Question

Carolina Company is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable.

WACC: 7.75%                                              

Year            0                 1           2           3          4

CFS        −$1,050     $675     $650              

CFL         −$1,050     $360     $360    $360   $360

1. If the decision is made by choosing the project with the higher IRR, how much value will be forgone?
2. What is the underlying cause of ranking conflicts between NPV and IRR?

Please include all equations including NPV. I have gone through the question myself a few times and I think I am getting the wrong answer/using the wrong equation for NPV or perhaps somewhere else. Thank you.

Answer 1

	The IRR and NPV of the projects are calculated below:
	CFS:
	Year	Cash Flow	PVIF at 7.75%	PV at 7.75%	PVIF at 18%	PV at 18%	PVIF at 17%	PV at 17%
	0	$             -1,050	1	$          -1,050	1	$        -1,050	1	$       -1,050
	1	$                  675	0.92807	$               626	0.84746	$ 572	0.85470	$ 577
	2	$                  650	0.86132	$               560	0.71818	$ 467	0.73051	$             475
	3	$                      -	0.79937	$                  -	0.60863	$                -	0.62437	$                -
	4	$                      -	0.74188	$                  -	0.51579	$                -	0.53365	$                -
	Total			$               136		$ -11		$                 2
	NPV = $136
	IRR = 17%+1%*2/(2+11) =		17.15%
	CFL:
	Year	Cash Flow	PVIF at 7.75%	PV at 7.75%	PVIF at 13%	PV at 13%	PVIF at 14%	PV at 14%
	0	$             -1,050	1	$          -1,050	1	$        -1,050	1	$       -1,050
	1	$                  360	0.92807	$               334	0.88496	$             319	0.87719	$             316
	2	$                  360	0.86132	$               310	0.78315	$             282	0.76947	$             277
	3	$                  360	0.79937	$               288	0.69305	$             249	0.67497	$             243
	4	$                  360	0.74188	$               267	0.61332	$             221	0.59208	$             213
	Total			$               149		$               21		$                -1
	NPV = $149
	IRR = 13%+1%*21/(21+1) =		13.95%
	ANSWERS:
a]	If the decision is made using IRR, Project CFS with the higher IRR of 17.15% will be chosen.
	If CFS is chosen, value equal to 149-136 = $13 will be foregone.
b]	The underlying cause of conflict in rankings between NPV and IRR, is the different reinvestment rate
	assumptions made by the two methods with respect to intervening cash flows.
	While NPV assumes that the intervening cash flows are reinvested at the WACC of MARR
	for all projects, the IRR assumes that the intervening cash flows of each project are reinvested at its own IRR.
	Thus, under the IRR method, the reinvestment rate is different for each of the projects.
	Due to this difference in the following situations for mutually exclusive projects would result in conflicting
	rankings.
	*Wide difference in initial investments of the different projects
	*Differing lives of the projects
	*Widely differing cash flow patterns