Corporate Finance Problem Set

1. You would like to endow a scholarship. In-state tuition is currently $10,000, payable at the end of each year. Tuition will grow by 3% per year. The opportunity cost of capital is 5%. How much money should you invest today to endow a scholarship that pays full tuition once every year starting 10 years from now?

2. In the past, the UK issued perpetual bonds called "consols", which pay a constant cash flow of 4 million each year forever. Suppose the consols were issued with a 4% coupon rate. Today, the government of the UK wants to fully repay part of these outstanding consols. To finance this repayment, the government would issue a bond with a constant yearly payment for 20 years (payable at the end of each year). Suppose the government's discount rate is 3% and that the next consol is paid in exactly one year.

a. Whatisthepresentvalueoftheoutstandingstockofconsols?

b. How much debt can the UK government issue through the new 20-

year bond if it keeps the yearly payment constant at 4 million?

c. What fraction of the stock of outstanding consols will the UK government be able to retire if it keeps the yearly payment constant

at 4 million?

d. What must the 20 year bond's yearly payment be in order to fully

repay the stock of outstanding consols?

3. Seahawk Lines is considering the purchase of a new bulk carrier for $5 million to operate for 15 years. Forecasted yearly revenues are $6 million, while operating costs are $4 million, both received at the end of each year. A major refit that costs $4 million will be required at the end of year 5 and

year 10. After 15 years the ship is expected to be sold for scrap at $0.5 million. If the discount rate is 10%, what is the ship's NPV?

4. Consider the following three stocks.

a. StockAisexpectedtoprovideadividendof$10ashareforever.

b. Stock B is expected to pay a dividend of $5 next year. Thereafter,

dividend growth is expected to be 4 % a year forever.

c. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20 % a year for 5 years (i.e., until

year 6) and zero thereafter.

If the discount rate for each stock is 10 %, which stock is the most valuable? What if the discount rate is 7 %?

Hint: The price of a stock is the PV of the dividends.

5. You have a $50,000 balance on your credit card, and you have set your checking account for monthly payments of $1,000. The monthly interest rate is 1.5%. How many years until you have paid off your debt? What if your balance is $70,000?