1. A firm expects to generate net income of $600 million, $550 million, and $500 million at the end of each of the next three years. Then, firm's net income is expected to grow at 4% constant rate thereafter. These net incomes are generated by firm's existing investments. This firm has a beta of 1.0 and has 100 million shares outstanding. Suppose the risk-free rate and market risk premium are 4% and 6%, respectively. Now, this firm considers a new investment, which will cost $300 million and $200 million at the end of first and second year. The, this project will provide an additional expected net income of $400 million and $350 million ONLY at the end of fifth and sixth year. Then this new project will be abandoned at no residual value at the end of sixth year. Also, assume that the firm's only financing alternative to support this investment project is to utilize its internally generated cash flows (net income). How much should you be willing to pay for this stock if firm decides to undertake this new investment?
2. The bond has a 30-year maturity, an 8% coupon, and sells at an initial yield to maturity of 8%. The modified duration of the bond is 11.26 years, and its price change is -18.27%. Assuming that the bond's yield increases from 8% to 10%, what is the "Convexity" of this bond?
3. Suppose that the stock now sells at $80, and the price will go up by 5% or down by 5% at the end of first six month (t = ½). Then, the price will either go up by 10% or down by 10% at the end of year (t = 1). A call option on the stock has an exercise price of $75 and a time to expiration of one year. Also, assume 10% annual interest rate and no dividend payment for this year. Calculate the put price at t=0.
4.There are two stocks, stock A and stock B. The price of stock A today is $70. The price of stock A next year will be $50 if the economy is in recession, $80 if the economy is normal and $95 if the economy is expanding. The attendant probabilities of recession, normal times, and expansion are 0.2, 0.6, 0.2, respectively. Stock A pays no dividend. Assume the CAPM is true. Other information about the market includes:
SD(Rm) = Standard deviation of the market portfolio = 0.10
SD(Rb) = Standard deviation of stock B's return = 0.12
Rb = Expected return on stock B = 0.10
Corr(Ra,Rm) = The correlation of stock A and the market = 0.7
Corr(Rb,Rm) = The correlation of stock B and the market = 0.34
Corr(Ra,Rb) = The correlation of stock A and stock B = 0.6
What is the beta of the portfolio consisting of 30% of stock A and 70% of stock B?
5. The stock of Russell Index Corporation is currently selling for $530.88 per share. The risk-free rate is 1.35% per quarter and it will not change for at least next six months. Russell Index Corp has an ordinary dividend yield of .25% per quarter. Ignoring marking to market, what should be the futures price for the futures contract on Russell Index Corp maturing in three months?