Question

A. Fethe Inc. is a custom manufacturer of guitars, mandolins, and other stringed instruments and is located near Knoxville, Tennessee. Fethe's current value of operations, which is also its value of debt plus equity, is estimated to be $8 million. Fethe has $5 million face value, zero coupon debt that is due in 2 years. The risk-free rate is 5%, and the standard deviation of returns for companies similar to Fethe is 40%. Fethe's owners view their equity investment as an option and would like to know the value of their investment.

The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

1. Using the Black-Scholes option pricing model, how much is Fethe's equity worth? Enter your answer in millions. For example, an answer of $1.21 million should be entered as 1.21, not 1,210,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $   million

2. How much is the debt worth today? Enter your answer in millions. For example, an answer of $1.21 million should be entered as 1.21, not 1,210,000. Do not round intermediate calculations. Round your answer to two decimal places.

   $ million

   What is its yield? Do not round intermediate calculations. Round your answer to one decimal place.

   %

3. How would the equity value change if Fethe's managers could use risk management techniques to reduce its volatility to 30%? Enter your answer in millions. For example, an answer of $1.21 million should be entered as 1.21, not 1,210,000. Do not round intermediate calculations. Round your answer to two decimal places.
   New equity value:

   $ million

   How would the yield on the debt change if Fethe's managers could use risk management techniques to reduce its volatility to 30%? Do not round intermediate calculations. Round your answer to one decimal place.

   New yield on the debt: %

Answer 1

Answer:

Value of share, St is $8 million (assets)

Value of strike price, K is $5 million (Value of debt)

Risk free rate, r is 5%

Volatility, v is 40%; term

t is 2 years

Using the Black-Scholes option pricing model, calculating Fethe's equity worth

d1 = (log(St/k) + (r+(v^2/2))(t))/(v*t^(1/2)) = 2.1567

; N(d1) = 0.9846

d2 = d1 - v*t^(1/2) = 1.591 ; N(d2) = 0.9441

C = 8millon* 0.9846 - 5millon * e^(-0.5*2year) * 0.9441

= 3.6055millon(value of equity)..........

(a)

value of debt =8 million - 3.6055millon = 4.3945millon......

(b)

Yiled calculation

Value of debt =5millon/1+y^2

y = (5/4.3945millon)^(1/2) - 1 = 6.67%........(b)

(C) if value of volatility is changed to 30%,

d1 = (log(St/k) + (r+(v^2/2))(t))/(v*t^(1/2)) = 2.7106 ; N(d1) = 0.9966

d2 = d1 - v*t^(1/2) = 2.2863 ; N(d2) = 0=9890

C = 8millon* 0.9966 - 5millon * e^(-0.5*2year) * 0.989

= 3.4984millon(value of equity)

value of debt =8 million - 3.4984millon = 4.5016millon

Yiled calculation

Value of debt =5millon/1+y^2

y = (5/4.5016millon)^(1/2) - 1 = 5.39%.

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