Question

A project will generate annual cash flows of $237,600 for each of the next three years, and a cash flow of $274,800 during the fourth year. The initial cost of the project is $765,600. What is the internal rate of return of this project?

Answer 1

IRR using excel:

Year	Cash flows
0	-$765,600
1	$237,600
2	$237,600
3	$237,600
4	$274,800
IRR =	10.76%

Excel formulas:

.

IRR using trial and error method: (without using excel function).

Here, guesswork is required. Take 2 discount rates, where one rate will discount the cash flows lower than the initial investment, and another rate which discounts the cash flows higher than the initial investment. Here I have taken 10% and 11%. You can take any other rate, but the closer the rates are the more accurate the IRR will be.

Cash outflow	$765,600
Year	Cash flows	Discount factor at 10%	Discounted cash flow at 10%	Discount factor at 11%	Discounted cash flow at 11%
1	$237,600	0.909091	$216,000.00	0.900901	$214,054.05
2	$237,600	0.826446	$196,363.64	0.811622	$192,841.49
3	$237,600	0.751315	$178,512.40	0.731191	$173,731.07
4	$274,800	0.683013	$187,692.10	0.658731	$181,019.27
Total			$778,568.13		$761,645.89

Here,
L = Lower Rate
H = Higher Rate
DCL = Discounted cash flow at the lower rate
DCH = Discounted cash flow at the higher rate

Note, there is a small difference in using trial and error method. If we take two closer rates, say 10.5% and 11%, it will give a more accurate answer.  

Discount factor formula:

Where,
i = rate of return
n = number of periods