Turner Video will invest $52,500 in a project. The firm’s cost of capital is 9 percent. The investment will provide the following inflows. Use Appendix A for an approximate answer but calculate your final answer using the formula and financial calculator methods.
|
| Year | Inflow |
| 1 | $ 12,000 |
| 2 | 14,000 |
| 3 | 18,000 |
| 4 | 22,000 |
| 5 | 26,000 |
| The internal rate of return is 12 percent. |
| a. |
If the reinvestment assumption of the net present value method is used, what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.) (Do not round intermediate calculations and round your answer to 2 decimal places.)
|
| Total value of inflows | $ |
| b. |
If the reinvestment assumption of the internal rate of return method is used, what will be the total value of the inflows after five years? (Use the given internal rate of return. Do not round intermediate calculations and round your answer to 2 decimal places.)
|
| Total value of inflows | $ |
| c. | Which investment assumption is better? |
| Reinvestment assumption of NPV |
Explanation:
a.
| FV of cash inflows | = | ($12,000 × 1.094) + ($14,000 × 1.093) + ($18,000 × 1.092) + ($22,000 × 1.09) + $26,000 |
| = | $106,435.19 |
b.
| FV of cash inflows | = | ($12,000 × 1.124) + ($14,000 × 1.123) + ($18,000 × 1.122) + ($22,000 × 1.12) + $26,000 |
| = | $111,770.42 |
c.
The net present value method is preferable. This is especially true if a project has a high IRR as it may be unrealistic to assume that reinvestments can earn an equally high rate.
|
a.
| Calculator Solution: |
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CF0, enter 0, press the Enter key. |
| Press down arrow, enter 12,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 14,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 18,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 22,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 26,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press NPV; calculator shows I = 0; enter 9 and press Enter. |
| Press down arrow; calculator shows NPV = 0. |
| Press CPT; calculator shows NPV = 69,175.57. |
| Next, find the FV of the $69,175.57 as of year 5 at an annual rate of 9 percent. |
N
|
I/Y
|
PV
|
PMT
|
FV
| ||||||||||
5
|
9
|
69,175.57
|
0
|
CPT FV − 106,435.19
| ||||||||||
| Answer: $106,435.19 |
| If your calculator will solve for a net future value you can compute the answer directly without going through this last step. |
b.
| Calculator Solution: |
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CF0, enter 0, press the Enter key. |
| Press down arrow, enter 12,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 14,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 18,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 22,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press down arrow, enter 26,000, and press Enter. |
| Press down arrow, enter 1, and press Enter. |
| Press NPV; calculator shows I = 0; enter 12 and press Enter. |
| Press down arrow; calculator shows NPV = 0. |
| Press CPT; calculator shows NPV = 63,421.54. |
| Next, find the FV of the $63,421.54 as of year 5 at an annual rate of 12 percent. |
N
|
I/Y
|
PV
|
PMT
|
FV
| ||||||||||
5
|
12
|
63,421.54
|
0
|
CPT FV − 111,770.42
| ||||||||||
| Answer: $111,770.42 |
| If your calculator will solve for a net future value you can compute the answer directly without going through this last step. |
Appendix Solutions:
a.
| Reinvestment assumption of NPV: |
| Year | Inflows | Rate | No. of Periods | Future Value Factor | Value | ||||
| 1 | $ | 12,000 | 9% | 4 | 1.412 | $ | 16,944 | ||
| 2 | 14,000 | 9% | 3 | 1.295 | 18,130 | ||||
| 3 | 18,000 | 9% | 2 | 1.188 | 21,384 | ||||
| 4 | 22,000 | 9% | 1 | 1.090 | 23,980 | ||||
| 5 | 26,000 | – | 0 | 1.000 | 26,000 | ||||
| $ | 106,438 | ||||||||
b.
| Reinvestment assumption of IRR: |
| Year | Inflows | Rate | No. of Periods | Future Value Factor | Value | ||||
| 1 | $ | 12,000 | 12% | 4 | 1.574 | $ | 18,888 | ||
| 2 | 14,000 | 12% | 3 | 1.405 | 19,670 | ||||
| 3 | 18,000 | 12% | 2 | 1.254 | 22,572 | ||||
| 4 | 22,000 | 12% | 1 | 1.120 | 24,640 | ||||
| 5 | 26,000 | – | 0 | 1.000 | 26,000 | ||||
| $ | 111,770 | ||||||||
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