Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $42,000 investment in new blending equipment that is expected to produce equal annual cash flows of $14,000 for each of seven years. Option 2 is a $48,000 investment in a new computer system that is expected to produce equal annual cash flows of $18,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $9,000. The computer system has no expected residual value at the end of the fifth year.
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
Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 15%. Use the present value tables appearing above.
a. Determine the net present values of the two projects.
Blending Equipment Computer System Total present value of cash flows $ $ Less amount to be invested $ $ Net present value $ $
b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.
Present Value Index Blending Equipment Computer System
Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
Computer System
Feedback
a. For each investment, determine the present value of the cash flows at 15% for 5 years, Exhibit 5. Use the residual value of the Blending Equipment to equate useful lives (Exhibit 2). Subtract the amount to be invested.
b. Divide the total present value of the cash flows by the amount to be invested. What do the present value indexes indicate about the net present values?
Learning Objective 3, Learning Objective 4.
Check My Work
Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $42,000 investment in new blending equipment that is expected to produce equal annual cash flows of $14,000 for each of seven years. Option 2 is a $48,000 investment in a new computer system that is expected to produce equal annual cash flows of $18,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $9,000. The computer system has no expected residual value at the end of the fifth year.
| 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 |
Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 15%. Use the present value tables appearing above.
a. Determine the net present values of the two projects.
| Blending Equipment | Computer System | |
| Total present value of cash flows | $ | $ |
| Less amount to be invested | $ | $ |
| Net present value | $ | $ |
b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.
| Present Value Index | |
| Blending Equipment | |
| Computer System |
Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
Computer System
Feedback
a. For each investment, determine the present value of the cash flows at 15% for 5 years, Exhibit 5. Use the residual value of the Blending Equipment to equate useful lives (Exhibit 2). Subtract the amount to be invested.
b. Divide the total present value of the cash flows by the amount to be invested. What do the present value indexes indicate about the net present values?
Learning Objective 3, Learning Objective 4.
Check My Work
Related questions
Average Rate of Return Method, Net Present Value Method, and Analysis
The capital investment committee of Cross Continent Trucking Inc. is considering two capital investments. The estimated income from operations and net cash flows from each investment are as follows:
| Warehouse | Tracking Technology | |||||||||
| Year | Income from Operations | Net Cash Flow | Income from Operations | Net Cash Flow | ||||||
| 1 | $61,600 | $186,000 | $129,000 | $298,000 | ||||||
| 2 | 61,600 | 186,000 | 99,000 | 251,000 | ||||||
| 3 | 61,600 | 186,000 | 49,000 | 177,000 | ||||||
| 4 | 61,600 | 186,000 | 22,000 | 121,000 | ||||||
| 5 | 61,600 | 186,000 | 9,000 | 83,000 | ||||||
| Total | $308,000 | $930,000 | $308,000 | $930,000 | ||||||
Each project requires an investment of $560,000. Straight-line depreciation will be used, and no residual value is expected. The committee has selected a rate of 15% for purposes of the net present value analysis.
| 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 |
Required:
1a. Compute the average rate of return for each investment. If required, round your answer to one decimal place.
| Average Rate of Return | |
| Warehouse | % |
| Tracking Technology | % |
1b. Compute the net present value for each investment. Use the present value of $1 table above. If required, use the minus sign to indicate a negative net present value.
| Warehouse | Tracking Technology | |
| Present value of net cash flow total | $ | $ |
| Less amount to be invested | $ | $ |
| Net present value | $ | $ |
2. The warehouse has a SelectlargersmallerItem 9 net present value because SelectlargersmallerItem 10 cash flows occur earlier in time compared to the tracking technology. Thus, if only one of the two projects can be accepted, the Selecttracking technologywarehouseItem 11 would be the more attractive.
