## Applied Corporate Finance

IBM Thomas J. Watson Research Center

Prof. Ian Giddy

E-mail: ian.giddy@nyu.edu Web: www.giddy.org
Course Web site: giddy.org/ibmfinance

Time Value of Money:

Questions

1. You have an expected liability (cash outflow) of \$500,000 in 10 years, and you use a discount rate of 10%.

a. How much would you need right now as savings to cover the expected liability?

b. How much would you need to set aside at the end of each year for the next 10 years to cover the expected liability?

3. You have just taken a 30-year mortgage loan for \$200,000. The annual percentage rate on the loan is 8%, and payments will be made monthly. Estimate your monthly payments.

5. A company is planning to set aside money to repay \$100 million in bonds that will be coming due in 10 years. If the appropriate discount rate is 9%,

a. how much money would the company need to set aside at the end of each year for the next 10 years to be able to repay the bonds when they come due?

b. how would your answer change if the money were set aside at the beginning of each year?

7. What is the value of stock in a company that currently pays out \$1.50 per share in dividends and expects these dividends to grow 6% a year forever? (You can assume that investors require a 13% return on stocks of equivalent risk.)

9. You buy a 10-year zero-coupon bond, with a face value of \$1000, for \$300. What is the rate of return you will make on this bond?

11. You have an relative who has accumulated savings of \$ 250,000 over his working lifetime and now plans to retire. Assuming that he wishes to withdraw equal installments from these savings for the next 25 years of this life, how much will each installment amount to if he is earning 5% on his savings?

13. A bill that is designed to reduce the nation's budget deficit passes both houses of legislature. Congress tells us that the bill will reduce the deficit by \$500 billion over 10 years. What it does not tell us is the timing of the reductions.

 Year Deficit Reduction 1 \$ 25 Billion 2 \$ 30 Billion 3 \$ 35 Billion 4 \$ 40 Billion 5 \$ 45 Billion 6 \$ 55 Billion 7 \$ 60 Billion 8 \$ 65 Billion 9 \$ 70 Billion 10 \$ 75 Billion

If the federal government can borrow at 8%, what is the true deficit reduction in the bill?

15. Poor Bobby Bonilla! The newspapers claim that he is making \$5.7 million a year. He claims that this is not true in a present value sense and that he will really be making the following amounts for the next 5 years:

 Year Amount 0 (now) \$ 5.5 million (Sign up Bonus) 1 \$ 4 million 2 \$ 4 million 3 \$ 4 million 4 \$ 4 million 5 \$ 7 million
a. Assuming that Bonilla can make 7% on his investments, what is the present value of his contract?

b. If you wanted to raise the nominal value of his contract to \$30 million, while preserving the present value, how would you do it? (You can adjust only the sign up bonus and the final year's cash flow.)

17. You bought a house for \$250,000, borrowing \$200,000 on a 30-year term loan (with monthly payments). You have two options to finance the
house. First paying interest rates at 10% in Bank A. Second paying interest rates at 9% in Bank B. Bank B charges a fee of 3% of the value
of the loan. Your opportunity cost is 8%. Ignore tax effects.

a. How much are your monthly payments if borrowing from Bank A (at 10%)?

b. How would your monthly payments be if you borrow from Bank B (at 9%)?

c. You plan to stay in this house for the next 5 years. Given the fee of Bank B (3% of the loan), which loan would you prefer?

d. At which interest rate would be you be indifferent between borrowing from Bank A or B (assuming again that you are going to stay in the house for five years)?

19. You have been hired to run a pension fund for TelDet Inc, a small manufacturing firm. The firm currently has \$5 million in the fund and expects to have cash inflows of \$2 million a year for the first 5 years followed by cash outflows of \$ 3 million a year for the next 5 years. Assume that interest rates are at 8%.

a. How much money will be left in the fund at the end of the tenth year?

b. If you were required to pay a perpetuity after the tenth year (starting in year 11 and going through infinity) out of the balance left in the pension fund, how much could you afford to pay?

21. You have been asked to estimate the value of a 10-year bond with a coupon that will be low initially but it is expected to grow later in the bond's life. The coupon is expected to be 5% of the face value of the bond (which is \$ 1000) for the first 5 years, and will increase by 1% every year for the next 5 years ñ the coupon rate will be 6% in year 6, 7% in year 7, 8% in year 8, 9% in year 9 and 10% in year 10. Estimate the value of this bond if the market interest rate is 8%.

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