Question

Net Present Value—Unequal Lives Project 1 requires an original investment of $76,700. The project will yield...

Net Present Value—Unequal Lives

Project 1 requires an original investment of $76,700. The project will yield cash flows of $12,000 per year for seven years. Project 2 has a calculated net present value of $16,500 over a five-year life. Project 1 could be sold at the end of five years for a price of $56,000.

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

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

a. Determine the net present value of Project 1 over a five-year life with residual value, assuming a minimum rate of return of 6%. If required, round to the nearest dollar.
$

b. Which project provides the greatest net present value?

Homework Answers

Answer #1

Requirement a.

Net present value of Project 1 over a five-year life = $ 15,676

Project 1
Year Cash Inflows PV factor at 6% Present value
1 $       12,000.00 0.943 $      11,316.00
2 $       12,000.00 0.890 $      10,680.00
3 $       12,000.00 0.840 $      10,080.00
4 $       12,000.00 0.792 $         9,504.00
5 $       12,000.00 0.747 $         8,964.00
5 $       56,000.00 0.747 $      41,832.00
Total $      92,376.00
(-) Initial Cost $      76,700.00
Net Present Value (NPV) $      15,676.00

Requirement b.

Project 2 has greater Net present value than Project 1

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