Question

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

Keystone Healthcare Corp. is proposing to spend $135,513 on a 10-year project that has estimated net cash flows of $27,000 for each of the 10 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 20%. 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 20%, (2) 20%, or (3) less than 20%?

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

a. Net present value = Present value annual cash flows

= annual cash flows × annuity factor at 20%.

= $27000 × 4.192

= $113184

Present value of annual cash flows	$113184
(-) amount to be invested	($135513)
Net present value	- $22329

b. 3) less than 20%

Because, when annual cash flows are converted to present value using 20% rate, the present value is less than amount to be invested. So rate of returns is less than 20%.

c. Internal rate of returns :

Internal rate of returns(IRR) is the rate at which present value of cash inflows(PVCIF) is equal to present value cash outflows(pvcof). So at the internal rate of returns PVCIF = PVCOF.

PVCIF = annual cash inflows × annuity factor at IRR.

$135513 = $27000 × annuity factor at IRR.

annuity factor at IRR = $135513/$27000.

annuity factor at IRR = 5.019

Therefore, IRR = 15% (based on annuity factor given in table).