Question

# Net Present Value Method and Internal Rate of Return Method for a service company Keystone Healthcare...

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.
%

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%

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