Financial Options and Applications in Corporate Finance - Chapter 8

© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted

to a publicly accessible website, in whole or in part.

Answers and Solutions: 8 - 1

Chapter 8

Financial Options and Applications in Corporate Finance

ANSWERS TO END-OF-CHAPTER QUESTIONS

8-1 a. An option is a contract which gives its holder the right to buy or sell an asset at some

predetermined price within a specified period oftime. A call option allows the holder

to buy the asset, while a put option allows the holder to sell the asset.

b. A simple measure of an option's value is its exercise value. The exercise value is

equal to the current price of the stock (underlying the option) less the striking price of

the option. The strike price is the price stated in the option contract at which the

security can be bought (or sold). For example, if the underlying stock sells for $50

and the striking price is $20, the exercise value of the option would be $30.

c. The Black-Scholes Option Pricing Model is widely used by option traders to value

options. It is derived from the concept of a riskless hedge. By buying shares of a

stock and simultaneously selling call options on that stock, the investor will create a

risk-free investment position. This riskless return must equal the risk-free rate or an

arbitrage opportunity would exist. People would take advantage of this opportunity

until the equilibrium level estimated by the Black-Scholes model was reached.

8-2 The market value of an option is typically higher than its exercise value due to the

speculative nature of the investment. Options allow investors to gain a high degree of

personal leverage when buying securities. The option allows the investor to limit his or

her loss but amplify his or her return. The exact amount this protection is worth is the

options time value, which is the difference between the option's price and its exercise

value.

8-3 (1) An increase in stock price causes an increase in the value of a call option. (2) An

increase in strike price causes a decrease in the value of a call option. (3) An increase in

the time to expiration causes an increase in the value of a call option. (4) An increase in

the risk-free rate causes an increase in the value of a call option. (1) An increase in the

standard deviation of stock return causes an increase in the value of a call option.© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted

to a publicly accessible website, in whole or in part.

Answers and Solutions: 8 - 2

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

8-1 Exercise value = Current stock price - strike price

= $30 - $25 = $5.

Time value = Option price - Exercise value

= $7 - $5 = $2.

8-2 Option's strike price = $15; Exercise value = $22; Time value = $5;

V = ? P0

= ?

Time Value = Market price of option - Exercise value

$5 = V - $22

V = $27.

Exercise value = P0 - Strike price

$22 = P0 - $15

P0

= $37.

8-3 P = $15; X = $15; t = 0.5; rRF = 0.06; σ

2

= 0.12; d1

= 0.24495;

d2

= 0.0000; N(d1) = 0.59675; N(d2) = 0.500000; V = ?

Using the Black-Scholes Option Pricing Model, you calculate the option's value as:

V = P[N(d1)] -

r

RFt

Xe−

[N(d2)]

= $15(0.59675) - $15e(-0.06)(0.5)(0.50000)

= $8.95128 - $15(0.9512)(0.50000)

= $1.6729 ≈ $1.67.

8-4 Put = V - P + X exp(-r

RF t)

= $6.56 - $33 + $32 e-0.06(1)

= $6.56 - $33 + $30.136 = $3.696 ≈ $3.70.© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted

to a publicly accessible website, in whole or in part.

Answers and Solutions: 8 - 3

8-5 0.3319.

0.5 0.33333

ln($30/$35) [0.05 (0.25/2)](0.333333)

σ t

/2)]t 2

(σ

RF ln(P/X) [r

1

d =−

+ +

=

+ +

=

d2

= d1 - σ (t)0.5

= -0.3319 - 0.5(0.33333)0.5

= -0.6206.

N(d1) = 0.3700 (from Excel NORMSDIST function).

N(d2) = 0.2674 (from Excel