Question

Consider the following project being analyzed for possible investment at ABC Corp. Initial Cost –$50 Inflow Year 1 $15 Inflow Year 2 $15 Inflow Year 3 $20 Inflow Year 4 $10 Inflow Year 5 $10 All amounts are in millions. The required return for the project is 8%. The project’s IRR is: (Enter your answer without a leading dollar sign out to four decimal places and in abbreviated millions. As an example, you would enter 5.42% as 0.0542.)

Answer 1

IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.

Lets find NPV at say 13%.

Year	Cashflow in millions	PVF@13%	Cashflow*PVF
0	(50)	1	(50.00)
1	15	0.8850	13.27
2	15	0.7831	11.75
3	20	0.6931	13.86
4	10	0.6133	6.13
5	10	0.5428	5.43

NPV = PV of inflows-PV of outflows

= (13.27+11.75+13.86+6.13+5.43)-50

= 50.44-50

= .44

Since NPV is positive, Take a higher rate say 14%

Year	Cashflow in millions	PVF@14%	Cashflow*PVF
0	(50)	1	(50.00)
1	15	0.8772	13.16
2	15	0.7695	11.54
3	20	0.6750	13.50
4	10	0.5921	5.92
5	10	0.5194	5.19

NPV = PV of inflows-PV of outflows

= (13.16+11.54+13.50+5.92+5.19)-50

= 49.31-50

= -.69

Now we got two rates R1 and R2 such that NPV at R1(NPV1) is higher and NPV at R2(NPV2) is lower.

IRR = R1 + ((NPV1 x (R2 - R1)) / (NPV1 - NPV2))

= 13+((.44*(14-13))/(.44+.69)

= 13+(.44/1.13)

= 13.39%

= 0.1339

You can use the equation 1/(1+i)^n to find PVF using calculator