Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

0

1

2

3

4

Project S	-$1,000	$877.71	$250	$15	$10
Project L	-$1,000	$10	$240	$380	$842.17

The company's WACC is 10.5%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.

Answer 1

IRR is the Discount rate at which present value of inflows equals present value of outflows. Unlike NPV method, which uses a known discount rate,IRR itself provide a discount rate at which NPV of the project is zero.IRR can be find out by trial and error method.For this,we have to find our NPV at two different discount rates,say DF1 and DF2.Let NPV1 and NPV2 are respective NPV for DF1 and DF2.IRR=DF1+{NPV1/(NPV1-NPV2)}*(DF2-DF1)

Project s-we may first use discount rates 11%

YEAR	DF@11%	Cash Flow	Discounted cash flow
0	1	-1000	(1,000.00)
1	0.900901	877.71	790.73
2	0.811622	250	202.91
3	0.731191	15	10.97
4	0.658731	10	6.59
	NPV@11%		11.19

As we got and NPV which is positive,Let us try with a higher NPV because for accurate IRR,it is better to get a negative NPV and a positive NPV ,as small as possible.

YEAR	DF@12%	Cash Flow	Discounted cash flow
0	1	$-1000	$(1,000.00)
1	0.892857	$877.71	$783.67
2	0.797194	$250	$199.30
3	0.71178	$15	$10.68
4	0.635518	$10	$6.36
	NPV@12%		0.00

At discount rate 12%,we get NPV=0,so for project S, no need to use formula.IRR=12% itself.

Project L

First try with 11%

YEAR	DF@11%	Cash Flow	Discounted cash flow
0	1	-1000	$(1,000.00)
1	0.900901	10	$9.01
2	0.811622	240	$194.79
3	0.731191	380	$277.85
4	0.658731	842.17	$554.76
	NPV@11%		$36.41

As NPV is $36.41,a little higher,we may us 13% instead of 12%,to get negative NPV

YEAR	DF@13%	Cash Flow	Discounted cash flow
0	1	$ (1,000.00)	$                      (1,000.00)
59.731	0.884956	$         10.00	$                                 8.85
2	0.783147	$       240.00	$                            187.96
3	0.69305	$       380.00	$                            263.36
4	0.613319	$       842.17	$                            516.52
	NPV@13%		$                            (23.32)

IRR=11%+{36.41/(36.41- -23.32)*(13-11)}

=11%+{(36.41/59.73)*2}

=11%+1.219%=12.22%

Thus IRR for project L is 12.219% better than IRR for project S which is 12%.

Higher IRR means project is profitable even at higher discount rate.So higher IRR is better

So IRR is better for project L and it 12.22%