Question

5. The Army Corps of Engineers is considering two designs for flood protection along the Mississippi River.

Option R requires an investment of $3 million and $30,000 per year in maintenance costs. Benefits from flood prevention are estimated to be $500,000 per year.

Option S would cost $5 million to build and $60,000 per year to maintain. Benefits from flood prevention would be $750,000 per year.

Assume that either design would be maintained and operated indefinitely. For an interest rate of 4% per year, determine which design (if any) should be chosen based on:

(a) Conventional benefit/cost analysis; and
(b) Modified benefit/cost analysis (subtracting maintenance costs from benefits).

Did both analyses recommend the same design? Explain.

Answer 1

Answer a

Option R:

Initial Investment = $3000000

Maintenance cost=$30000

Benefits =$500000

PV of Benefits for perpetuity= Benefit per year/ rate=500000/4% = $12500000

PV of Maintenance cost for perpetuity= Maintenance cost per year/ rate=30000/4% = $750000

Hence Benefit cost Ratio = PV of Benefits/(PV of Initial Investment+ PV of maintenance cost) = 12500000/(3000000+750000) = 12500000/3750000 = 3.33

Option S:

Initial Investment = $5000000

Maintenance cost=$60000

Benefits =$750000

PV of Benefits for perpetuity= Benefit per year/ rate=750000/4% = $18750000

PV of Maintenance cost for perpetuity= Maintenance cost per year/ rate=60000/4% = $1500000

Hence Benefit cost Ratio = PV of Benefits/(PV of Initial Investment+ PV of maintenance cost) = 18750000/(5000000+1500000) = 18750000/5500000 = 3.41

Hence Option S has higher B/C ratio by conventional method

Answer b

Option R

Modified B/C = (PV of Benefit- PV of Maintenance cost)/ PV if initial cost = (12500000-750000)/(3000000) = 11750000/3000000 = 3.92

Option S

Modified B/C = (PV of Benefit- PV of Maintenance cost)/ PV if initial cost = (18750000-1500000)/(5000000) = 17250000/5000000 = 3.45

Hence Option R has higher B/C ratio by Modified B/C method

Hence both method is giving different results