Fethe Inc. is a custom manufacturer of guitars, mandolins, and other stringed instruments and is located near Knoxville, Tennessee. Fethe$$s current value of operations, which is also its value of debt plus equity, is estimated to be $$100$ million. Fethe has $$50$ million face value, zero coupon debt that is due in $10$ years. The risk$-$free rate is $6\%,$ and the standard deviation of returns for companies similar to Fethe is $50\%.$ Fethe$$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?

b$.$ How much is the debt worth today? What is its yield?

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

$30\%?$ Please explain.