Question

Net Present Value—Unequal Lives

Project 1 requires an original investment of $54,000. The project will yield cash flows of $10,000 per year for eight years. Project 2 has a calculated net present value of $10,800 over a six-year life. Project 1 could be sold at the end of six years for a price of $41,000.

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 six-year life with residual value, assuming a minimum rate of return of 10%. If required, round to the nearest dollar.
$

b. Which project provides the greatest net present value?

Answer 1

For project 1

Initial investment = $54,000

Annual cash inflow = $10,000

Residual value = $41,000

Time period (n) = 6 years

Interest rate (i) = 10%

Present value of cash inflows = Annual cash inflow x Present value annuity factor (i%,n) + Residual value x Present value factory (i%,n)

= 10,000 x Present value annuity factor (10%,6) + 41,000 x Present value factor (10%,6)

= 10,000 x 4.355 + 41,000 x 0.564

= 43,550+23,124

= $66,674

Net present value = Present value of cash inflows- Initial investment

= 66,674-54,000

= $12,674

b.

For project 2

Net present value = $10,800

Project 1 has higher net present value.

Kindly comment if you need further assistance.

Thanks‼!