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 $$60$ million. Fethe has $$15$ million face value, zero coupon debt that is due in $5$ years. The risk$-$free rate is $7\%,$ and the standard

deviation of returns for companies similar to Fethe is $50\%.$ Fethe's owners view their equity investment as an option, and they would like to know the value of their investment.

a$.$ Using the Black$-$Scholes option pricing model, how much is Fethe's equity worth? Do not round intermediate calculations. Enter your answer in millions. For example, an

answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round your answer to two decimal places.

$

million

b$.$ How much is the debt worth today? What is its yield? Do not round intermediate calculations. Enter your answer for debt worth in millions. For example, an answer of

$$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round the monetary value to two decimal places and percentage value to one decimal place.

Debt worth today: $

million

Yield on the debt:

$\%$

c$.$ 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 $40\%?$ Can you explain

this? Do not round intermediate calculations. Enter your answer for equity worth in millions. For example, an answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not

$1,230,000.$ Round the monetary value to two decimal places and percentage value to one decimal place.

The equity value would

to $

million becuase Fethe has

$-$Select$-$

of a chance of a "home run." The yield on the debt would

to

$\%$ because the investment becomes less risky.