Solution 7/16/2015
Chapter: 15
Problem: 14
a. Using the Black-Scholes Option Pricing Model, how much is the equity worth?
Black-Scholes Option Pricing Model
Total Value of Firm 200.00 this is the current value of operations
Face Value of Debt 100.00
Risk Free rate 5%
Maturity of debt (years) 3.00
Standard Dev. 0.45 this is sigma–also known as volatility
d11.4715 use the formula from the text
d20.6920 use the formula from the text
b. How much is the debt worth today? What is its yield?
Debt value = Total Value – Equity Value = 79.15$ million
Debt yield = 8.107%
50 5.64%
Higgs Bassoon Corporation is a custom manufacturer of bassoons and other wind
instruments. Its current value of operations, which is also its value of debt plus equity, is
estimated to be $200 million. Higgs has $110 million face value, zero coupon debt that is
due in 3 years. The risk-free rate is 5%, and the standard deviation of returns for similar
companies is 60%. The owners of Higgs Bassoon view their equity investment as an
option and would like to know the value of their investment.
c. How much would the equity value and the yield on the debt change if Fethe’s
management were able to use risk management techniques to reduce its volatility to 45
percent? Can you explain this?
10.00%
Yield on Debt
1 of 4
60 5.99%
70 6.42%
80 6.92%
90 7.49%
100 8.11%
110 8.77%
120 9.47%
130 10.20%
140 10.96%
150 11.74%
160 12.54%
b. Graph the values of debt and equity for volatilities from 0.10 to 0.90 when the face value of the debt is $2 million.
Value of Debt Value of Equity
Volatility Face Value of Debt Volatility Face Value of Debt
79.15$ 100.00 120.85$ 100.00
0.1 86.0708 0.1 113.9292
0.2 85.9606 0.2 114.0394
0.8 59.4584 0.8 140.5416
0.9 53.5949 0.9 146.4051
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
050 100 150
Yield on Debt
Face Value of Debt
120.0000
140.0000
160.0000
0 0.2 0.4 0.6 0.8 1
Volatility (sigma)
Equity and Debt Values
3 of 4
200
Series1
4 of 4