Question

An enterprise has to decide between two investment projects from which the next information is known: The investment X requires an initial investment of 150 million euros, generating annual cash flow (also in million euros) of 30 the first year, 56 the second year and 150 the third one. Meanwhile, the investment “Y” also requires an initial investment of 150 million euros, but it generates annual cash flow (also in million euros) of 40 the first year, 50 the second year and 135 the third one. If the discount rate that the enterprise demand to their investments is 15%, it is request to establish, in relation to the rate of profitability, if the investments are profitable and which one of both of them is preferable.

Answer 1

Project X

Statement shoiwng NPV

Year	Cash flow (euros in mln)	PVIF @ 15%	PV
1	30	0.8696	26.09
2	56	0.7561	42.34
3	150	0.6575	98.63
Sum of PV of Cash inflow	167.06
Initial Investment	150
NPV	17.06

Thus NPV = Euro 17.06 million

Noe Lets find IRR

IRR is rate at which NPV is 0

Assume rate = 20%, Then NPV=

Year	Cash flow (euros in mln)	PVIF @ 20%	PV
1	30	0.8333	25.00
2	56	0.6944	38.89
3	150	0.5787	86.81
Sum of PV of Cash inflow	150.69
Initial Investment	150
NPV	0.69

Assume rate = 21% ,Then NPV=

Year	Cash flow (euros in mln)	PVIF @ 21%	PV
1	30	0.8264	24.79
2	56	0.6830	38.25
3	150	0.5645	84.67
Sum of PV of Cash inflow	147.71
Initial Investment	150
NPV	-2.29

Now, using interpolation we can find IRR

R	NPV
20%	0.69
21%	-2.29
1%	2.98
?	0.69

=0.69/2.98

=0.23

Thus IRR = 20+0.23 = 20.23%

Project Y

Statement shoiwng NPV

Year	Cash flow (euros in mln)	PVIF @ 15%	PV
1	40	0.8696	34.78
2	50	0.7561	37.81
3	135	0.6575	88.76
Sum of PV of Cash inflow	161.35
Initial Investment	150
NPV	11.35

Thus NPV = Euro 11.35 million

Now lets find IRR

Assume rate = 18% ,Then NPV=

Year	Cash flow (euros in mln)	PVIF @ 18%	PV
1	40	0.8475	33.90
2	50	0.7182	35.91
3	135	0.6086	82.17
Sum of PV of Cash inflow	151.97
Initial Investment	150
NPV	1.97

Assume rate = 19% ,Then NPV=

Year	Cash flow (euros in mln)	PVIF @ 19%	PV
1	40	0.8403	33.61
2	50	0.7062	35.31
3	135	0.5934	80.11
Sum of PV of Cash inflow	149.03
Initial Investment	150
NPV	-0.97

Now, using interpolation we can find IRR

R	NPV
18%	1.97
19%	-0.97
1%	2.94
?	1.97

=1.97/2.94

=0.67

Thus IRR = 18+0.67 = 18.67%

Thus both the projects are profitable but since NPV ond IRR of Project X is more than Y , Project X should be selected