Question

You are choosing between two projects. The cash flows for the projects are given in the following table ($ million): Project Year 0 Year 1 Year 2 Year 3 Year 4 - $50 $18 $19 $17 - $101 $21 $40 $51 $26 $59 a. What are the IRRs of the two projects? b. If your discount rate is 5.1%, what are the NPVs of the two projects? c. Why do IRR and NPV rank the two projects differently? a. What are the IRRs of the two projects? The IRR for project Ais %. (Round to one decimal place.) The IRR for project B is %. (Round to one decimal place.) b. If your discount rate is 5.1%, what are the NPVs of the two projects? If your discount rate is 5.1%, the NPV for project A is $ million. (Round to two decimal places.) If your discount rate is 5.1%, the NPV for project B is $ million. (Round to two decimal places.) c. Why do IRR and NPV rank the two projects differently? (Select from the drop-down menus.) NPV and IRR rank the two projects differently because they are measuring different things. measuring value creation, while is measuring return on investment. Because returns do not scale with different levels of investment, the two measures may give different rankings when the initial investments are different.

Answer 1

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

Project A:

Using Excel we get the IRR = 23.80% rounded to two decimal places

Year	CF	Discount Factor		Discounted CF
0	$-50.00	1/(1+0.237960337354944)^0=	1	1*-50=	$ -50.00
1	$ 26.00	1/(1+0.237960337354944)^1=	0.807780322	0.807780322055086*26=	$   21.00
2	$ 18.00	1/(1+0.237960337354944)^2=	0.652509049	0.652509048699419*18=	$   11.75
3	$ 19.00	1/(1+0.237960337354944)^3=	0.52708397	0.527083969502274*19=	$   10.01
4	$ 17.00	1/(1+0.237960337354944)^4=	0.425768059	0.42576805863462*17=	$     7.24
				NPV = Sum of all Discounted CF	$     0.00

Project B

Using Excel we get the IRR = 20.99% rounded to two decimal places

Year	CF	Discount Factor		Discounted CF
0	$-101.00	1/(1+0.209945773643538)^0=	1	1*-101=	$ -101.00
1	$    21.00	1/(1+0.209945773643538)^1=	0.82648332	0.826483319982743*21=	$     17.36
2	$    40.00	1/(1+0.209945773643538)^2=	0.683074678	0.683074678209698*40=	$     27.32
3	$    51.00	1/(1+0.209945773643538)^3=	0.564549828	0.564549827842895*51=	$     28.79
4	$    59.00	1/(1+0.209945773643538)^4=	0.466591016	0.466591016011282*59=	$     27.53
				NPV = Sum of all Discounted CF	$       0.00

b) NPV calculation @ 5.1%:

Project A

Year	CF	Discount Factor		Discounted CF
0	$-50.00	1/(1+0.051)^0=	1	1*-50=	$ -50.00
1	$ 26.00	1/(1+0.051)^1=	0.951474786	0.951474785918173*26=	$   24.74
2	$ 18.00	1/(1+0.051)^2=	0.905304268	0.905304268238034*18=	$   16.30
3	$ 19.00	1/(1+0.051)^3=	0.861374185	0.861374184812591*19=	$   16.37
4	$ 17.00	1/(1+0.051)^4=	0.819575818	0.819575818090001*17=	$   13.93
				NPV = Sum of all Discounted CF	$   21.33

Project B

Year	CF	Discount Factor		Discounted CF
0	$-101.00	1/(1+0.051)^0=	1	1*-101=	$ -101.00
1	$    21.00	1/(1+0.051)^1=	0.951474786	0.951474785918173*21=	$     19.98
2	$    40.00	1/(1+0.051)^2=	0.905304268	0.905304268238034*40=	$     36.21
3	$    51.00	1/(1+0.051)^3=	0.861374185	0.861374184812591*51=	$     43.93
4	$    59.00	1/(1+0.051)^4=	0.819575818	0.819575818090001*59=	$     48.35
				NPV = Sum of all Discounted CF	$     47.48

c)

NPV is measuring value creation

IRR is measuring the return on investment