Solution 11/26/2018
Chapter: 15
Problem: 17
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
b. How much is the debt worth today? What is its yield?
Debt value = Total Value – Equity Value = 76.37$ million
Debt yield = 12.934%
Equity value at 60% volatility 128.76748 million
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 zero coupon debt outstanding that matures in 3
years with $110 million face value. The risk-free rate is 5%, and the standard deviation of
returns for similar companies is 60%. The owners of Higgs Bassoon view their equity
investment as an option and would like to know its value.
c. How much would the equity value and the yield on the debt change if the company
were able to use risk management techniques to reduce its volatility to 45 percent? Can
you explain this?
1 of 3
Face Value of Debt 110.00
Risk Free rate 5%
Maturity of debt (years) 3.00
Standard Dev. 60.0% this is sigma–also known as volatility
Call Price = Equity Value 123.63$ million
d. Graph the yield to maturity on debt versus the face value of debt for values of the face value from $10 to $160 million.
Yield to Maturity on Debt
Face Value of Debt
12.934% hint: use a data table
10 5.18%
20 5.47%
30 5.98%
40 6.65%
50 7.42%
60 8.26%
70 9.15%
e. Graph the values of debt and equity for volatilities from 0.10 to 0.90 when the face value of the debt is $110 million.
Value of Debt Value of Equity
Volatility Face Value of Debt Volatility Face Value of Debt
76.37$ 110.00 123.63$ 110.00
Percent change -11.1% million
120.0000
140.0000
160.0000
Equity and Debt Values
3 of 3