Question

# Net Present Value—Unequal Lives Project 1 requires an original investment of \$50,300. The project will yield...

Net Present Value—Unequal Lives

Project 1 requires an original investment of \$50,300. The project will yield cash flows of \$12,000 per year for five years. Project 2 has a calculated net present value of \$14,600 over a three-year life. Project 1 could be sold at the end of three years for a price of \$49,000.

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 three-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

A. Determination of NPV

NPV=Present value of cash flows- Initial Investment

Initial Investment=50300

Present Value of future cash flows= 12000 PVAF(12%,3yr)+ 49000 PVIF(12%,3)

Present Value of future cash flows= (12000*2.402)+(49000*0.712)

Present Value of future cash flows= 28824+34888

Present Value of future cash flows=63712

So, NPV of Project= 63712-50300

NPV of Project=13412

B. It is not clear which required rate of return is to be used, so we are using 12%. Further it is clear that net present value of project 1 will always be greater when it will be sold in 3year.

NPV of Project A= 13412

NPV of Project B= 14600

Conclusion- Project B has greater NPV.