Question

# Keystone Healthcare Corp. is proposing to spend \$150,570 on a 10-year project that has estimated net...

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.
%

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%