Question

Machine A costs $850,000 and would produce cash flows of $220,000 per year for the first two years, $350,000 per year for the next two years, and $150,000 in the final year. Machine B costs $650,000 and would produce cash flows of $250,000 per year for the first two years, $200,000 the following year, $150,000 in its fourth year, and $140,000 in its final year. Your required return is 11%. What is the IRR of buying machine B?

Answer 1

		11.0000%	15%	17.00%	18.00%	19.00%
Period	Cash Flow	Discountig Factor [1/(1.11^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.15^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.17^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.18^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.19^period)]	PV of cash flows (cash flow*discounting factor)
0	-650000	1	-650000	1	-650000	1	-650000	1	-650000	1	-650000
1	250000	0.9009009	225225.225	0.8695652	217391.3043	0.8547009	213675.2137	0.8474576	211864.41	0.8403361	210084.03
2	250000	0.8116224	202905.608	0.7561437	189035.9168	0.7305136	182628.3878	0.7181844	179546.11	0.7061648	176541.2
3	200000	0.7311914	146238.276	0.6575162	131503.2465	0.6243706	124874.1113	0.6086309	121726.17	0.5934158	118683.16
4	150000	0.658731	98809.6461	0.5717532	85762.98684	0.53365	80047.50723	0.5157889	77368.331	0.4986688	74800.313
5	140000	0.5934513	83083.1859	0.4971767	69604.74294	0.4561112	63855.56133	0.4371092	61195.29	0.4190494	58666.912
		NPV =	106261.942	NPV =	43298.19744	NPV =	15080.78128	NPV =	1700.3103	NPV =	-11224.37

IRR is the rate of return at which NPV=0

Here, NPV@18% is positive and @19% is negative.

Therefore, IRR is between 18% and 19%

IRR = Rate at which positive NPV + [Positive NPV/(Positive NPV-Negative NPV)]

= 18% + [1700.31/(1700.31-(-11224.37)]

= 18% + [1700.31/12924.68]

= 18% + 0.1316% = 18.1316%

(Explanation & Logic of the method: NPV @18% is 1700.31 and NPV@19% is -11224.37. i.e. 1% increase in required rate of return reduces NPV by 1700.31+11224.37 =12924.68. We want NPV=0. Therefore, Proportionate increase in required rate of return to reduce NPV by 1700.31 is calculated)

As IRR is GREATER than Required Rate of Return, Machine B CAN BE bought.