QUESTION $5$

A$.$ Consider three $30-$year bonds with annual coupon payments. One bond has a $10\%$ coupon rate, one has a $5\%$ coupon rate, and one has a $3\%$ coupon rate. If the yield to maturity of each bond is $5\%,$ what is the price of each bond per $$100$ face value? Which bond trades at a premium, which trades at a discount, and which trades at par? $(4$ marks$)$

B$.$ You are running a hot Internet company. Analysts predict that its earnings will grow at $30\%$ per year for the next five years. After that, as competition increases, earnings growth is expected to slow to $2\%$ per year and continue at that level forever. Your company has just announced earnings of $$1,000,000.$ What is the present value of all future earnings if the interest rate is $8\%?($Hint: first five years should be treated as an annuity and subsequent years should be treated as a perpetuity and also assume all cash flows occur at the end of the year.$)(6$marks$)$

c$.$ Ebay, Inc. went public in September of $1998.$ The following information on shares outstanding was listed in the final prospectus filed with the SEC. In the IPO, the Ebay issued $5,500,000$ new shares. The initial price to the public was $$20\mathrm{.}00$ per share. The final first$-$day closing price was $$55\mathrm{.}88.$ If the investment bankers retained $$2\mathrm{.}50$ per share as fees, what was the net proceeds to Ebay? What was the market capitalization of new shares of Ebay $(5$ Marks$)$

D$.$ Consider two firms, Ying Corporation and Yang Corporation. Both corporations will either make $$50$ million or lose $$20$ million every year with equal probability. The only difference is that firms' profits are perfectly negatively correlated. That is$,$ any year Yang Corporation earns $$50$ million, Ying Corporation loses $$20$ million, and vice versa. Assume that the corporate tax rate is $34\%.$ What are the total expected after$-$tax profits if the two firms' when they are two separate firms? What are the expected after$-$tax profits if the two firms are combined into one corporation called Ying$-$Yang Corporation, but are run as two independent divisions? $($Assume it is not possible to carry back or forward any loses.$)(5$ marks$)$