Question

1. You are trying to decide which 2 devices to install. The following are the details for the devices with a useful life of 5 years. Your MARR is 10%. What is the Benefit-Cost Ratio of Device 1?:

Device 1 Device 2 Device 3

Initial Cost $110,000 $200,000 $150,000

Salvage Value $10,000 $30,000 $20,000

O&M Costs $5,000 $2,000 $6,000

Annual Benefits $35,000 $40,000 $35,00 Year 1, increasing $5,000 each subsequent year

2.

what is the benefit - cost ratio for Device 2?

3. what is the benefit - cost ratio for Device 3?

4. what is the incremental benefit-cost ratio of the best alternatives?

Answer 1

1.) B/C Ratio for Device 1 = 4.547

Year	Annual Benefits	PV of Annual Benefits
1	35000	$31,818.18
2	40000	$69,421.49
3	45000	$111,908.34
4	50000	$158,493.27
5	55000	$208,493.27
		$580,134.55

Device	Initial Investment	Estimated life	Salvage Value	O&M Costs	PV of Salvage Value	PV of O&M Cost	PV of Annual Benefits	PWBENEFITS	PWCOSTS	B/C
1	110000	5	10000	5000	$6,209.21	$18,953.93	$580,134.55	$586,343.77	$128,953.93	4.547

2.) B/C Ratio for Device 2 = 3.176

Year	Annual Benefits	PV of Annual Benefits
1	40000	$36,363.64
2	45000	$78,099.17
3	50000	$124,342.60
4	55000	$174,342.60
5	60000	$227,447.21
		$640,595.22

Device	Initial Investment	Estimated life	Salvage Value	O&M Costs	PV of Salvage Value	PV of O&M Cost	PV of Annual Benefits	PWBENEFITS	PWCOSTS	B/C
2	200000	5	30000	2000	$18,627.64	$7,581.57	$640,595.2152	$659,222.85	$207,581.57	3.176

3.) B/C Ratio for Device 3 = 3.43

Year	Annual Benefits	PV of Annual Benefits
1	35000	$31,818.18
2	40000	$69,421.49
3	45000	$111,908.34
4	50000	$158,493.27
5	55000	$208,493.27
		$580,134.55

Device	Initial Investment	Estimated life	Salvage Value	O&M Costs	PV of Salvage Value	PV of O&M Cost	PV of Annual Benefits	PWBENEFITS	PWCOSTS	B/C
3	150000	5	20000	6000	$12,418.43	$22,744.72	$580,134.55	$592,552.98	$172,744.72	3.43

4.) the highest Benefit-Cost Ratio is 4.547 for Device 1 among alternatives so this is the best device.

Incremental Benefit-Cost Ratio of device 1 in compare to Device 2 which is the cheapest option.

ΣB1 = total benefits for Device‘1’

ΣB2 = total benefits for Device‘2’

ΣC1 = total costs for project ‘1’

ΣC2 = total benefits for Device‘2’

Incremental Benefit-Cost Ratio = (ΣB1 - ΣB2) / (ΣC1 - ΣC2)

= ($586,343.77 - $659,222.85) / ($128,953.93 - $207,581.57)

= -$72,879.08 / -$75,627.64 = 0.93