. The value of a call option depends on the total variance of the underlying asset, not just the

systematic variance.

8. (LO1) The call option will sell for more since it provides an unlimited profit opportunity, while the potential

profit from the put is limited (the stock price cannot fall below zero).

9. (LO2) The value of a call option will increase, and the value of a put option will decrease.

10. (LO1) The reason they don’t show up is that the government uses cash accounting; i.e., only actual cash

inflows and outflows are counted, not contingent cash flows. From a political perspective, they would make

the deficit larger, so that is another reason not to count them! Whether they should be included depends on

whether we feel cash accounting is appropriate or not, but these contingent liabilities should be measured and

reported. They currently are not, at least not in a systematic fashion.

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Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to

space and readability constraints, when these intermediate steps are included in this solutions manual, rounding

may appear to have occurred. However, the final answer for each problem is found without rounding during any

step in the problem.

Basic

1. (LO2)

a. The value of the call is the stock price minus the present value of the exercise price, so:

C0 = $55 – [$45/1.055] = $12.35

The intrinsic value is the amount by which the stock price exceeds the exercise price of the call, so the

intrinsic value is $10.

b. The value of the call is the stock price minus the present value of the exercise price, so:

C0 = $55 – [$35/1.055] = $21.82

The intrinsic value is the amount by which the stock price exceeds the exercise price of the call, so the

intrinsic value is $20.

c. The value of the put option is $0 since there is no possibility that the put will finish in the money. The

intrinsic value is also $0.

2. (LO1)

a. The calls are in the money. The intrinsic value of the calls is $4 = $94 - $90.

b. The puts are out of the money. The intrinsic value of the puts is $0.

c. The Mar call and the Oct put are mispriced. The call is mispriced because it is selling for less than its

intrinsic value. If the option expired today, the arbitrage strategy would be to buy the call for $3.20,

exercise it and pay $90 for a share of stock, and sell the stock for $94. A riskless profit of $0.80 results.

The October put is mispriced because it sells for less than the July put. To take advantage of this, sell the

July put for $3.90 and buy the October put for $3.65, for a cash inflow of $0.25. The exposure of the

short position is completely covered by the long position in the October put, with a positive cash inflow

today.

3. (LO1)

a. Each contract is for 100 shares, so the total cost is:

Cost = 10(100 shares/contract)($7.90)

Cost = $7,900

b. If the stock price at expiration is $140, the payoff is:

Payoff = 10(100)($140 – 112)

Payoff = $28,000

If the stock price at expiration is $125, the payoff is:

Payoff = 10(100)($125 – 112)

Payoff = $13,000

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c. Remembering that each contract is for 100 shares of stock, the cost is:

Cost = 10(100)($4.70)

Cost = $4,700

The maximum gain on the put option would occur if the stock price goes to $0. We also need to subtract

the initial cost, so:

Maximum gain = 10(100)($112) – $4,700

Maximum gain = $107,300

If the stock price at expiration is $102, the position will have a profit of:

Profit = 10(100)($112 – 102) – $4,700

Profit = $10,000 – $4,700 = $5,300

d. At a stock price of $104 the put is in the money. As the writer you will make:

Net loss = $4,700 – 10(100)($112 – 104)

Net loss = –$3,300

At a stock price of $134 the put is out of the money, so the writer will make the initial cost:

Net gain = $4,700

At the breakeven, you would recover the initial cost of $4,700, so:

$4,700 = 10(100)($112 – ST)

ST = $107.30

For terminal stock prices above $107.30, the writer of the put option makes a net profit (ignoring

transaction costs and the effects of the time value of money).

4. (LO2)

a. The value of the call is the stock price minus the present value of the exercise price, so:

C0 = $85 – 75/1.06

C0 = $14.25

b. Using the equation presented in the text to prevent arbitrage, we find the value of the call is:

$85 = [($95 – 80)/($95 – 90)]C0 + $80/1.06

C0 = $3.17

5. (LO2)

a. The value of the call is the stock price minus the present value of the exercise price, so:

C0 = $70 – $45/1.05

C0 = $27.14

b. Using the equation presented in the text to prevent arbitrage, we find the value of the call is:

$70 = 2C0 + $60/1.05

C0 = $6.43

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