In Example 8–2 Machine X was assumed to be “replaced with an identical machine” for a 12-year analysis period. In Chapter 6 this was shown to be equivalent to using EUAW as the comparison measure. Construct a choice table using EUAW.

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The first step is to construct the EUAW graph for Machines X and Y. If Figures 8–2 and 8–3 are compared, it is easy to see that there are only two differences. The first is the scale of the y-axis, where one is for NPW and the other is for EUAW. The second difference is the shape of the curves, where the EUAW curves are straighter than the NPW curves. The important similarity is that in both cases Machine Y is preferred for very low interest rates, and Machine X is preferred for other interest rates.

Finding the rate of return where Machines X and Y have the same EUAW is equivalent to finding the incremental IRR on Y − X. This was done for Example 8–2 by using the IRR spreadsheet function on the cash flows. Here we will use the GOAL SEEK function that was introduced in Example 7–15.

The 5-BUTTON SOLUTION starts by finding the EUAW for each machine at the 10% minimum attractive rate of return (MARR) that was used in Example 8–2. Note that this solution must add the annual benefit to the negative equivalent annual value of the initial cost and salvage value. To show this with the GOAL SEEK results, the 5-button calculations are duplicated in rows 9 to 16.

The GOAL SEEK function is found under DATA/WHAT-IF ANALYSIS. To use the GOAL SEEK function, the goal must be expressed in a single cell. Cell H16 simply calculates the difference in the EUAW values for each machine—the goal is a value of 0. GOAL SEEK varies a single cell to try to achieve the goal—in this case cell B10, the interest rate for Machine X. Cell B13 must contain =B10, so that both interest rates change at the same time.

When the lives of alternatives differ, this is the easiest way to find the breakeven interest rate. For the EUAWs of Machines X and Y the incremental [latex]IRR_{Y−X}[/latex] is 1.32%.

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Alternative	1
$39	PMT	50	-200		6	10%	Machine X	2
-39	Change sign							3
56	EUAW				annual benefit 95			4
96	PMT	150	-700		12	10%	Machine Y	5
-96	Change sign							6
24	EUAW				annual benefit 120			7
Difference in EUAW 31								8
								9
27	PMT	50	-200		6	1.32%	Machine X	10
-27	Change sign							11
68	EUAW				annual benefit 95			12
52	PMT	150	-700		12	1.32%	Machine Y	13
-52	Change sign							14
68	EUAW				annual benefit 120			15
Difference in EUAW 0								16

Question 8.3: In Example 8–2 Machine X was assumed to be “replaced with an...

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