Question

Question 14:

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

r:	6.00%
Year	0	1	2	3	4
CFS	−$1,025	$380	$380	$380	$380
CFL	−$2,150	$765	$765	$765	$765

The CEO wants to use the IRR criterion, while the CFO favors the NPV method.

You were hired to advise on the best procedure. If the wrong decision criterion is used, how much potential value would the firm lose?

(this question is very challenging. It is fine if you can figure out the solution.)

Answer 1

IRR is the internal rate of return such that the Net Present Value of a set of cashflows from an investment/project will equal to its initial investment. This inturn determines the performance return of the project investment.

NPV on the other hand is the sum of the discounted values of all the cashflows to today's value discounted by the interest rate.

In the example, we will calculate IRR using Excel IRR method which takes in the set of cash flows and NPV by discounting each cash flow by 6%. This is copied in the table below:

Year	Year	CFS	CFL		PV	PV
01-Jan-10	0	-1025	-2150		-1025	-2150
01-Jan-11	1	$380	$765		$358.49	$721.70
01-Jan-12	2	$380	$765		$338.20	$680.85
01-Jan-13	3	$380	$765		$319.06	$642.31
01-Jan-14	4	$380	$765		$301.00	$605.95
	IRR	17.861%	15.781%	NPV	$291.74	$500.81

Copying the formula sheet below:

r	0.06
Year	CFS	CFL		PV	PV
0	-1025	-2150		=B4	=C4
1	380	765		=B5/(1+$B$1)^$A5	=C5/(1+$B$1)^$A5
2	380	765		=B6/(1+$B$1)^$A6	=C6/(1+$B$1)^$A6
3	380	765		=B7/(1+$B$1)^$A7	=C7/(1+$B$1)^$A7
4	380	765		=B8/(1+$B$1)^$A8	=C8/(1+$B$1)^$A8
IRR	=IRR(B4:B8)	=IRR(C4:C8)	NPV	=SUM(E4:E8)	=SUM(F4:F8)

IRR criterion is best suited when multiple projects that are compared have the same initial investment. This gives a fair comparison criteria as the one with higher returns will be preferred.

When it comes to improving the profitability of the firm, then the project with higher NPV will be profitable because it gives higher profit as compared to other projects.

In this case, IRR of CFS is higher than CFL, however NPV of CFL is higher than CFS.

Hence, if IRR is used instead of NPV, then there is a potential loss of NPV(CFL) - NPV(CFS) = 500.81 - 291.74 = $209.07