Question

Net Present Value

A project has estimated annual net cash flows of $11,250 for five years and is estimated to cost $46,950. Assume a minimum acceptable rate of return of 15%. Use the Present Value of an Annuity of $1 at Compound Interest table below.

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

Determine (1) the net present value of the project (if required, round to the nearest dollar) and (2) the present value index (rounded to two decimal places). If required, use the minus sign to indicate a negative net present value.

(1) Net present value of the project	$
(2) Present value index

Answer 1

1. Determination of the net present value of the project:

Computation of net present value (NPV):

NPV = Net present value (NPV) = present value of cash inflows – present value of cash outflows

Given information,

Initial cost $46,950

Cash inflows for 5 years = $11,250

salvage value =0

rate of return = 15%

Period – 5 years

Net Present Value = $11,250 (P/A, 15%, 5) - $46,950 x 1.00

NPV = 11,250 x 3.352 – 46,950

= 37,710 – 46,950

NPV = - $9,240

Net Present Value of the Project = ($9,240)

1. Present value index:

Present value index = present value of future cash inflows/initial investment

Present value index = 37,710/46950 = 0.803

The present value index is less than 1, which indicates that the project is not profitable.