Question

The FIN340 Company is evaluating a project with the following projected annual cash flows: Period 0: ($450), Period 1: ($610), Period 2: $120, Period 3: $630, Period 4: $850, Period 5: $250. The company has a WACC of 12%. Calculate the Internal Rate of Return (IRR) for this project.

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 15%.

Year	Cashflow	PVF@15%	Cashflow*PVF
0	(450)	1	(450.00)
1	(610)	0.8696	(530.43)
2	120	0.7561	90.74
3	630	0.6575	414.24
4	850	0.5718	485.99
5	250	0.4972	124.29

NPV = PV of Inflows - PV of Outflows

= (90.74+414.24+485.99+124.29)-)450+530.43)

= 1115.26-980.43

= $134.82

Since NPV is positive, Take a higher rate say 20%

Year	Cashflow	PVF@20%	Cashflow*PVF
0	(450)	1	(450.00)
1	(610)	0.8333	(508.33)
2	120	0.6944	83.33
3	630	0.5787	364.58
4	850	0.4823	409.92
5	250	0.4019	100.47

NPV = PV of Inflows - PV of Outflows

= (83.33+364.58+409.92+100.47)-(450+508.33)

= 958.30-958.33

= -.03

either you can stop here, or continue as follows.

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))

= 15+((134.82*(20-15))/(134.82+.03)

= 19.9988876529

= 20.00%

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

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"