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Answers to EndofChapter Problems
B367
Chapter 24: Options and Corporate Finance:
Extensions and Applications
24.1
a.
The inputs to the BlackScholes model are the current price of the underlying asset (S), the
strike price of the option (K), the time to expiration of the option in fractions of a year (t), the
variance of the underlying asset (
s
2
), and the continuouslycompounded riskfree interest rate
(r).
Mr. Levin has been granted 20,000 European call options on Mountainbrook’s stock with 4
years until expiration.
Since these options were granted atthemoney, the strike price of each
option is equal to the current value of one share, or $50.
Therefore, the BlackScholes inputs are:
S = $50
s
2
= 0.25
K = $50
r = 0.06
t = 4
After identifying the inputs, solve for d
1
and d
2
:
d
1
= [ln(S/K) + (r + ½
s
2
)(t) ] / (
s
2
t)
1/2
= [ln(50/50) + {0.06 + ½(0.25)}(4) ] / (0.25*4)
1/2
= 0.7400
d
2
= d
1
 (
s
2
t)
1/2
= 0.7400  (0.25*4)
1/2
= 0.2600
Find N(d
1
) and N(d
2
), the area under the normal curve from negative infinity to d
1
and
negative infinity to d
2
, respectively.
N(d
1
) = N(0.7400) = 0.7704
N(d
2
) = N(0.2600) = 0.3974
According to the BlackScholes formula, the price of a European call option (C) on a non
dividend paying common stock is:
C = SN(d
1
) – Ke
rt
N(d
2
)
= (50)(0.7704) – (50)e
(0.06)(4)
(0.3974)
= $ 22.8897
The BlackScholes Price of one call option is $ 22.8897.
Since Mr. Levin was granted 20,000 options, the current value of his options package is
$457,794 (= 20,000 * $ 22.8897).
b.
Because Mr. Levin is riskneutral, you should recommend the alternative with the highest net
present value. Since the expected value of the stock option package is worth more than
$450,000, Mr. Levin would prefer to be compensated with the options rather than with the
immediate bonus.
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View Full Document Answers to EndofChapter Problems
B368
c.
If Mr. Levin is riskaverse, he may or may not prefer the stock option package to the
immediate bonus.
Even though the stock option package has a higher net present value, he
may not prefer it because it is undiversified.
The fact that he cannot sell his options
prematurely makes it much more risky than the immediate bonus.
Therefore, we cannot say
which alternative he would prefer.
24.2
Kimberleigh’s total compensation package consists of an annual salary of $500,000 for 3
years in addition to 10,000 atthemoney stock options.
First, find the present value of the salary payments.
Since the payments occur at the end of
the year, the payments can be valued as a threeyear annuity, discounted at 10%.
PV(Annual Salary Payments)
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This note was uploaded on 04/04/2009 for the course FIN FIN/554 taught by Professor Timothydreyer during the Summer '06 term at University of Phoenix.
 Summer '06
 TimothyDreyer
 Finance, Corporate Finance, Options

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