X-treme Vitamin Company is considering two investments, both of which cost $11,000. The cash flows are as follows:
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| Year | Project A | Project B | ||||
| 1 | $ | 15,000 | $ | 8,000 | ||
| 2 | 6,000 | 5,000 | ||||
| 3 | 5,000 | 10,000 | ||||
Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.
|
| a-1. |
Calculate the payback period for Project A and Project B. (Round your answers to 2 decimal places.)
|
| Payback Period | |
| Project A | year(s) |
| Project B | year(s) |
| a-2. | Which of the two projects should be chosen based on the payback method? |
| Project A |
| b-1. |
Calculate the net present value for Project A and Project B. Assume a cost of capital of 8 percent.(Do not round intermediate calculations and round your final answers to 2 decimal places.)
|
| Net Present Value | |
| Project A | $ |
| Project B | $ |
| b-2. |
Which of the two projects should be chosen based on the net present value method?
|
| Project A |
| c. | Should a firm normally have more confidence in the payback method or the net present value method? |
| Net present value method |
Explanation:
a-1.
| Project A: |
| Cash flows | Amount yet to be Recovered | |||||
| Initial investment | $ | 11,000 | ||||
| Year 1 | $ | 15,000 | 0 | |||
| Year 2 | 6,000 | 0 | ||||
| Year 3 | 5,000 | 0 | ||||
| The initial investment is fully recovered between Year 0 and Year 1. The partial year is computed as the amount that still needs to be recovered at the end of Year 0 divided by the Year 1 cash flow, so: |
| Payback periodA | = 0 + ($11,000 / $15,000) |
| = .73 year(s) |
| Project B: |
| Cash flows | Amount yet to be Recovered | |||||
| Initial investment | $ | 11,000 | ||||
| Year 1 | $ | 8,000 | 3,000 | |||
| Year 2 | 5,000 | 0 | ||||
| Year 3 | 10,000 | 0 | ||||
| The initial investment is fully recovered between Year 1 and Year 2. The partial year is computed as the amount that still needs to be recovered at the end of Year 1 divided by the Year 2 cash flow, so: |
| Payback periodB | = 1 + ($3,000 / $5,000) |
| = 1.60 year(s) |
a-2.
| Under the payback method, you should select Project A because of the shorter payback period. |
b-1.
| Net present valueA | = | −$11,000 + ($15,000 / 1.08) + ($6,000 / 1.082) + ($5,000 / 1.083) |
| = | $12,002.08 | |
| Net present valueB | = | −$11,000 + ($8,000 / 1.08) + ($5,000 / 1.082) + ($10,000 / 1.083) |
| = | $8,632.42 |
b-2.
Under the net present value method, you should select Project A because of the higher net present value.
|
c.
A firm should normally have more confidence in the net present value method because it considers all of a project's cash flows and also the time value of money.
|
| Calculator Solution: |
| b-1. |
Project A:
|
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CF0, enter 11,000 +|- key, press the Enter key. |
| Press down arrow, enter 15,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press down arrow, enter 6,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press down arrow, enter 5,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press NPV; calculator shows I = 0; enter 8 and press Enter. |
| Press down arrow; calculator shows NPV = 0. |
| Press CPT; calculator shows NPV = 12,002.08. |
b-2.
Project B:
|
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CF0, enter 11,000 +|- key, press Enter key |
| Press down arrow, enter 8,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press down arrow, enter 5,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press down arrow, enter 10,000 and press Enter. |
| Press down arrow, enter 1 and press Enter. |
| Press NPV; calculator shows I = 0; enter 8 and press Enter. |
| Press down arrow; calculator shows NPV = 0. |
| Press CPT; calculator shows NPV = 8,632.42. |
Under the net present value method, you should select Project A because of the higher net present value.
|
| Appendix Solutions: |
| Project A | |||||||||||
| Year | Cash Flow | PVIF | Present Value | ||||||||
| 1 | $ | 15,000 | .926 | $ | 13,890 | ||||||
| 2 | 6,000 | .857 | 5,142 | ||||||||
| 3 | 5,000 | .794 | 3,970 | ||||||||
| Present value of inflows | $ | 23,002 | |||||||||
| Present value of outflows | 11,000 | ||||||||||
| Net present value | $ | 12,002 | |||||||||
| Project B | |||||||||||
| Year | Cash Flow | PVIF | Present Value | ||||||||
| 1 | $ | 8,000 | .926 | $ | 7,408 | ||||||
| 2 | 5,000 | .857 | 4,285 | ||||||||
| 3 | 10,000 | .794 | 7,940 | ||||||||
| Present value of inflows | $ | 19,633 | |||||||||
| Present value of outflows | 11,000 | ||||||||||
| Net present value | $ | 8,633 | |||||||||
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