Please find attached.

Assume that you own equity of a private firm (called PRIVATE) whose assets are currently valued at $100M. The firm has 5-year zero coupon debt with face value of $90M. The 5-year Treasury bond yield is 5%.

a) Draw the payoff diagram for the aggregate equity holders at year 5 as a function of firm value at year 5.

In order to calculate how much your equity position is worth, you gather information about a comparable public firm (called PUBLIC). Because firm PUBLIC and PRIVATE have similar businesses, the asset values of the two firms move almost one to one. That is, if PUBLIC?s asset value goes up by 1 percent, PRIVATE?s asset value also goes up by 1 percent, and vice versa. Firm PUBLIC is an all equity firm with 5M shares outstanding. PUBLIC?s current stock price is $100 per share. Below is the option prices of firm PUBLIC. The option prices are for the right to buy/sell one share of PUBLIC.

American Call / Put

Maturity

Strike price

Option price

Call A

5 yr

70.52

54.50

Call B

5 yr

90

46.43

Call C

5 yr

100

42.88

Put D

5 yr

70.52

9.42

Put E

5 yr

90

16.52

Put F

5 yr

100

20.76

b) How much is the total equity of PRIVATE worth?

c) How much is PRIVATE?s debt worth?

d) What is the annual yield (i.e. annual discount rate) on PRIVATE?s debt?