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BD_SM_c04 - Chapter 4 The Time Value of Money 4-1 0 1 2 3 4...

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Chapter 4 The Time Value of Money 4-1. 0 1 2 3 4 5 4000 –1000 –1000 –1000 –1000 –1000 From the bank’s perspective the timeline is the same except all the signs are reversed. 4-2. 0 1 2 3 4 312 –1500 –1500 –1500 –1500 –1500 From the bank’s perspective the timeline would be identical except with opposite signs. 4-3. a. Timeline: 0 1 2 5 2000 FV= ? 5 5 FV 2,000 1.05 2,552.56 = × = b. Timeline: 0 1 2 10 2000 FV=? 10 10 FV 2,000 1.05 3,257.79 = × =
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16 Berk/DeMarzo • Corporate Finance c. Timeline: 0 1 2 5 2000 FV= ? 5 5 FV 2,000 1.1 3,221.02 = × = d. Because in the last 5 years you get interest on the interest earned in the first 5 years as well as interest on the original $2,000. 4-4. a. Timeline: 0 1 2 3 12 PV=? 10,000 12 10,000 PV 6, 245.97 1.04 = = b. Timeline: 0 1 2 3 20 PV=? 10,000 20 10,000 PV 2,145.48 1.08 = = c. Timeline: 0 1 2 3 4 5 6 PV=? 10,000 6 10,000 PV 8,879.71 1.02 = =
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Chapter 4 The Time Value of Money 17 4-5. Timeline: 0 1 2 3 4 10 PV=? 10,000 10 10, 000 PV 5,083.49 1.07 = = So the 10,000 in 10 years is preferable because it is worth more. 4-6. Timeline: 0 1 2 3 10 PV=? 100,000 10 100,000 PV= 74, 409.39 1.03 = 4-7. Timeline: Same for all parts 0 1 2 3 4 5 PV=? 350,000 a. 5 350,000 PV 350,000 1.0 = = So you should take the 350,000 b. 5 350,000 PV 238, 204 1.08 = = You should take the 250,000. c. 5 350,000 PV 140,657 1.2 = = You should take the 250,000.
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18 Berk/DeMarzo • Corporate Finance 4-8. a. Timeline: 18 19 20 21 25 0 1 2 3 7 3,996 FV=? 7 FV 3,996(1.08) 6,848.44 = = b. Timeline: 18 19 20 21 65 0 1 2 3 47 3,996 FV ? 47 FV 3,996(1.08) 148,779 = = c. Timeline: 0 1 2 3 4 18 PV=? 3,996 18 3,996 PV 1,000 1.08 = = 4-9. a. Timeline: 0 1 2 3 10,000 20,000 30,000 2 3 10,000 20,000 30,000 PV 1.035 1.035 1.035 9,662 18,670 27, 058 55,390 = + + = + + =
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Chapter 4 The Time Value of Money 19 b. Timeline: 0 1 2 3 10,000 20,000 30,000 3 FV 55,390 1.035 61, 412 = × = 4-10. Timeline: 0 1 2 3 1,000 1,000 1,000 First, calculate the present value of the cash flows: 2 3 1,000 1,000 1,000 PV 952 907 864 2,723 1.05 1.05 1.05 = + + = + + = Once you know the present value of the cash flows, compute the future value (of this present value) at date 3. 3 3 FV 2,723 1.05 3,152 = × = 4-11. Timeline: 0 1 2 3 10 -10,000 500 1,500 10,000 a. 2 10 500 1,500 10,000 NPV 10,000 10,000 471.70 1,334.99 5,583.95 2,609.36 1.06 1.06 1.06 = − + + + = − + + + = − Since the NPV < 0, don’t take it. b. 2 10 500 1,500 10,000 NPV 10,000 10,000 490.20 1, 441.75 8, 203.48 135.43 1.02 1.02 1.02 = − + + + = − + + + = Since the NPV > 0, take it.
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20 Berk/DeMarzo • Corporate Finance 4-12. Timeline: 0 1 2 3 –1,000 4,000 –1,000 4,000 ( ) ( ) ( ) 2 3 4,000 1,000 4,000 NPV 1,000 1.02 1.02 1.02 1,000 3,921.57 961.17 3,769.29 5,729.69 = − + + = − + + = Yes, make the investment. 4-13. Timeline: 0 1 2 3 –1,000 100 100 100 To decide whether to build the machine you need to calculate the NPV. The cash flows the machine generates are a perpetuity, so by the PV of a perpetuity formula: 100 PV 1,052.63 0.095 = = So the NPV 1,052.63 1,000 52.63 = = . He should build it. 4-14. Timeline: 0 1 2 3 –1,000 100 100 To decide whether to build the machine you need to calculate the NPV: The cash flows the machine generates are a perpetuity with first payment at date 2. Computing the PV at date 1 gives 1 100 PV 1,052.63 0.095 = = So the value today is 0 1,052.63 PV 961.31 1.095 = = So the NPV 961.31 1,000 38.69 = = − He should not build the machine
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Chapter 4 The Time Value of Money 21 4-15. Timeline: 0 1 2 3 100 100 100 a. The value of the bond is equal to the present value of the cash flows. By the perpetuity formula: 100 PV 2,500 0.04 £ = = b. The value would be the same, £2,500 after each payment. 4-16. Timeline: 0 1 2 3 100 1,000 1,000 1,000 1,000 The cash flows are a 100 year annuity, so by the annuity formula: 100 1,000 1 PV 1- 14, 269.25 0.07 1.07 = = 4-17. Timeline: 0 5 10 20 0 1 2 3 1,000,000 1,000,000 1,000,000 First we need the 5-year interest rate. If the annual interest rate is 8% per year and you invest $1 for 5 years you will have, by the 2 nd
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