Question

Internal Rate of Return

A project is estimated to cost $537,280 and provide annual net cash flows of $73,000 for 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	3.353	2.991
6	4.917	4.355	4.111	3.785	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

Determine the internal rate of return for this project, using the Present Value of an Annuity of $1 at Compound Interest table shown above.

Answer 1

Internal Rate of Return (IRR) is a method of capital budgeting and a discounted cash flow technique that takes into consideration the time value of money. IRR is that particular discounting rate at which the Net Present Value (NPV) of an investment becomes zero.

In this question, below are the given information:

a) Estimated cost of project = $537,280

b) Annual net cash flows = $73000 for next10 years (net cash flows means Inflows minus outflows)

c) A table of Present Value of an Annuity of $1 at Compound Interest

How to read this table's inputs?

Let's take the present value of an annuity of $1 at Compound Interest of 6% on the 10th year is given to be 7.360. This means that if we are to receive $1 at the end of every year for the next 10 years then after 10 years it won't be $10 (i.e. $1 x 10 years). Instead, it will be $7.360 because this takes into consideration the time value of money! (the value of money reduces with passing time)

*(Please do not confuse these inputs to be present value 'factors')

Now as mentioned above, IRR is that discount rate where NPV of the project = 0

(NPV = PV of all the cash inflows - PV of all the cash outflows over a period of time)

Therefore, NPV of the project @6% on 10th year = ($73,000 x 7.360) - ($537,280) = 0

Since at the rate of 6% the NPV is coming to be zero, our IRR is 6%

Please note: IRR usually requires a hit and trial method. So in case if we did not get NPV = 0 at 6% then we would have to calculate it for 10%, 12%, 15%, and 20% and then check at what % NPV is becoming 0 and that would have been our answer. Also, if in case NPV wouldn't be 0 at any of the above-mentioned rates, then we would have used the Interpolation formula of IRR by taking a higher (where NPV is negative) and lower rate of interest (where NPV is positive).