Two machines are being considered for purchase. If the MARR is 10%, which machine should be bought? Use an IRR analysis comparison.

Question

Machine Y	Machine X	All $ values in 1000s
$700	$200	Initial cost
120	95	Uniform annual benefit
150	50	End-of-useful-life salvage value
12	6	Useful life, in years

Accepted Answer

The solution is based on a 12-year analysis period and a replacement machine X that is identical to the present Machine X. The cash flow for the differences between the alternatives is as follows:

Machine Y	Machine X	All $ values in 1000s
$700	$200	Initial cost
120	95	Uniform annual benefit
150	50	End-of-useful-life salvage value
12	6	Useful life, in years

[latex]PW=-500+25(P/A,i,12)+150(P/F,i,6)+100(P/F,i,12)[/latex]

The cash flow sum over years 1 to 12 is $550, which is only a little greater than the $500 additional cost. This indicates that the rate of return is quite low. Try i = 1%.

[latex]PW_{1\%}=-500+25(11.255)+150(0.942)+100(0.887)=11[/latex]

The interest rate is too low. Try i = 1½ %:

[latex]PW_{1.5\%}=-500+25(10.908)+150(0.914)+100(0.836)=-6[/latex]

The internal rate of return on the Y − X increment, [latex]IRR_{ Y−X}[/latex] , is about 1.3%, far below the 10% minimum attractive rate of return. The additional investment to obtain Machine Y yields an unsatisfactory rate of return, therefore X is the preferred alternative.

Many problems compare mutually exclusive alternatives for a continuing requirement where the horizon is longer than the lives of the current alternatives. In Example 6–8 pumps with lives of 9 and 12 years were compared, and the pump with the lower EUAC was recommended. The discussion before the example noted that this common approach assumes identical cost repetition for a horizon equal to the least common multiple of the lives.

To analyze that problem for an incremental rate of return, a horizon of 36 years could be used with repetitions like Machine X in Example 7–14. Example 7–15 in the next section illustrates another approach.

Question 7.14: Two machines are being considered for purchase. If the MARR ...

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