Question

The state of Indiana has decided to implement a new food control system, and is choosing between two competing proposals. Each alternative is expected to provide a functioning flood control system for the next 50 years. Proposal A would result in estimated annual benefits to the public of $400,000 due to increased safety, an initial cost of $2,500,000, an annual maintenance cost of $150,000, and annual disbenefits to the public of $100,000. Proposal 8 would result in estimated annual benefits to the public of $350,000, an initial cost of $2,000,000, an annual maintenance cost of $130,000, and annual disbenefits to the public of $50,000 Use the annual worth method to compute the conventional B-C ratio for each proposal, while including disbenefits in the numerator Determine which proposal should be chosen and explain why. Assume 8% MARR, and no additional cash flows at the end of the 50 year project period.

Answer 1

Basic Calculations:

Discount Factor (given) = 8%

Project Life = 50 Years

Present value of an annuity of 50 years discounted at 8% = PVIFA(8%, 50)

= 12.2336

(1) B-C ratio for Proposal A:

a. Present Value of Cost

$

Initial Cost 2500000

Present value of Annual Maintenance Cost

[150000 * 12.2336] 1835040

Total Cost (At present value)    4335040

b. Present Value of Benefits

(i) Annual Benefits to the public 400000

Less: Annual disbenefit to the public 100000 300000

(ii) PVIFA(8%, 50) 12.2336

(iii) Total Benefits (At present value) [(i) * (ii)] 3670080

B-C Ratio = b/a

= 3670080/4335040

= .8466

(2) B-C ratio for Proposal B:

a. Present Value of Cost

$

Initial Cost 2000000

Present value of Annual Maintenance Cost

[130000 * 12.2336] 1590368

Total Cost (At present value)    3590368

b. Present Value of Benefits

(i) Annual Benefits to the public 350000

Less: Annual disbenefit to the public    50000 300000

(ii) PVIFA(8%, 50) 12.2336

(iii) Total Benefits (At present value) [(i) * (ii)] 3670080

B-C Ratio = b/a

= 3670080/3590368

= 1.022

So, Proposal B is beneficial as its B-C Ratio is greater than the B-C Ratio of Proposal A