Question

Net Present Value

A project has estimated annual net cash flows of $10,000 for ten years and is estimated to cost $32,500. Assume a minimum acceptable rate of return of 20%. 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.The present value of annuity Factor at the rate of 20% for 10 years is 4.192.

Initial Cost= $32500

Life of Project=10 years

Annual cash inflow=$10000

Rate of Return =20%

Annual Cash Inflow=10000*4.192=$41,920

Less:Initial Investment=$32500

Net Present Value=41920-32500=$9420.

2.Present Value Index=(Present value of cash inflow)/(Investment required)

=41,920/32500 =1.29