Question

A portable concrete test instrument used in construction for evaluating and profiling concrete surfaces (MACRS-GDS 5-year property class) is under consideration by a construction firm for $25,500. The instrument will be used for 6 years and be worth $2,500 at that time. The annual cost of use and maintenance will be $13,000. Alternatively, a more automated instrument (same property class) available from the manufacturer costs $26,000, with use and maintenance costs of only $7,500 and salvage value after 6 years of $3,000. The marginal tax rate is 25%, and MARR is an after-tax 12%.

Determine which alternative is less costly, based upon comparison of after-tax annual worth. Show the AW values used to make your decision.

Answer 1

Given in the question following information,

Tax Rate= 25%, MARR (after tax)= 12%(i)

Equipment 1:(A portable concrete ) Initial Cost-$25,500, Life-6 years(n), Salvage value= 2500, Annual cost= $13,000

Year	Initial cost (A)	Annual cost (B)	Salavge C)	Depreciation Rate (D)	Dep Amount(cost *rate)=(25500*D)	Discounting factor @ 12% (E)	Cash flow F=(A+B+C+D)	After tax cash flow G=(F*0.75)	Discounted cash flow H = (G*E)
0	(25500)					1	(25500)	(19125)	(15300)
1		(13000)		20%	5100	0.8928	(7900)	(5925)	(5290)
2		(13000)		32%	8160	0.7972	(4840)	(3630)	(2894)
3		(13000)		19.20%	4896	0.7118	(8104)	(6078)	(4326)
4		(13000)		11.52%	2937.60	0.6355	(10062.40)	(7546.8)	(4769)
5		(13000)		11.52%	2937.60	0.5674	((10062.40)	(7546.8)	(4282)
6		(13000)	2500	5.76%	1468.8	0.5066	(9031.20)	(6773.40)	(3431)
Total								PW	(40292)
								AW	PMT(12%,6,-40292)=9800.05

Present Worth = (Sum of H above)= $(40,292)

Annual Worth =$9800.05

[I have attached the PMT Calculation Excel sheet below]

Equipment 1:( More automated instrument) Initial Cost-$26000, Life-6 years(n), Salvage value= 3000, Annual cost= $7500

Year	Initial cost (A)	Annual cost (B)	Salavge C)	Depreciation Rate (D)	Dep Amount(cost *rate)=(26000*D)	Discounting factor @ 12% (E)	Cash flow F=(A+B+C+D)	After tax cash flow G=(F*0.75)	Discounted cash flow H = (G*E)
0	(26000)					1	(26000)	(19500)	(19500)
1		(7500)		20%	(5200)	0.8928	(12700)	(9525)	(8504)
2		(7500)		32%	(8320)	0.7972	(15820)	(11865)	(9459)
3		(7500)		19.20%	(4992)	0.7118	(12492)	(9369)	(6669)
4		(7500)		11.52%	(2995)	0.6355	(10495)	(7871)	(5002)
5		(7500)		11.52%	(2995)	0.5674	(10495)	(7871)	(4466)
6		(7500)	3000	5.76%	(1498)	0.5066	(5998)	(4499)	(2279)
Total								PW	(55876)
								AW	PMT(12%,6,-55876)=13590.48

Present worth= (Sum of H above)= (55876)

Annual Worth =$13590.48

[I have attached the PMT Calculation Excel sheet below]

Comparison table

Particular	Alt 1	Alt 2
After-Tax Annual Worth	-$9800.05	-$13590.48

It can be seen that After-Tax Annual worth of Alt 2 is higher than Alt 1, so Alt 1 should be Preferred

Decision: Alt 1 that is Portable concrete should be preferred as it is more cost-effective as per after-tax Annual worth

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