eBook Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two
ID: 2464560 • Letter: E
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Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $73,000 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 $77,000 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 4.192
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 10%. 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
Explanation / Answer
a)
Net Present value = Present value of cash inflows - Present values of cash outflows
It hasbeen assumed that the depreciation has already been taken into account for calculating cash flows (however, as there is no tax, there will be no tax advantage of depreciation)
Blending Equipment
PV of cash inflow
= PV of annual additional cash inflow of $21000 for seven years + PV of cash inflow from the salvage value of the machine at the end of the seventh year
= $21000 * PVIFA (10%, 7) + $14000*PVIF (7%, 7)
= $21000*6.145 + $14000 * 0.386
= $134449
NPV = $134449 - $73000 = $61449
Computer System
PV of cash inflow
= PV of annual additional cash inflow of $27000 for seven years (there is no salvage value)
= $27000 * PVIFA (10%, 7)
= $27000*6.145
= $ 165915
NPV
= $ 165915 - $77000
= $ 88915
b) Present Value Index = NPV / Initial investment
PV index for blending equipment = $61449/$73000 = 0.842
PV of Computer System = $88915 / $77000 = 1.152
Recommendation: As the NPV as well as PV index for the computer system is higher than the blending machine, the computer system should be selected.
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