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Value of equity, Hedging, Call Options

Question 7
A firm has current market value of assets (the sum of debt and equity values) equal to $1 billion. The debt is all zero coupon, with maturity five years and face value $900 million. The firm will pay no dividends over the next five years, the volatility of its asset value is 50% per year, and the risk-free rate is 5% per year, continuously compounded. What is the current value of equity?

a. $100.0 million
b. $299.1 million
c. $504.7 million
d. $526.0 million
e. $636.6 million

Question 20
A portfolio manager has 50,000 shares in stock X. She wishes to use put options on stock X to hedge her position. The puts under consideration have Black Scholes parameter d1=.794. To have the most fully hedged position, how many puts should the manager buy (to the nearest 100)?

a. 39,320
b. 63,600
c. 234,100
d. 242,700
e. 439,500

Question 25
Shares of Deepin Damoni are priced at $80.00 per share. The stock pays no dividends and has an annual volatility of 32 percent. The risk less rate of interest is 5 percent. Call options on Deepin Damoni with an exercise price of $20.00 and one year to maturity are worth:

a. $20.00
b. $57.14
c. $60.00
d. $60.98
e. none of the above

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Question 7

A firm has current market value of assets (the sum of debt and equity values) equal to $1 billion. The debt is all zero coupon, with maturity five years and face value $900 million. The firm will pay no dividends over the next five years, the volatility of its asset value is 50% per year, and the risk-free rate is 5% per year, continuously compounded. What is the current value of equity?

a. $100.0 million
b. $299.1 million
c. $504.7 million
d. $526.0 million
e. $636.6 million

Answer: d. $526.0 million

"Equity can be viewed as a call option on the company's assets when the firm is leveraged
The exercise price is the value of the debt
If the assets are worth more than the debt when it comes due, the option will be exercised and the stockholders retain ownership
If the assets are worth less than the debt, the stockholders will let the option expire and the assets will belong to the bondholders
"

We will use Black Scholes Pricing Formula
Value of call= S N(d1) - X * e -r(T-t) * N(d2)
We therefore need to calculate the values of d1 and d2
d1= {ln (S/X) + ( ...

Solution Summary

Answers to 3 Multiple choice questions that deal with current value of equity, number of put options to purchase for hedging and value of call options

$2.19