Net Present Value—Unequal Lives
Project 1 requires an original investment of $76,700. The project will yield cash flows of $12,000 per year for seven years. Project 2 has a calculated net present value of $16,500 over a five-year life. Project 1 could be sold at the end of five years for a price of $56,000.
Use the Present Value of $1 at Compound Interest and the Present Value of an Annuity of $1 at Compound Interest tables shown below.
| Present Value of $1 at Compound Interest | |||||
| Year | 6% | 10% | 12% | 15% | 20% |
| 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 0.890 | 0.826 | 0.797 | 0.756 | 0.694 |
| 3 | 0.840 | 0.751 | 0.712 | 0.658 | 0.579 |
| 4 | 0.792 | 0.683 | 0.636 | 0.572 | 0.482 |
| 5 | 0.747 | 0.621 | 0.567 | 0.497 | 0.402 |
| 6 | 0.705 | 0.564 | 0.507 | 0.432 | 0.335 |
| 7 | 0.665 | 0.513 | 0.452 | 0.376 | 0.279 |
| 8 | 0.627 | 0.467 | 0.404 | 0.327 | 0.233 |
| 9 | 0.592 | 0.424 | 0.361 | 0.284 | 0.194 |
| 10 | 0.558 | 0.386 | 0.322 | 0.247 | 0.162 |
| Present Value of an Annuity of $1 at Compound Interest | |||||
| Year | 6% | 10% | 12% | 15% | 20% |
| 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 |
| 3 | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 |
| 4 | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 |
| 5 | 4.212 | 3.791 | 3.605 | 3.352 | 2.991 |
| 6 | 4.917 | 4.355 | 4.111 | 3.784 | 3.326 |
| 7 | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 |
| 8 | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 |
| 9 | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 |
| 10 | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 |
a. Determine the net present value of Project 1
over a five-year life with residual value, assuming a minimum rate
of return of 6%. If required, round to the nearest dollar.
$
b. Which project provides the greatest net
present value?
Requirement a.
Net present value of Project 1 over a five-year life = $ 15,676
| Project 1 | |||
| Year | Cash Inflows | PV factor at 6% | Present value |
| 1 | $ 12,000.00 | 0.943 | $ 11,316.00 |
| 2 | $ 12,000.00 | 0.890 | $ 10,680.00 |
| 3 | $ 12,000.00 | 0.840 | $ 10,080.00 |
| 4 | $ 12,000.00 | 0.792 | $ 9,504.00 |
| 5 | $ 12,000.00 | 0.747 | $ 8,964.00 |
| 5 | $ 56,000.00 | 0.747 | $ 41,832.00 |
| Total | $ 92,376.00 | ||
| (-) Initial Cost | $ 76,700.00 | ||
| Net Present Value (NPV) | $ 15,676.00 | ||
Requirement b.
Project 2 has greater Net present value than Project 1
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