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CHAPTER 6
DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions
1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and the
9. The problem is that the subsidy makes it easier to repay the loan, not obtain it. However, ability to
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10. In general, viatical settlements are ethical. In the case of a viatical settlement, it is simply an exchange
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
1. The time line is:
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2. The times lines are:
3. The time line is:
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4. To find the PVA, we use the equation:
5. The time line is:
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6. The time line is:
7. Here we need to find the FVA. The equation to find the FVA is:
8. The time line is:
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9. The time line is:
10. The time line is:
11. The time line is:
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12. For discrete compounding, to find the EAR, we use the equation:
13. Here we are given the EAR and need to find the APR. Using the equation for discrete compounding:
14. For discrete compounding, to find the EAR, we use the equation:
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15. The reported rate is the APR, so we need to convert the EAR to an APR as follows:
16. The time line is:
17. For this problem, we simply need to find the FV of a lump sum using the equation:
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18. The time line is:
19. The APR is simply the interest rate per period times the number of periods in a year. In this case, the
20. The time line is:
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21. The time line is:
22. The time line is:
23. The time line is:
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24. The time line is:
25. The time line is:
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26. The time line is:
27. The time line is:
28. The time line is:
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Intermediate
29. The total interest paid by First Simple Bank is the interest rate per period times the number of periods.
30. Here we need to convert an EAR into interest rates for different compounding periods. Using the
31. Here we need to find the FV of a lump sum, with a changing interest rate. We must do this problem in
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32. Although the stock and bond accounts have different interest rates, we can draw one time line, but we
33. We need to find the FV of a lump sum in one year and two years. It is important that we use the
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period is the same as the number of periods we use to calculate the FV.
34. Here we are finding the annuity payment necessary to achieve the same FV. The interest rate given is
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35. The time line is:
36. Here we need to compare two cash flows, so we will find the value today of both sets of cash flows.
37. We can use the present value of a growing annuity equation to find the value of your deposits today.
38. Since your salary grows at 3 percent per year, your salary next year will be:
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39. The time line is:
40. The time line is:
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41. The time line is:
42. The time line is:
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43. The time line is:
44. To solve this problem, we simply need to find the PV of each lump sum and add them together. It is
45. Here we are finding the interest rate for an annuity cash flow. We are given the PVA, number of
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Using the PVA equation:
46. The time line is:
47. The time line is:
