Question 25.5: Project 1 requires an original investment of $50,000. The pr...
Project 1 requires an original investment of $50,000. The project will yield cash flows of $12,000 per year for seven years. Project 2 has a calculated net present value of $8,900 over a five-year life. Project 1 could be sold at the end of five years for a price of $30,000. (a) Determine the net present value of Project 1 over a five-year life, with residual value, assuming a minimum rate of return of 12%. (b) Which project provides the greatest net present value?
Project 1
a. Present value of $12,000 per year at 12% for 5 years $43,260 [$12,000 × 3.605 (Exhibit 2, 12%, 5 years)]
Present value of $30,000 at 12% at the end of 5 years 17,010 [$30,000 × 0.567 (Exhibit 1, 12%, 5 years)]
Total present value of Project 1 $60,270
Total cost of Project 1 50,000
Net present value of Project 1 \underline{\underline{\$ \ 10,270}}
| EXHIBIT 1 : Partial Present Value of $1 Table | |||||
| 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 |
| EXHIBIT 2 : Partial Present Value of an Annuity Table | |||||
| 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 | 3.353 | 2.991 |
| 6 | 4.917 | 4.355 | 4.111 | 3.785 | 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 |
b. Project 1—$10,270 is greater than the net present value of Project 2, $8,900