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Unformatted text preview: University of Pennsylvania The Wharton School FNCE 100 A. Craig MacKinlay PROBLEM SET #1 Fall Term 2005 Present Value and Term Structure 1. Given an annual interest rate of 10 percent, what is the present ( t = 0) value of a stream of $100 annual payments starting in one year and ending in 20 years? 2. An investment of $1,000 earns 8 percent interest per year for three years. A second $1,000 investment earns 1 percent for the first and second years and 22 percent the third year. (a) What is the average (arithmetic) of the returns on each of the investments over the three years? (b) Compute the terminal value of each investment. Which is larger? (c) What is the compound rate of interest at which the initial $1,000 rises to the terminal value of each investment? (d) What is the geometric mean of the returns on each project? (e) How do your results in Part d compare with your results in Part c? Comment on the implications. 3. You purchase a bond for $900 and are promised coupon payments of $50 per year for the next 15 years and then a maturity payment of $1000. (The coupon payments come at year end.) Your ordinary income is taxed at the 25 percent rate while your capital gains are taxed at the 10 percent rate. What is the after-tax yield to maturity on this investment? Your capital gains tax is paid when the gain is realized, i.e., when the bond matures. 4. Calculate the present value of the following stream of payments: $2100 in 2 years $2100 in 4 years $2100 in 6 years . . . . . . $2100 continuing in this pattern forever . The annual rate of interest is 10 percent. 1 5. You need $129,200 at the end of seventeen years. You know that the best you can do is to make equal payments into an account on which you can earn 9 percent interest compounded annually. Your first payment is to be made at the end of the first year and the final payment is to be made at the end of the 17th year. (a) What amount must you plan to pay annually to achieve your objective? (b) Instead of making annual payments, you decide to make one lump-sum payment today. To achieve your objective of $129,200 at the end of the seventeen year pe- riod, what should this sum be? (You can still earn 9 percent interest compounded annually on your account.) 6. At a growth rate of x percent, how long does it take a sum to double? 7. A woman wants to invest enough on her 40th birthday to provide her with a $5,000 annual pension that begins (the first payment is received) on her 60th birthday and ends (the last payment is received) on her 74th birthday. If the interest rate is 6 percent a year, what must she invest on her 40th birthday to assure herself of this pension? 8. A firm is attempting to arrange a loan from a bank to purchase some equipment. The firm has talked to four different banks and received loan terms from each. Calculate the rate of return the firm would be paying in each case: (a) Bank A loans $10,000 today to the firm; the firm pays the bank $15,385 at the end of five years....
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