Question

ABC Industries is considering an expansion project with cash flows of -$325,000, $67,500, $116,100, $110,500, and $152,700 for years 0 through 4. Compute the IRR.

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 12%.

Year	Cashflow	PVF@12%	Cashflow*PVF
0	(325,000)	1	(325,000.00)
1	67,500	0.8929	60,267.86
2	116,100	0.7972	92,554.21
3	110,500	0.7118	78,651.72
4	152,700	0.6355	97,043.61

NPV = PV of inflows-PV of outflows

= (60267.86+92554.21+78651.72+97043.61)-325000

= 328517.39-325000

= 3517.39

Since NPV is positive, Take a higher rate say 13%

Year	Cashflow	PVF@13%	Cashflow*PVF
0	(325,000)	1	(325,000.00)
1	67,500	0.8850	59,734.51
2	116,100	0.7831	90,923.33
3	110,500	0.6931	76,582.04
4	152,700	0.6133	93,653.76

NPV = PV of inflows-PV of outflows

= (59734.51+90923.33+76582.04+93653.76)-325000

= 320893.64-325000

= -4106.34

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))

= 12+((3517.39*(13-12))/(3517.39+4106.34)

= 12.46%

Formula to calculate PV in excel is as follows "=PV(interest rate,Year,0,cashflow)"

Formula to calculate NPV in excel is as follows "=NPV(Rate,cashflows)+initial investment"

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