Question

A firm is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO wants to use the IRR criterion, while the CFO favors the NPV method, and you were hired to advise the firm on the best procedure. If the CEO's preferred criterion is used, how much value will the firm lose as a result of this decision?
WACC:		13.00%
			0		1	2	3	4
CFS			-$1,025		$375	$380	$385	$390
CFL			-$2,150		$750	$759	$768	$777

Answer 1

Let irr be x%
At irr,present value of inflows=present value of outflows.

S:

1025=375/1.0x+380/1.0x^2+385/1.0x^3+390/1.0x^4

Hence x=irr=18.06%(Approx)

L:

2150=750/1.0x+759/1.0x^2+768/1.0x^3+777/1.0x^4

Hence x=irr=15.58%(Approx)

Hence S must be chosen having higher IRR as per CEO.

However:

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

S:

Present value of inflows=375/1.13+380/1.13^2+385/1.13^3+390/1.13^4

=$1135.47

NPV=Present value of inflows-Present value of outflows

=$1135.47-$1025

=$110.47(Approx)

L:

Present value of inflows=750/1.13+759/1.13^2+768/1.13^3+777/1.13^4

=$2266.94

NPV=Present value of inflows-Present value of outflows

=$2266.94-$2150

=$116.94

Hence firm would lose NPV of =$116.94-$110.47

=$6.47(Approx)