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Unformatted text preview: 1710 a. The inputs to the Black and Scholes option pricing model are P = 5, X = 2, rRF = 6%,
σ = 50%, and t = 2 years. Given these inputs, the value of a call option is calculated
as:
d1 = ln( P / X ) + [ rRF + σ 2 / 2]t
σt = ln(5 / 2) + [0.06 + 0.5 2 / 2]2
0.5 2 = 1.8191 . d 2 = d1 − σ t = 1.819 − 0.5 2 = 1.1120 . Using Excel’s Normsdist function N(d1) = 0.9656, and N(d2) = 0.8669. This gives a
value of the call option equal to:
V = P[N(d 1)] − Xe rRF t [N(d 2 )] = 5[0.9656] − 2e 0.06( 2 ) [0.8669] = 3.29 .
b. The debt must therefore be worth 53.29 = $1.71 million. Its yield is
2.0 / 1.71 − 1 = 0.81 = 8.1% .
c. At a volatility of 30% d1 = 2.6547 and N(d1) = 0.9960. d2 = 2.2304 and N(d2) =
0.9871. This gives an option value of $3.23 million. The debt value is then 5.0 –
3.23 = $1.77 million. Its yield is 6.3%. The value of the stock goes down and the
value of the debt goes up because with lower risk, Fethe has less of a chance of a
“home run.” Answers and Solutions: 17  12 ...
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This note was uploaded on 07/13/2011 for the course FIN 4414 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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