Question

A new water treatment plant proposed for Anytown, has an initial cost of P56 million. The new plant will service the 7,500 residential customers for the next 30 years. It is expected to save each customer P125 per year. The plant will require a major overhaul every 5 years, costing P1million. Determine the benefit/cost ratio at the city’s interest rate of 6%. Use PW and EUAC.

Answer 1

Given data:

Initial cost = P56 Million

Savings per year = P125 per customer

Customers benefitted = 7500

Total Savings per year = 125 * 7500 = P 937500

Overhaul costs = P 1 Million every 5 years

Interest rate = 6%

Tenure = 30 years

Benefit-cost ratio is the ratio of the present worth of benefits to present worth of costs, If the Benefit-cost ratio is greater than 1 then the project is profitable, Benefit-cost ratio is equal to 1 then the project is breakeven and Benefit-cost ratio is less than 1 then the project is not profitable

Benefit-cost ratio = Present worth of benefits / Present worth of costs

Benefit-cost ratio = 937500(P/A,6%,30) / [56000000 + 1000000(P/F,6%,5) + 1000000(P/F,6%,10) + 1000000(P/F,6%,15) + 1000000(P/F,6%,20) + 1000000(P/F,6%,25) + 1000000(P/F,6%,30)]

Using DCIF tables

Benefit-cost ratio = 937500(13.765) / (56000000 + 1000000(0.7473) + 1000000(0.5584) + 1000000(0.4173) + 1000000(0.3118) + 1000000(0.2330) + 1000000(0.1741))

Benefit-cost ratio = 0.2208

Benefit-cost ratio is the ratio of the Annual worth of benefits to Annual worth of costs, If the Benefit-cost ratio is greater than 1 then the project is profitable, Benefit-cost ratio is equal to 1 then the project is breakeven and Benefit-cost ratio is less than 1 then the project is not profitable.

Benefit-cost ratio = Annual worth of benefits / Annual worth of costs

Benefit-cost ratio = 937500 / [56000000(A/P,6%,30) + (1000000(P/F,6%,5) + 1000000(P/F,6%,10) + 1000000(P/F,6%,15) + 1000000(P/F,6%,20) + 1000000(P/F,6%,25) + 1000000(P/F,6%,30) (A/P,6%,30)]

Using DCIF tables

Benefit-cost ratio = 937500 / (56000000(0.0726) + [(1000000(0.7473) + 1000000(0.5584) + 1000000(0.4173) + 1000000(0.3118) + 1000000(0.2330) + 1000000(0.1741)](0.0726))

Benefit-cost ratio = 0.2209