Chapter%20(4) - Chapter 4 NPV and The Time Value of Money...

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Chapter 4 NPV and The Time Value of Money Note: A shaded box ( ) indicates problems available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty. All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty. 1. 0 1 2 3 4 5 4,000 –1,000 –1,000 –1,000 –1,000 –1,000 From the bank’s perspective the timeline is the same except all the signs are reversed. 2. 0 1 2 3 4 48 –300 –300 –300 –300 –300 From the bank’s perspective the timeline would be identical except with opposite signs. 3. Plan: Determine the Future Values of the different interest rates and the different time periods. Compare the differences in Future Values. Execute: a. 5 5 FV 2,000 1.05 2,552.56 = 0 1 2 5 2,000 FV = ? b. 10 10 FV 2,000 1.05 3,257.79 = 0 1 2 10 2,000 FV = ?
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18 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance c. 5 5 FV 2,000 1.1 3,221.02 = 0 1 2 5 2,000 FV = ? Evaluate: Since with compound value 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, the value at the end of 5 years ($3,257,79) is significantly greater than the value after 10 years ($2,552,56). 4. a. 12 10,000 PV 1.04 6,245.97 = = 0 1 2 3 12 PV = ? 10,000 b. 20 10,000 PV 1.08 2,145.48 = = 0 1 2 3 20 PV = ? 10,000 c. 6 10,000 PV 1.02 8,879.71 = = 0 1 2 3 4 5 6 PV = ? 10,000 5. Plan: You are being offered a choice between $5,000 today and $10,000 in 10 years. One way to evaluate this decision is determine how much the $10,000 in 10 years is worth today. In this way we can compare the $5,000 today against the present value of the $10,000 in 10 years. Execute: 10 10,000 PV 1.07 5,083.49 = = 0 1 2 3 4 10 PV = ? 10,000 Evaluate: The 10,000 in 10 years is worth $5083.49 today. It is preferable to the $5,000 payment today because it is worth more.
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Chapter 4 NPV and The Time Value of Money 19 6. Plan: What your aunt and uncle want to know is what is the present value of $100,000 in six years, discounted at 4% annually. Most likely they do not think of this decision in these terms and do not use or understand this terminology. Execute: 6 100,000 PV 1.04 79,031.45 = = 0 1 2 3 6 PV = ? 100,000 Evaluate: Your aunt and uncle would have to invest $79,031.45 today at 4% compounded annual interest for it to grow in 6 years into the $100,000 they will need to finance your cousin’s education. 7. Plan: Your mom is being offered a choice in how she will take her retirement benefit: either $250,000 today or $350,000 in five years. If mom wants the alternative that is going to give her the most wealth, then she should take the alternative with the highest net present value. Your job is to determine the present values of the $350,000 in five years at different interest rates. Execute: 0 1 2 3 4 5 PV = ? 350,000 a. 5 350,000 PV 1.0 350,000 = = b. 5 350,000 PV 1.08 238,204 = = c. 5 350,000 PV 1.2 140,657 = = Evaluate: a. If the interest rate is zero, an unlikely situation, then your mom should take the 350,000 in five years. If she takes the $250,000 today and invests it zero percent for 5 years, she will have $250,000 in five years. $350,000 is better in 5 years than $250,000.
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Chapter%20(4) - Chapter 4 NPV and The Time Value of Money...

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