Financial Options and Applications in Corporate Finance – Chapter 8
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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 options 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 options 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 Options 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
= $37.
8-3 P = $15; X = $15; t = 0.5; rRF = 0.06; σ
= 0.12; d1
= 0.24495;
= 0.0000; N(d1) = 0.59675; N(d2) = 0.500000; V = ?
Using the Black-Scholes Option Pricing Model, you calculate the options value as:
V = P[N(d1)] –
[N(d2)]
= $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)
/2)]t 2
RF ln(P/X) [r
= 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