Question

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

Answer 1

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.