Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two inves
ID: 2500384 • Letter: N
Question
Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $51,000 investment in new blending equipment that is expected to produce equal annual cash flows of $15,000 for each of seven years. Option 2 is a $57,000 investment in a new computer system that is expected to produce equal annual cash flows of $19,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $10,000. 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 10%. 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.
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 0.162Explanation / Answer
Net present value =CF1/(1+r)+ CF2/(1+r)^2 +CF3/(1+r)^3+CF4/(1+r)^4+CF5/(1+r)^5
New Blending Equipment =15000/ (1+.10) + 15000/ (1+.10) ^2 +15000/ (1+.10) ^3+15000/ (1+.10) ^4+15000/ (1+.10) ^5+15000/(1+.10)^6+15000/(1+.10)^7 – 51000=41168.51
New computer system=19000/(1+.10) + 19000/(1+.10)^2 + 19000/(1+.10)^3+19000/(1+.10)^4+19000/(1+.10)^5+10000/(1+.10)^5-51000=78234.16
Profitability index=Present value of cash inflows/Present value of cash outflows
New Blending Equipment
=92168.51/51000=1.80
New computer system
=78234.16/51000=1.53
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