Question

NPV versus IRR [LO1, 5] Bruin, Inc., has identified the following two mutually exclusive projects:

a. What is the IRR for each of these projects? Using the IRR decision rule, which project should the company accept? Is this decision necessarily correct? 

b. If the required return is 11 percent, what is the NPV for each of these projects? Which project will the company choose if it applies the NPV decision rule?

Answer 1

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash oUtflows

Project A:

Year	CF	PVf @19%	Disc CF	PVF @20%	Disc CF
0	$ -37,500.00	1.0000	$ -37,500.00	1.0000	$ -37,500.00
1	$ 17,300.00	0.8403	$ 14,537.82	0.8333	$ 14,416.67
2	$ 16,200.00	0.7062	$ 11,439.87	0.6944	$ 11,250.00
3	$ 13,800.00	0.5934	$    8,189.14	0.5787	$    7,986.11
4	$    7,600.00	0.4987	$    3,789.88	0.4823	$    3,665.12
NPV			$        456.71		$      -182.10

IRR = rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in diusc Rate ] * 1%

= 19% + [ 456.71 / 638.80 ] * 1%

= 19% + 0.71%

= 19.71%

Project B:

Year	CF	PVf @18%	Disc CF	PVF @19%	Disc CF
0	$ -37,500.00	1.0000	$ -37,500.00	1.0000	$ -37,500.00
1	$    5,700.00	0.8475	$    4,830.51	0.8403	$    4,789.92
2	$ 12,900.00	0.7182	$    9,264.58	0.7062	$    9,109.53
3	$ 16,300.00	0.6086	$    9,920.68	0.5934	$    9,672.68
4	$ 27,500.00	0.5158	$ 14,184.19	0.4987	$ 13,713.39
NPV			$        699.96		$      -214.49

IRR = rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in diusc Rate ] * 1%

= 18% + [ 699.96 / 914.45 ] * 1%

= 18% + 0.77%

= 18.77%

\Project A is selected as it has higher IRR

NPV = PV of Cash Inflows - PV of Cash Outflows

Project A:

Year	CF	PVf @11%	Disc CF
0	$ -37,500.00	1.0000	$ -37,500.00
1	$ 17,300.00	0.9009	$ 15,585.59
2	$ 16,200.00	0.8116	$ 13,148.28
3	$ 13,800.00	0.7312	$ 10,090.44
4	$    7,600.00	0.6587	$    5,006.36
NPV			$    6,330.67

Project B:

Year	CF	PVf @11%	Disc CF
0	$ -37,500.00	1.0000	$ -37,500.00
1	$    5,700.00	0.9009	$    5,135.14
2	$ 12,900.00	0.8116	$ 10,469.93
3	$ 16,300.00	0.7312	$ 11,918.42
4	$ 27,500.00	0.6587	$ 18,115.10
NPV			$    8,138.59

Project B is selected as it has higher NPV