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.
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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.
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