Question

Question 2 : Option M: benefits of $500,000 a year, initial cost of $5,000,000, indirect annual net revenue of $70,000, useful life of 25 years Option N: benefits of $600,000 a year, disbenefits of $150,000 a year, initial cost of $6,500,000, indirect annual net revenue of $80,000, useful life of 30 years Option P: benefits of $600,000 a year, disbenefits of $120,000 a year, initial cost of $3,600,000, annual M&O of $60,000, useful life of 20 years If the options are mutually exclusive and MARR is 8%, use benefit-cost analysis to select the best alternative.

Answer 1

ANSWER:

First we will find the benefits and then the costs of each option.

Option m :

benefits = $500,000 , initial cost = $5,000,000 , indirect annual net revenue = $70,000 , n = 25 years , i = 8%

total benefits = $500,000 + $70,000 = $570,000

pw of total benefits = total benefits(p/a,i,n)

pw of total benefits = 570,000(p/a,8%,25)

pw of total benefits = 570,000 * 10.675 = $6,084,750

costs = $5,000,000

benefit - cost analysis = pw of total benefits / costs = $6,084,750 / $5,000,000 = 1.21695

Option n :

benefits = $600,000 , initial cost = $6,500,000 , indirect annual net revenue = $80,000 , disbenefits = $150,000 , n = 30 years , i = 8%

total benefits = $600,000 + $80,000 = $680,000

pw of total benefits = total benefits(p/a,i,n)

pw of total benefits = 680,000(p/a,8%,30)

pw of total benefits = 680,000 * 11.258 = $7,655,440

costs = $6,500,000

pw of disbenefits = disbenefits(p/a,i,n)

pw of disbenefits = 150,000(p/a,8%,30)

pw of disbenefits = 150,000 * 11.258

pw of disbenefits = 1,688,700

total costs = initial cost + pw of disbenefits = $6,500,000 + $1,688,700 = $8,188,700

benefit - cost analysis = pw of total benefits / costs = $7,655,440 / $8,188,700 = 0.9348

option p :

benefits = $600,000 , disbenefits = $120,000 , initial cost = $3,600,000 , annual m and o = $60,000 , n = 20 years and i = 8%

pw of benefits = benefits(p/a,i,n)

pw of benefits = $600,000(p/a,8%,20)

pw of benefits = 600,000 * 9.818 = $5,890,800

pw of disbenefits = disbenefits(p/a,i,n)

pw of disbenefits = 120,000(p/a,8%,20)

pw of disbenefits = 120,000 * 9.818 = $1,178,160

pw of a and o = a and o (p/a,i,n)

pw of a and o = 60,000(p/a,8%,20)

pw of a and o = 60,000 * 9.818

pw of a and o = $589,080

total costs = pw of disbenefits + pw of a and o + initial cost = $1,178,160 + $589,080 + $3,600,000 = $5,367,240

benefit - cost analysis = pw of total benefits / costs = $5,890,800 / $5,367,240 = 1.0975

since the b/c ratio of m is the highest that is 1.21 , therefore we choose option M.