Question

Keystone Healthcare Corp. is proposing to spend $150,570 on a 10-year project that has estimated net cash flows of $30,000 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.NPV = present value of cash flows-Initial outlay

we will iuse annuity factor of $1 at 20% to find present value of cash flows.

As there is uniform series of cash flow each year we will use annuity

PV factor at 20% for year 10 =4.192

Present value of annual net cash flows	$125,760[$30,000*4.192]
Less amount to be invested	$150,570
Net present value	-$24,810

Cash outflow> present value of cash inflows. So, NPV is -$24,810

b.As NPV is negative at 20%, The rate of return is lower than 20%.

C. IRR is the rate at which the present value of cash inflows= Initial cash outlay.

at IRR, NPV = 0

SUppose annuity factor is X

NPV = $30,000*X-$150,570

0=$30,000X-$150,570

X=5.019

As we can see from the table at 15% annuity factor is 5.019 at year 10

so IRR = 15%

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