Homework Answers
Alternative A:
B/C ratio = PW of benefits / PW of costs
PW of benefits = (Annual benefit / MARR) × [1 – (1 + MARR) ^(-year)]
= (37,000 / 0.15) × [1 – (1 + 0.15) ^ (- 5)]
= 246,666.666 × [1 - (1/1.15^5)]
= 246,666.666 × [1 – (1/2.01135)]
= 246,666.666 × [1.01135 / 2.01135]
= 246,666.666 × 0.50282
= 124,028.93
B/C ratio = PW of benefits / PW of costs
= 124,028.93 / 100,000
= 1.24
Alternative B:
B/C ratio = PW of benefits / PW of costs
PW of benefits = (Annual benefit / MARR) × [1 – (1 + MARR) ^(-year)]
= (83,000 / 0.15) × [1 – (1 + 0.15) ^ (- 5)]
= 553,333.333 × [1 - (1/1.15^5)]
= 553,333.333 × [1 – (1/2.01135)]
= 553,333.333 × [1.01135 / 2.01135]
= 553,333.333 × 0.50282
= 278,227.07
B/C ratio = PW of benefits / PW of costs
= 278,227.07 / 300,000
= 0.93
Alternative C:
B/C ratio = PW of benefits / PW of costs
PW of benefits = (Annual benefit / MARR) × [1 – (1 + MARR) ^(-year)]
= (150,000 / 0.15) × [1 – (1 + 0.15) ^ (- 5)]
= 1,000,000 × [1 - (1/1.15^5)]
= 1,000,000 × [1 – (1/2.01135)]
= 1,000,000 × [1.01135 / 2.01135]
= 1,000,000 × 0.50282
= 502,820
B/C ratio = PW of benefits / PW of costs
= 502,820 / 500,000
= 1.01
Alternative has the highest B/C ratio should be considered for selection. Alternative A should be selected, since it has the highest B/C ratio.
Answer: 1st option
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