Question

Tesar Chemicals is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will have no effect on the value gained or lost.

WACC:	7.50%
Year	0	1	2	3	4
CFS	-$1,100	$550	$600	$100	$100
CFL	-$2,700	$650	$725	$800	$1,400

		$138.10
		$149.21
		$160.31
		$171.42
		$182.52

Answer 1

NPV of CFS is as follows:

Year	CF	Discount Factor		Discounted CF
0	$     -1,100.00	1/(1+0.075)^0=	1	1*-1100=	$     -1,100.00
1	$ 550.00	1/(1+0.075)^1=	0.930232558	0.930232558139535*550=	$           511.63
2	$ 600.00	1/(1+0.075)^2=	0.865332612	0.865332612222823*600=	$           519.20
3	$ 100.00	1/(1+0.075)^3=	0.80496057	0.804960569509603*100=	$             80.50
4	$ 100.00	1/(1+0.075)^4=	0.74880053	0.748800529776375*100=	$             74.88
				NPV = Sum of all Discounted CF	$             86.20

IRR is the rate at which NPV = 0
IRR can be calculated using either a financial calculator or excel or through hit and trial:

Using Excel we get the IRR = 12.24% rounded to two decimal places as per the below schedule:

Year	CF	Discount Factor		Discounted CF
0	$-1,100.00	1/(1+0.122415662123375)^0=	1	1*-1100=	$     -1,100.00
1	$ 550.00	1/(1+0.122415662123375)^1=	0.890935536	0.890935536402094*550=	$           490.01
2	$ 600.00	1/(1+0.122415662123375)^2=	0.79376613	0.793766130024086*600=	$           476.26
3	$ 100.00	1/(1+0.122415662123375)^3=	0.707194453	0.707194452830823*100=	$             70.72
4	$ 100.00	1/(1+0.122415662123375)^4=	0.630064669	0.630064669173415*100=	$             63.01
				NPV = Sum of all Discounted CF	$               0.00

NPV of the CFL is as follows:

Year	CF	Discount Factor		Discounted CF
0	$     -2,700.00	1/(1+0.075)^0=	1	1*-2700=	$     -2,700.00
1	$ 650.00	1/(1+0.075)^1=	0.930232558	0.930232558139535*650=	$           604.65
2	$ 725.00	1/(1+0.075)^2=	0.865332612	0.865332612222823*725=	$           627.37
3	$ 800.00	1/(1+0.075)^3=	0.80496057	0.804960569509603*800=	$           643.97
4	$       1,400.00	1/(1+0.075)^4=	0.74880053	0.748800529776375*1400=	$       1,048.32
				NPV = Sum of all Discounted CF	$           224.31

Using Excel we get the IRR = 10.71 % rounded to two decimal places as per the below schedule:

Year	CF	Discount Factor		Discounted CF
0	$-2,700.00	1/(1+0.107118091843484)^0=	1	1*-2700=	$ -2,700.00
1	$      650.00	1/(1+0.107118091843484)^1=	0.903246011	0.903246010852266*650=	$      587.11
2	$      725.00	1/(1+0.107118091843484)^2=	0.815853356	0.815853356120532*725=	$      591.49
3	$      800.00	1/(1+0.107118091843484)^3=	0.736916289	0.736916289356304*800=	$      589.53
4	$ 1,400.00	1/(1+0.107118091843484)^4=	0.665616699	0.665616698693136*1400=	$      931.86
				NPV = Sum of all Discounted CF	$         -0.00

So even though CFL has a higher NPV at 7.5% discount rate, but CFS is chosen as it has a higher IRR.

So the NPV given up =224.30 - 86.20 = 138.10 so the correct option is the first 1