Stock and bond pricing, leverage, option pricing

Problem 2. Bond and Stock Values

This problem has three parts.
2a. A certain bond has a face (par) value of $10,000.00 and pays a coupon of $100 annually. The current rate of interest on similar bonds is 12%. The bond is a 10 year maturity. What is a fair price for the bond in the bond market?
2b. Bonds selling at par in the market have a coupon of about 10%. If the interest rate in the market suddenly changes to 12% for these bonds, what would the market price of the bond be expressed as a percent of par, if the maturity of the bond is 5 years? 10 years? How does the change in interest rate effect bonds of differing maturities?
2c. A certain stock has the following earnings per share record for the past ten years:

Year EPS
1 $5.00
2 $3.00
3 $6.00
4 $4.00
5 $7.00
6 $5.00
7 $9.00
8 $7.00
9 $10.00
10 $12.00

If the firm retains 60% of its earnings and has a cost of debt of 12% before taxes, with a 40% tax rate, what is the value of the firms stock if 1,000,000 shares are outstanding?
Assume the firm is a normal constant growth firm over time, that the risk free rate is 7%, and that the weighted average cost of capital is 17.5%. Further, assume the firms Debt to Equity Ratio is 0.50 and that no preferred stock is outstanding.

Problem 3. Leverage
This problem has three parts.
J&S Snowmobile Repair has the following cost structure:

Fixed costs:
Rent: 100 Product mix is given in terms of number of jobs.
Labor 200
Company Vehicle 20
Office Supplies 5
Phone 2
Utilities 10

There are two kinds of repairs: big and small. Big repairs have an average billable price of 10, but have high variable costs of 40% of billable cost.
Small repairs have an average billable cost of 3, but have a variable cost of only 10% of billable cost value.
Large jobs required 4 units of labor each while small jobs require only 1 unit of labor. Labor costs 1 per unit.

3a. Breakeven. Assuming a mix of 50/50 big and small jobs, how many hours of labor are necessary to hit breakeven for J&S snowmobile, assuming that variable labor can only be used if fixed labor is exhausted?

3b. Product Mix. If the mix changes to 20/80 big to small jobs (20% big, 80% small) as measured by number of jobs completed, what is the effect on breakeven?
What is the effect of the change in mix on operating leverage?

3c. Assume that a firm has a beta of 1.0 and a D/E ratio of 1.5. If the firms tax rate T is 35%, what would the firms beta likely be if the firm had no debt on its balance sheet?

Problem 4. Option Pricing

This problem has four parts.

4a. Using the Black Scholes Option pricing model, price the following option:

The Wall Street Journal reports that the current price of a stock is $100.00 per share and that a call option exists at an exercise price of $105 with a time to maturity of 3 months. The annualized variation of stock returns is 0.20. The risk free rate is taken as 6%. What is the value of this option on a per-share basis?

4b. Using the data from 4a, prepare a chart showing the effect of the following changes on the option value:

4.b.1 Increase stock price by $5
4.b.2 Increase the exercise price by $5.00
4.b.3 Increase the time to maturity from 3 months to 6 months
4.b.4 Increase the risk free rate from 6% to 8%
4.b.5 Increase the market variance from 0.20 to 0.30

(2 points each, total of 10 points this part)

4c. Explain why options have value.

4d. Explain the difference between a natural hedge and a typical financial market hedge. Explain why hedging is good for the economy, even when natural hedges do not exist.