Question

Consider projects A and B:

	Cash Flows (dollars)
Project	C0	C1	C2	NPV at 10%
A	−33,000	23,400	23,400	+$7,612
B	−53,000	36,000	36,000	+9,479

a. Calculate IRRs for A and B. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Project A

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 26%.

Year	Cashflow	PVF@26%	Cashflow*PVF
0	(33,000)	1	(33,000.00)
1	23,400	0.7937	18,571.43
2	23,400	0.6299	14,739.23

NPV = PV of Inflows-PV of Outflows

= (18571.43+14739.23)-33000

= 33310.66-33000

= $310.66

Since NPV is positive, Take a higher rate say 27%

Year	Cashflow	PVF@27%	Cashflow*PVF
0	(33,000)	1	(33,000.00)
1	23,400	0.7874	18,425.20
2	23,400	0.6200	14,508.03

NPV = PV of Inflows-PV of Outflows

= (18425.20+14508.03)-33000

= 32933.23-33000

= -66.77

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))

= 26+((310.66*(27-26))/(310.66+66.77)

= 26+(310.66/377.43)

= 26.82%

Project B

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 23%.

Year	Cashflow	PVF@23%	Cashflow*PVF
0	(53,000)	1	(53,000.00)
1	36,000	0.8130	29,268.29
2	36,000	0.6610	23,795.36

NPV = PV of Inflows-PV of Outflows

= (29268.29+23795.36)-53000

= 53063.65-53000

= $63.65

Since NPV is positive, Take a higher rate say 24%

Year	Cashflow	PVF@24%	Cashflow*PVF
0	(53,000)	1	(53,000.00)
1	36,000	0.8065	29,032.26
2	36,000	0.6504	23,413.11

NPV = PV of Inflows-PV of Outflows

= (29032.26+23413.11)-53000

= 52445.37-53000

= -554.63

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))

= 23+((63.65*(24-23))/(63.65+554.63)

= 23+(63.65/618.28)

= 23.10%