978-0077861704 Chapter 24 Solutions Manual Part 1

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CHAPTER 24

OPTIONS AND CORPORATE FINANCE

Answers to Concepts Review and Critical Thinking Questions

1. 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

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

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

5. The call is selling for less than its intrinsic value; an arbitrage opportunity exists. Buy the call for

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

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

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

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

cash inflows and outflows are counted, not contingent cash flows. From a political perspective, debt

11. The option to abandon reflects our ability to shut down a project if it is losing money. Since this

CHAPTER 27 – 2

12. The option to expand reflects our ability to increase production if the new product sells more than

14. With oil, for example, we can simply stop pumping if prices drop too far, and we can do so quickly.

15. There are two possible benefits. First, awarding employee stock options may better align the

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

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

so the intrinsic value is $11.

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

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

so the intrinsic value is $21.

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

CHAPTER 27 – 3

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

b. If the stock price at expiration is $43, the payoff is:

If the stock price at expiration is $39, the payoff is:

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

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:

If the stock price at expiration is $32, the position will be worth:

And your profit will be:

d. At a stock price of $34 the put is in the money. As the writer you will lose:

At a stock price of $34 the put is out of the money, so the writer will make the initial cost:

At the breakeven, you would recover the initial cost of $3,560, so:

CHAPTER 27 – 4

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

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

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

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

6. Each option contract is for 100 shares of stock, so the price of a call on one share is:

Using the no arbitrage model, we find that the price of the stock is:

7. a. The equity can be valued as a call option on the firm with an exercise price equal to the value

of the debt, so:

b. The current value of debt is the value of the firm’s assets minus the value of the equity, so:

We can use the face value of the debt and the current market value of the debt to find the

interest rate, so:

CHAPTER 27 – 5

8. a. Using the no arbitrage valuation model, we can use the current market value of the firm as the

stock price, and the par value of the bond as the strike price to value the equity. Doing so, we

get:

The current value of the debt is the value of the firm’s assets minus the value of the equity, so:

b. Using the no arbitrage model as in part a, we get:

The stockholders will prefer the new asset structure because their potential gain increases while

their maximum potential loss remains unchanged.

9. The conversion ratio is the par value divided by the conversion price, so:

The conversion value is the conversion ratio times the stock price, so:

10. a. The minimum bond price is the greater of the straight bond value or the conversion price. The

straight bond value is:

The conversion ratio is the par value divided by the conversion price, so:

The conversion value is the conversion ratio times the stock price, so:

CHAPTER 27 – 6

b. The option embedded in the bond adds the extra value.

11. a. The minimum bond price is the greater of the straight bond value or the conversion value. The

straight bond value is:

The conversion ratio is the par value divided by the conversion price, so:

The conversion price is the conversion ratio times the stock price, so:

b. The conversion premium is the difference between the current stock price and conversion price,

divided by the current stock price, so:

12. The value of the bond without warrants is:

The value of the warrants is the selling price of the bond minus the value of the bond without

warrants, so:

Since the bond has 20 warrants attached, the price of each warrant is:

13. If we purchase the machine today, the NPV is the cost plus the present value of the increased cash

flows, so:

CHAPTER 27 – 7

We should not necessarily purchase the machine today, but rather we would want to purchase the

machine when the NPV is the highest. So, we need to calculate the NPV each year. The NPV each

year will be the cost plus the present value of the increased cash savings. We must be careful

however. In order to make the correct decision, the NPV for each year must be taken to a common

date. We will discount all of the NPVs to today. Doing so, we get:

Year 1: NPV1 = [–$1,305,000 + $273,000(PVIFA14%,9)] / 1.14

NPV1 = $39,789.05

Year 2: NPV2 = [–$1,210,000 + $273,000(PVIFA14%,8)] / 1.142

NPV2 = $43,405.54

The company should purchase the machine two years from now when the NPV is the highest.

Intermediate

14. a. The base-case NPV is:

b. We would abandon the project if the cash flow from selling the equipment is greater than the

present value of the future cash flows. We need to find the sale quantity where the two are

equal, so:

$1,400,000 = ($68)Q(PVIFA14%,9)

Abandon the project if Q < 4,162 units, because the NPV of abandoning the project is greater

than the NPV of the future cash flows.

15. a. If the project is a success, present value of the future cash flows will be:

CHAPTER 27 – 8

From the previous question, if the quantity sold is 3,900, we would abandon the project, and the

cash flow would be $1,400,000. Since the project has an equal likelihood of success or failure

in one year, the expected value of the project in one year is the average of the success and

failure cash flows, plus the cash flow in one year, so:

The NPV is the present value of the expected value in one year minus the cost of the

equipment, so:

b. If we couldn’t abandon the project, the present value of the future cash flows when the quantity

is 3,900 will be:

The gain from the option to abandon is the abandonment value minus the present value of the

cash flows if we cannot abandon the project, so:

We need to find the value of the option to abandon times the likelihood of abandonment. So, the

value of the option to abandon today is:

16. If the project is a success, present value of the future cash flows will be:

If the sales are only 4,162 units, from Problem 14, we know we will abandon the project, with a

The NPV is the present value of the expected value in one year minus the cost of the equipment, so:

CHAPTER 27 – 9

The gain from the option to expand is the present value of the cash flows from the additional units

sold, so:

Gain from option to expand = $68(11,200)(PVIFA14%,9)

Gain from option to expand = $3,767,156.79

We need to find the value of the option to expand times the likelihood of expansion. We also need to

find the value of the option to expand today, so:

Option value = (.50)($3,767,156.79) / 1.14

Option value = $1,652,261.75