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 $5 million. Fethe has $3 million face value, zero coupon debt that is due in 2 years. The risk-free rate is 7%, and the standard deviation of returns for companies similar to Fethe is 30%. Fethe's owners view their equity investment as an option and they would like to know the value of their investment.

Using the Black-Scholes option pricing model, how much is Fethe's equity worth? Do not round intermediate calculations. Round your answer to two decimal places. $ million

How much is the debt worth today? What is its yield? Do not round intermediate calculations. Round your answer for the debt worth to two decimal places. Round your answer for the yield on the debt to one decimal place.

Debt worth today: $ million

Yield on the debt: %

How would the equity value and the yield on the debt change if Fethe's managers could use risk management techniques to reduce its volatility to 20%? Do not round intermediate calculations. Round your answer for the equity worth to two decimal places. Round your answer for the yield on the debt to one decimal place.

New equity worth: $ million

New yield on the debt: %

Can you explain this? The value of the stock goes down and the value of the debt goes up because with lower risk, Fethe has (more/less) of a chance of a "home run".

Answer 1

NOTE: In this context, the equity can be valued as a call option because the payoff upon maturity of a call option would be similar to the payoff of the firm's equity holders upon the firm's liquidation. Since, two instruments with similar payoffs should have the same price, the equity can be reliably valued as a call option.

(a) Firm Value = $ 5 million, Debt Face Value = $ 3 million, Standard Deviation = 30 %, Risk-Free Rate = 7 % and Maturity = 2 years

Using an online calculator to solve for the call option value we have:

Equity Value = Call Option Price = $ 2.43 million

Debt Value = Firm Value - Equity Value = 5 - 2.43 = $ 2.57 million

Let the annual yield be y

Therefore, 2.57 = 3 / (1+y)^(2)

y = 0.0804 or 8.04 %

(b)

Firm Value = $ 5 million, Debt Face Value = $ 3 million, Standard Deviation = 20 %, Risk-Free Rate = 7 % and Maturity = 2 years

Using an online calculator to solve for the call option value we have:

Equity Value = Call Option Value = $ 2.4 million

Debt Value = 5 - 2.4 = $ 2.6 million

Let the yield be y

2.6 = 3 / (1+y)^(2)

y = 0.0742 or 7.42 %

Lower risk will implicitly lead to more chances of success, thereby Fethe's chances of a "home run" (success) are more.