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Homework answers / question archive / Given the data for two alternatives, choose the better alternative using the B/C ratio analysis
Given the data for two alternatives, choose the better alternative using the B/C ratio analysis. MARR 8%
Show detail of your work for each Alternative.
Alternative X Y
First cost $100,000 $140,000
Operating costs/year 50,000 60.000
Benefits /year 100,000 120,000
Dis-benefits/year 30,000 25,000
Life in years 5 10
1. A) Alt. X 2. B) Alt. Y
Alternative Y must be chosen because it has a better B/C ratio
Explanation
Initial cost = $100000
Operating costs (annual) = $50000
Net benefits (annual) = Benefits - Dis-benefits
= 100000 - 30000
= $70000
Life in years = 5
MARR = 8%
Total Cost (present value) = 100000 + 50000/ (1+0.08) + .... + 50000/(1+0.08)5
= $299635.5
Total Benefits (present value) = 70000/ (1+0.08) + .... + 70000/(1+0.08)5
= $279489.7
B/C ratio = 279489.7/299635.5 = 0.933
Alternative Y:
initial cost = $140000
Operating costs (annual) = $60000
Net benefits (annual) = Benefits - Dis-benefits
= 120000 - 25000
= $95000
Life in years = 10
MARR = 8%
Total Cost (present value) = 140000 + 60000/ (1+0.08) + .... + 60000/(1+0.08)10
= $542604.9
Total Benefits (present value) = 95000/ (1+0.08) + .... + 95000/(1+0.08)10
= $637457.7
B/C ratio = 637457.7/542604.9
= 1.175
