5. Net Present Value—Unequal Lives Project 1 requires an original investment of

Question

5.

Net Present Value—Unequal Lives

Project 1 requires an original investment of $125,000. The project will yield cash flows of $50,000 per year for 10 years. Project 2 has a calculated net present value of $135,000 over an eight-year life. Project 1 could be sold at the end of eight years for a price of $8,000.

Use the Present Value of $1 at Compound Interest and the Present Value of an Annuity of $1 at Compound Interest tables shown below.

a. Determine the net present value of Project 1 over an eight-year life, with residual value, assuming a minimum rate of return of 12%. If required, round to the nearest dollar.
$

b. Which project provides the greatest net present value?
Project 2

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

Explanation / Answer

a) Present value of cash inflows of $50,000 over 8 years = $50,000*Annuity factor(8 years,12%)

= $50,000*4.968 = $248,400

Present value of sale of project 1 at the end of 8 years = Sale value*PVF(8 years,12%)

= $8,000*0.404 = $3,232

Present value of cash outflow = $125,000

Total Present value of cash inflows = $248,400+$3,232 = $251,632

Net present value of project 1 for 8 years = PV of cash inflows - PV of cash outflows

= $251,632 - $125,000 = $126,632

b) The net present value of project 1 is $126,632 whereas the net present value of project 2 is $135,000. Therefore the project 2 provides the greatest net present value.

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