Solve Example 7–14 by means of an NPW graph. Two machines are being considered for purchase. If the minimum attractive rate of return (MARR) is 10%, which machine should be bought?

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

Since the useful lives of the two alternatives are different, for an NPW analysis we must adjust them to the same analysis period. If the need seems continuous, then the “replace with an identical machine” assumption is reasonable and a 12-year analysis period can be used. The annual cash flows and the incremental cash flows are as follows:

Cash Flows
Y−X	Machine Y	Machine X	End of Year
-$500	-$700	-$200	0
25	120	95	1
25	120	95	2
25	120	95	3
25	120	95	4
25	120	95	5
175	120	-55	6
25	120	95	7
25	120	95	8
25	120	95	9
25	120	95	10
25	120	95	11
125	270	145	12

By means of a spreadsheet program, the NPWs are calculated for a range of interest rates and then plotted on an NPW graph (Figure 8–2).

For a MARR of 10%, Machine X is clearly the superior choice. In fact, as the graph clearly illustrates, Machine X is the correct choice for most values of MARR. The intersection point of the two graphs can be found by calculating ΔIRR, the rate of return on the incremental investment. From the spreadsheet IRR function applied to the incremental cash flows for Y − X:

ΔIRR=1.32%

We can see from the graph that for MARR greater than 1.32%, Machine X is the right choice, and for MARR values less than 1.32%, Machine Y is the right choice.

NPW
Machine Y	Machine X	Rate
$890.00	$840.00	0%
752.24	752.24	1.32
687.31	710.89	2
519.90	604.26	4
380.61	515.57	6
263.90	441.26	8
165.44	378.56	10
81.83	325.30	12
10.37	279.77	14
-51.08	240.58	16
-104.23	206.65	18
-150.47	177.10	20

Examples 8–3 through 8–6 increase the number of alternatives being considered, but the same approach is used: graph the PW, EUAW, or EUAC, and for each possible interest rate choose the best alternative. Generally this means maximising the PW or EUAW, but for Example 8–4 the EUAC is minimized. Once the best choices have been identified from the graph, calculate the incremental rates of return.

Example 8–4 is a typical design problem where the most cost-effective solution must be chosen, but the dollar value of the benefit is not defined. For example, every building must have a roof, but deciding whether it should be metal, shingles, or a built-up membrane is a cost decision. No value is placed on a dry building; it is simply a requirement. In Example 8–4 having the pressure vessel is a requirement.

Question 8.2: Solve Example 7–14 by means of an NPW graph. Two machines ar...

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