Question

Net Present Value Method and Internal Rate of Return Method for a service company

Keystone Healthcare Corp. is proposing to spend $138,216 on a nine-year project that has estimated net cash flows of $24,000 for each of the nine years.

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. Compute the net present value, using a rate of return of 12%. Use the table of present value of an annuity of $1 presented above. If required, round to the nearest dollar. Use the minus sign to indicate a negative net present value.

Present value of annual net cash flows	$
Less amount to be invested	$
Net present value	$

b. Based on the analysis prepared in part (a), is the rate of return (1) more than 12%, (2) 12%, or (3) less than 12%?
Less than 12%

c. Determine the internal rate of return by computing a present value factor for an annuity of $1 and using the table of the present value of an annuity of $1 presented above.
%

Answer 1

Net present value = Present value of cash inflows - Present value of cash outflows
Present value of annual net cash flows	127,872
Less amount to be invested	138,216
Net present value	(10,344)
IRR is the rate at which NPV = 0
Since NPV is negative at 12%, IRR is less than 12%
c.Factor value = Investment/Annual inflows
5.759
Using PVAF table, IRR = 10%