Question

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

Keystone Healthcare Corp. is proposing to spend $228,160 on a 10-year project that has estimated net cash flows of $31,000 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 10%. 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 10%, (2) 10%, or (3) less than 10%?

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

Solution:

a)Calculation of Net Present Value :

Net Present Value = Present Value of Net Cash Inflow - Intial Amount to be Invested

Here,

Present Value of Cash Inflow = Net Cash Flows * Compound PV factor of $1 Annuity @ 10 % for 10 Years

= $ 31,000 * 6.145

= $ 190,495

Therefore,

Net Present Value = $190,495 - $ 228,160

Net Present Value = ( $37,665)

b)

Based on analysis calculated above Net present Value is Negative at 10 %. Therefore the rate of return of the project is less than 10%.

c) Calculation of Internal Rate of Return

Present Value Factor = Initial Investment / Annual Cash Inflow

= $ 228,160 / $31,000

= 7.360

As we can see in Annuity Table for $1 given in question, Compound PV Factor of $1 Annuity @ 6% for 10 Years is 7.360

Therefore, Internal Rate of Return will be = 6%