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What is the IRR for the following project if its initial after-tax cost is $6,000,000 and...

What is the IRR for the following project if its initial after-tax cost is $6,000,000 and it is expected to provide after-tax operating cash flows of (-$1,500,000) in year 1, $2,900,000 in year 2, $2,700,000 in year 3 and $2,300,000 in year 4?

19.47%

1.93%

7.56%

12.14%

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Answer #1

IRR is the rate at which NPV is 0. It is calculated by trial and error method

let find NPV at 1%

Year Cashflow PVF@1% Cashflow*PVF
0        (60,00,000) 1 (60,00,000.00)
1        (15,00,000) 0.9901 (14,85,148.51)
2          29,00,000 0.9803      28,42,858.54
3          27,00,000 0.9706      26,20,593.40
4          23,00,000 0.9610      22,10,254.79

NPV = PV of inflows - PV of outflows

= (-1485148.51+2842858.54+2620593.4+2210254.79)-6000000

= 6188558.22-6000000

188558.22

Since NPV is positive take a higher rate say 2%

Year Cashflow PVF@2% Cashflow*PVF
0        (60,00,000) 1 (60,00,000.00)
1        (15,00,000) 0.9804 (14,70,588.24)
2          29,00,000 0.9612      27,87,389.47
3          27,00,000 0.9423      25,44,270.30
4          23,00,000 0.9238      21,24,844.48

NPV = PV of inflows - PV of outflows

= (-1470588.24+2787389.47+2544270.3+2124844.48)-6000000

= 5985916.01-6000000

= -14083.99

Now we gor two rates R1 and R2

IRR = R1+((NPV at R1*(R2-R1))/(NPV at R1-NPV at R2))

= 1 + ((188558.22*(2-1))/(188558.22+14083.99)

= 1+(188558.22*1)/202642.21

= 1+0.93049824121

= 1.93%

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