## Present Value

Problem 1. (solution) The Treasury wishes to conduct a yield auction to sell T-bonds with a maturity of 2 years. It would like to sell T-bonds with a face value of \$2 million. The following bids were received:

 Investor Quantity Demanded(Face Value) Yield demanded(percent p.a.) 1 300,000 15 2 200,000 14 3 500,000 14.38 4 500,000 10 5 300,000 12 6 200,000 15.5 7-10 1,000,000 Noncompetitive
1. What will the coupon rate be?
2. What price will each investor pay?

Notes:

1. The coupon rate is selected so that the average price paid is per \$100 of face value.
2. Non-competitive tenders are filled completely at the average price.
3. Assume coupons are paid annually.
4. The Treasury uses annual compounding.

Problem 2. (solution) a) You own 500 acres of timberland, with young timber worth \$40,000 if logged now. This represents 1000 cords of wood worth \$40 per cord net of costs of cutting and hauling. A paper company has offered to purchase your tract for \$140,000. Should you accept the offer? You have the following information:

 Years Yearly Growth Rate of Cords per acre 1-4 16% 5-8 111% 9-13 4% 14 and subsequent years 1%

b) You expect the price per cord to increase at 4% per year indefinitely.

c) The cost of capital is 9 percent. Ignore taxes.

d) The market value of your land would be \$100 per acre if you cut and removed the timber this year. The value of cut-over land is also expected to grow at 4 percent per year indefinitely.

Problem 3. (solution) The Fischer Corporation is considering an average risk investment in a mineral water spring project that has a cost of \$150,000. The project will produce 1,000 cases of mineral water per year indefinitely. The current sales price is \$138 per case, and the current cost per case is \$105. Fischer is taxed at a rate of 46%. Both prices and costs are expected to rise at a rate of 6% per year. Fischer's cost of capital is 15%.

(a) Should Fischer accept the project?

(b) If total costs consisted of a fixed cost of \$10,000 per year and variable costs of \$95 per unit, and if only the variable costs were expected to increase with inflation, would this make the project better or worse? Continue with the assumption that the output price will rise with inflation.

Problem 4. (Fall 1999) You have recently won a jackpot in your state's lottery.  You have the following options:

a.       You receive \$160,000 at the beginning of each year for 31 years.  The income would be taxed at an average rate of 28%.  Taxes are withheld when the checks are issued.

b.      You receive \$1,750,000 now, but you do not have access to the full amount immediately.  The \$1,750,000 would be taxed at an average rate of 28 percent.  You are able to take \$446,000 of the after-tax amount now.  The remaining \$814,000 will be placed in a 30-year annuity account that pays \$72,664 on a tax-free basis at the end of each year.

Using a discount rate of 10 percent, which option should you select?

Problem 5 (Spring 1999): You need to borrow \$300,000 to buy your yacht. The bank kindly agrees to lend you the money at an effective annual interest rate of 12% (note; this is not an APR). The terms of the loan are as follows. You will pay the bank a fixed sum of money at the end of every month for 10 years, plus \$50,000 at the end of the 10 years. The first payment is to be made one month from now. What is the amount of the monthly payment?

Problem 6: (Spring 1999) 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 five years followed by cash outflows of \$3 million a ear for the next five years.  Assume that interest rates are at 8%.

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

2. 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?

Problem 7