Question

To purchase a new piece of equipment, a company must spend $4,800 in time 0. By using the new equipment, the company estimates that it will generate $1,000 in profit each year. The annual operating and maintenance (O&M) costs are projected to be $550 per year. At the end of its useful life in 8 years, the company expects that it can sell the piece of equipment for $3,500 (salvage value). The minimum attractive rate of return (MARR) that the company has established for the purchase is 9%. Use the benefit/cost (B/C) method to determine whether purchasing the equipment is economically justified. Base the B/C ratio on the present worth of the benefits and costs.

Answer 1

Cost of the new equipment = $4,800 (Present worth)

Useful life of the equipment = 8 years

MARR = 9%

Annual Operating and Maintenance cost = $550

The present worth of Annual O&M cost = $500 x (P/A, 9%, 8)

From the Compound Interest Table, we obtain (P/A, 9%, 8) = 5.535

Therefore, Present worth of Annual O&M cost = $550 x 5.535 = $3,044.25

Profit generated by the new equipment each year = $1,000

The present worth of the annual profit for 8 years = $1,000 x (P/A, 9%, 8) = $1,000 x 5.535 = $5,535

Salvage value at the end of 8 years = $3,500 x (P/F, 9%, 8) = $3500 x 1/(1+0.09)⁸ = $1,756.53

Present Worth(PW) of total costs = Cost of the equipment + PW of annual O&M costs = $4,800 + $3,044.25 = $7,844.25

PW of total benefits = PW of annual profits + PW of Salvage Value of the equipment = $5,535 + $1,756.53 = $7,291.53

Benefit-Cost Ratio using PW = PW of benefits/PW of costs = $7,291.53/ $7,844.25 = 0.93 (<1)

As B/C is less than 1, purchasing the equipment is not economically justified