Question

Upon graduating from College, you have taken a job as a design analyst at Acme Widgets. Your first assignment is to evaluate two alternatives for improving efficiency in the production of anvils for one of Acme’s biggest clients, Wile E. Coyote. Both options have a useful lifetime of 15 years, because that is the estimated remaining lifetime for Acme’s anvil production facility. Acme uses a 10% per year MARR.

A basic reconfiguration of the assembly line will initially cost $9.8 million and require annual maintenance costs of $150,000. Once the line is reconfigured, the greater efficiency will result in savings of $1.6 million per year, relative to the current assembly process. The second option is a more extensive upgrade to the existing process. It would cost an additional $4.2 million in initial investment, compared to the basic reconfiguration. It also would cost an additional $75,000 in annual maintenance costs compared to the basic alternative. However, the second option is more fragile, meaning that the benefits degrade over time. In the first year after the more extensive upgrade is completed, it would produce $700,000 more in savings than the basic alternative. In each subsequent year, for the rest of the 15-year useful lifetime, the incremental benefits would decrease by $20,000 compared to the previous year.

a. What is the conventional benefit-cost ratio associated with the basic reconfiguration?

b. Is the more extensive upgrade option worth pursuing? To answer this question, you can either find the incremental benefit-cost ratio or the incremental present worth, but you must

use an incremental analysis to receive full credit. Note: the cash flows associated with the more extensive upgrade are already provided as incremental values.

c. You believe there is uncertainty in how much the incremental savings associated with the extensive upgrade would be reduced from year to year, so you decide to conduct a

breakeven analysis. What is the maximum magnitude of this uniform gradient that would result in the more extensive upgrade being justified?

Answer 1

	a	Benefit Cost ratio of basic reconfiguration
	PC	Present Value of Cost	$9,800,000
		BENEFIT:
	A	Annual savings	$1,600,000
	B	Annualmaintenance cost	$150,000
	C=A-B	Net Annual benefit	$1,450,000
	Rate	Discount Rate	10%
	Nper	Number of years	15
	Pmt	Annual Benefit	$1,450,000
	PV	Present Value of benefits	$11,028,815
		(Using PV function of excel)
	BC=PV/PC	Benefit Cost Ratio	1.125389315
	b	Incremental benefit-Cost ratio
	PIC	Present Value ofIncremental Cost	$4,200,000
		Present Value of Cash flow=(Cash Flow)/((1+i)^N)
		i=discount rate=10%=0.1
		N=Year of cash flow
			N	A	B	C=B-A	D=C/(1.1^N)
			Year	Incremental Savings	Incremental maintenance	Incremental Benefit	Present Value
			1	$700,000	$75,000	$625,000	$568,182
			2	$680,000	$75,000	$605,000	$500,000
			3	$660,000	$75,000	$585,000	$439,519
			4	$640,000	$75,000	$565,000	$385,903
			5	$620,000	$75,000	$545,000	$338,402
			6	$600,000	$75,000	$525,000	$296,349
			7	$580,000	$75,000	$505,000	$259,145
			8	$560,000	$75,000	$485,000	$226,256
			9	$540,000	$75,000	$465,000	$197,205
			10	$520,000	$75,000	$445,000	$171,567
			11	$500,000	$75,000	$425,000	$148,960
			12	$480,000	$75,000	$405,000	$129,045
			13	$460,000	$75,000	$385,000	$111,521
			14	$440,000	$75,000	$365,000	$96,116
			15	$420,000	$75,000	$345,000	$82,590
						SUM	$3,950,760
	PIB	Present Value of incremental benefit	$3,950,760
	IBC=PIB/PIC	Incremental Benefit Cost Ratio	0.940657128
		Benefit Cost ratio is less than 1
		Hence more extensive upgrade is not justified

In order to justify, the value of IBC should be at least =1 Present Value of incremental benefit $4,200,000 Maximum Uniform gradient= 13792 A IN B C=B-A D=C/(1.14N) Year Incremental Incremental Incremental Present Savings maintenance Benefit Value 1 $700,000 $75,000 $625,000 $568,182 2 $686,208 $75,000 $611,208 $505,131 3 $672,416 $75,000 $597,416 $448,847 4 $658,624 $75,000 $583,624 $398,623 5 $644,832 $75,000 $569,832 $353,821 6 $631,040 $75,000 $556,040 $313,870 7 $617,248 $75,000 $542,248 $278,259 8 $603,456 $75,000 $528,456 $246,529 9 $589,664 $75,000 $514,664 $218,268 10 $575,872 $75,000 $500,872 $193,108 11 $562,080 $75,000 $487,080 $170,719 12 $548,288 $75,000 $473,288 $150,804 13 $534,496 $75,000 $ 459,496 $133,100 14 $520,704 $75,000 $445,704 $117,368 15 $506,912 $75,000 $431,912 $103,396 SUM $4,200,023