Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two inves
ID: 2560850 • Letter: N
Question
Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $68,000 investment in new blending equipment that is expected to produce equal annual cash flows of $21,000 for each of seven years. Option 2 is a $76,000 investment in a new computer system that is expected to produce equal annual cash flows of $27,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $14,000. The computer system has no expected residual value at the end of the fifth year.
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 12%. Use the present value tables appearing above.
a. Determine the net present values of the two projects.
b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.
Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
SelectBlending EquipmentComputer SystemItem 9
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Exercise 26-22 (Algorithmic)
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Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $68,000 investment in new blending equipment that is expected to produce equal annual cash flows of $21,000 for each of seven years. Option 2 is a $76,000 investment in a new computer system that is expected to produce equal annual cash flows of $27,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $14,000. 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 4.192Assume 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 12%. 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 SystemWhich project should be selected? (If both present value indices are the same, either project will grade as correct.)
SelectBlending EquipmentComputer SystemItem 9
Explanation / Answer
Present value of Annual Cash inflows of both the projects: Blending Equipment: Annual Cash inflows: $21,000 Life: 7 years Minimum rate of return 12% Annuity factor for 7 years at 12% 4.564 (0.893+0.797+0.712+0.636+0.567+0.507+0.452) Present Value of Cash inflows ( 21,000 * Annuity factor i.e. 4.564 ) = $95844 Computer System: Annual Cash inflows: $27,000 Life: 5 years Minimum rate of return 12% Annuity factor for 5 years at 12% 3.605 (0.893+0.797+0.712+0.636+0.567) Present Value of Cash inflows ( 27,000 * Annuity factor i.e. 3.605 ) = $97335 ReqA:Net Present values of projects: Blending Computer Machine System Total Present values of cash inflows 95,844 97,335 (See note) Less: Amount to be invested 68,000 76,000 Net Present Values 27,844 21,335 Project of Blending Machine to be accepted ReqB: Present Value index for both projects Blending Computer Machine System Present value of Cash inflows 95844 97335 Initial Investment 68000 76000 Present Value iNdex 1.41 1.28 (Present value of inflow/Outflow) Present value iNdex Project Blending Machine 1.41 Project Computer System 1.28 Project Blending Machine should be accepted