Question

Net Present Value—Unequal Lives Project 1 requires an original investment of $79,500. The project will yield cash flows of $11,000 per year for 9 years. Project 2 has a computed net present value of $21,200 over a seven-year life. Project 1 could be sold at the end of seven years for a price of $57,000. Use the Present Value of $1 at Compound Interest and the Present Value of an Annuity of $1 at Compound Interest tables shown below.

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	3.353	2.991
6	4.917	4.355	4.111	3.785	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

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	3.456	3.170	3.037	2.855	2.589
5	4.212	3.791	3.605	3.353	2.991
6	4.917	4.355	4.111	3.785	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

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

Answer 1

Original investment = $79,500

Annual cash inflow = $11,000

Time period (n) = 7 years

Residual value after 7 years = $57,000

Interest rate (i) = 6%

Present value of cash inflows = Annual cash inflow x Present value annuity factor (i%, n) + Residual value after 7 years x Present value factor (i%, n)

= 11,000 x Present value annuity factor (6%, 7) + 57,000 x Present value factor (6%, 7)

= 11,000 x 5.582 + 57,000 x 0.665

= 61,402 + 37,905

= $99,307

net present value of Project 1 = Present value of cash inflows - Original investment

= 99,307 - 79,500

= $19,807

Please ask if you have any query related to the question. Thank you