A firm is considering which of twodevices to install to reduce costs. Both devices have useful lives of 5 years and no salvage value. Device A costs $10,000 and can be expected to result in $3000 savings annually. Device B costs $13,500 and will provide cost savings of $3000 the first year but will

Question

A firm is considering which of twodevices to install to reduce costs. Both devices have useful lives of 5 years and no salvage value. Device A costs $10,000 and can be expected to result in $3000 savings annually. Device B costs $13,500 and will provide cost savings of $3000 the first year but will increase $500 annually, making the second-year savings $3500, the third-year savings $4000, and so forth. For a 7% MARR, which device should the firm purchase?

Accepted Answer

TABLE SOLUTION

This problem has been solved by present worth analysis (Example 5–1) and annual cost analysis (Example 6–5). This time we will use rate of return analysis, which must be done on the incremental investment.

Difference Between Alternatives: Device B − Device A	Device B	Device A	Year
−$3500	−$ 13,500	−$ 10,000	0
0	3000	3000	1
500	3500	3000	2
1000	4000	3000	3
1500	4500	3000	4
2000	5000	3000	5

For the difference between the alternatives, write a single equation with i as the only unknown.

[latex]PW(i)=0=-3500+500(P/G,i,5)[/latex]

[latex](P/G,i,5)=7;[/latex] so i is between [latex]9\%,(P/G,9\%,5)=7.111[/latex] and [latex] 10\%,(P/G,10\%,5)=6.862[/latex]

[latex]i=9\%+(10\%-9\%)(7.111-7)/(7.111-6.862)=9.45\%[/latex]

The 9.45% IRR is greater than the 7% MARR; therefore, the increment is desirable. Reject Device A and choose Device B.

SPREADSHEET SOLUTION

G	F	E	D	C	B	A
	Cash flow	Year	Incremental initial cost for B vs. A			$3,500	1
	-$3,500	0	Initial incremental savings for B vs. A			0	2
=A2	0	1	Gradient in incremental savings for B vs. A			$500	3
=F3+$A$3	500	2			Horizon	5	4
	1,000	3					5
	1,500	4					6
	2,000	5					7
=IRR(F2:F7	9.44%	IRR					8

Example 7–15 will show how GOAL SEEK can be used to solve for the interest rate that makes two values, such as [latex]NPV_{A} and NPV_{B}[/latex], equal.

Question 7.13: A firm is considering which of twodevices to install to redu...

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