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Practice_Problems_2_Time_Value_of_Money

# Practice_Problems_2_Time_Value_of_Money - FIN340 PRACTICE...

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1 FIN340 PRACTICE PROBLEM SET 2 TIME VALUE OF MONEY 1. As winner of a breakfast cereal competition, you can choose one of the following prizes: (A) \$100,000 now (B) \$180,000 at the end of 5 years. (C) \$11,400 a year forever. (D) \$19,000 for each of 10 years. (E) \$6500 next year and increasing thereafter by 5% a year forever. For a discount rate is 12%, which is the most valuable prize? SOLUTION: 000 , 100 \$ = A PV ( ) 83 . 136 , 102 \$ 12 . 1 000 , 180 \$ 5 = = B PV 000 , 95 \$ 12 . 0 400 , 11 \$ = = C PV 10 \$19,000 1 1 \$107,354.24 0.12 1.12 D PV = × = \$6,500 \$92,857.14 0.12 0.05 E PV = = Therefore, choose prize D, as it offers the higest present value. 1. Calculate the present value of a “consol bond” that is expected to pay \$50 of interest per year forever. The investor requires an 8% rate of return (discount rate) and the first payment is in one year? SOLUTION: PV = 50/.08=625 2. Calculate the present value of a “consol bond” that is expected to pay \$50 of interest per year forever. The investor requires an 8% rate of return (discount rate) and the first payment is immediately? SOLUTION: PV = 50 + (50/.08) =675

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2 3. An investment offers the following year-end cash flows: 1 st year: \$20,000; 2 nd year: \$30,000; and 3 rd year: \$15,000. Using a 15% discount rate, convert this series of irregular cash flows to an equivalent (in present value terms) 3-year annuity. SOLUTION: First we need to discount the three payments to figure out their present value: PV = 17,391+22,684+9,863=49,938.36 Solving for PMT in: PVA(PMT, 3 years,15%) = 49,938.36, yields PMT = 21,871.85. 4. You have just won the Publisher’s Sweepstakes and you can either have a lump sum payment of \$1,000,000 immediately or annuity of \$100,000 per year for the rest of your life with the first payment in one year. If you expect to live 20 years and the discount rate is 10%, which alternative should you choose (ignoring taxes)? SOLUTION: PVA (\$100,000, 20 years, 10%) = 851,356.37 Take the lump payment. 5. If the interest rate in problem #5 is 7%, does this change your answer? SOLUTION: PVA (\$100,000, 20 years, 7%) = 1,059,401.42 Take the annuity. 6. What is the present value of \$1,000,000 received 10 years from now at a discount rate of 300% per year? SOLUTION: PV=\$1,000,000/(1+3.0) 10 = ¢95.37 7. It is 1/1/2001 and you will receive \$100,000 per year for the next 25 years. The payments are made on June 30 th of each year. If the annual discount rate is 10% and the 6 month rate is (1+.10) 1/2 , then what is the value of this annuity today?
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