Question

Net Present Value

A project has estimated annual net cash flows of $5,000 for nine years and is estimated to cost $30,000. Assume a minimum acceptable rate of return of 12%. 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	3.353	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 (a) the net present value of the project and (b) the present value index. If required, use the minus sign to indicate a negative net present value.

Net present value of the project (round to the nearest dollar)	$
Present value index (rounded to two decimal places)

Answer 1

Required answers are as follows

Net Present Value (NPV)	- $3,360	See working notes 1
Present Value Index	- 0.11	See working notes 2

Working Notes

1. Calculation of Net Present Value (NPV ) of the project if minimum acceptable rate of return is 12% and project generate cash flows for 9 years

By formula Net Presen Value (NPV) = Present value of future cash flows - Present value of Initial Investment Costs

Present value of future cash flows = Annual net cash flows X sum of present value of annuity for nine years

= $ 5,000 X 5.328

= $ 26,640

Present value of Initial Investment Costs = $ 30,000 given in the question

Now NPV = $ 26,640 - $ 30,000

NPV = - $ 3,360

2. Calculation of Present Value Index

By formula Present Value Index = NPV / Initial Investment Costs

= - $ 3,360 / $ 30,000

= - 0.11