5-12 Present value concept Answer each of the following questions. a. What single investment made today, earning 12% annual interest, will be work $6,000 at the end of 6 years? b. What is the present value of $6,000 to be received at the end of 6 years if the discount rate is 12%? c. What is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your opportunity cost is 12%? d. Compare, contrast, and discuss your findings in parts a through c. CHAPTER 5 Time Value of Money 195 LG 2 P5-131 Personal Finance Problem Time value Jim Nance has been offered in that will pay him $500 three years from today. a. If his op opportunity cost is 7% compounded annually, what value should be place on this opportunity today? b. What is the most he should pay to purchase this payment today? c. Jim can purchase this investment for less than the amount calculated in part a, what does that imply about the rate of return that he will earn on the investment LG 2 P5-14 T Time value An lowa state synes hand can be converted to $100 at maturity 6 years from purchase. If the state bonds are to be competitive with U.S. savings bonds, which pay 8% annual interest compounded annually), at what price must the state sell its bonds? Assume no cash payments on savings bonds prior to redemption. G P 5-15 Personal Finance Problem Time value and discount rates You just won a lottery that promises to pay you $1,000,000 exactly 10 years from today. Because the $1.000.000 payment is guar- anteed by the state in which you live o rtunities exist to sell the claim today for an immediate single cash payment. a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10-year period? (1) 6% (2) 9% (3) 12% b. Rework part a under the assumption that the $1,000,000 payment will be received in 15 rather than 10 years. c. On the basis of your findings in parts a and b, discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum. LG P5-16 Personal Finance Problem Time value comparisons of single amounts in exchange for a $20,000 payment to day, a well-known company will allow you to choose one of the alternatives shown in the following table. Your opportunity cost is 11%. Alternative Single amount $28,500 at end of 3 years $54,000 at end of 9 years $160,000 at end of 20 years a. Find the value today of each alternative. b. Are all the alternatives acceptable? That is, are they worth $20,000 today? c. Which alternative, if any, will you take? LB 2 P5-17 Personal Finance Problem Cash flow investment decision Tom Alexander has an opportunity to push of the investments shown in the following table. The purchase price, the the single cash inflow, and its year of receipt are given for each investmen purchase recommendations would you make, assuming that Tom can can his investments? t Investment Y ear of sci Price $18.000 600 3.500 1.000 Single cash inflow $30,000 3,000 10,000 13,000 LG 2) P5-18 Calculating deposit needed You put $10,000 in an account earning 5%. A years, you make another deposit into the same account. Four years later the years after your original $10,000 deposit), the account balance is $20.000 was the amount of the deposit at the end of year 3? later (that is? 20.000. What LG 3 P5-19 Future value of an annuity For each case in the accompanying table, answer questions that follow. Case Amount of annuity Interest rate Deposit period varsi 8 $2,500 500 30,000 11,500 6,000 a. Calculate the future value of the annuity, assuming that it is (1) An ordinary annuity. (2) An annuity due. b. Compare your findings in parts (1) and a(2). All else being identical, which te of annuity-ordinary or annuity due-is preferable? Explain why. LG 3 P5-20 Present value of an annuity Consider the following cases. Case Amount of annuity Interest rate Period (years) $ 12,000 55,000 7% 700 140,000 22,500