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

Formula = Present Value of Costs/ Present Value of Benefits

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

Benefits = 500,000 + annual net revenue 70,000

MARR = 8%

Present value of benefits = Benefits* Present value annuity factor

= 500,000*10.6748 = 5,337,400 +70000*10.6748 = 747,236 =6,084,636

Present value of cost = 5,000,000

= 6,084,636/5,000,000 = = 1.2169 = It is greater than one so, the option M can be accepted.

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

Benefits 600,000

Disbenefits = 150,000

Initial cost = 6,500,000

Indirect annual Net revenue = 80,000

Life = 30 years

Benefits – Disbenefits / Costs = 600,000-150,000 = 450,000 a year + annual revenue = 80,000

Benefits = 450,000+80,000

= 530,000*11.2578= 5,966,634

5,966,634/6,500,000 = 0.9179

It is less than one so, the option N cannot be accepted.

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

Benefits = 600,000-120,000 =480,000

Costs=3,600,000+60,000 annual cost

Present Value of Benefits = 480,000*10.6748 = 5,123,904

Present Value of Costs = 3, 600, 000, + 60, 000,* 10.6748 = 4,240,488

= 5,123,904/4,240,488 = 1.2083

This option can also be accepted because the ratio is more than one.

For mutually exclusive decision, we can select the option M compared to N and P