Suppose that the State of Colorado is considering a new environmental regulation

Question

Suppose that the State of Colorado is considering a new environmental regulation to improve water quality along the South Platte River. The regulation will require municipalities to install new control equipment that is estimated to cost $1 million upon installation and then maintenance costs of $50,000 per year. The equipment will last 20 years. A state economist estimates that the recreation benefits from the water quality improvement will be $125,000 per year as soon as the control equipment is installed. Calculate the present value of net benefits to this regulation and determine it passes the benefit cost test if r=0.03 and if r=0.06.

Explanation / Answer

Benefit-Cost ratio (BCR) = Present value (PV) of benefits / PV of costs

(i) r = 3%

PV of benefits ($) = 125,000 x PVIFA(3%, 20) = 125,000 x 14.8775 = 1,859,688

PV of costs ($) = 1,000,000 + 50,000 x PVIFA(3%, 20) = 1,000,000 + 50,000 x 14.8775

= 1,000,000 + 743,875 = 1,743,875

BCR = 1,859,688 / 1,743,875 = 1.07

Since BCR > 1, project is acceptable.

(ii) r = 6%

PV of benefits ($) = 125,000 x PVIFA(6%, 20) = 125,000 x 1.4699 = 1,433,738

PV of costs ($) = 1,000,000 + 50,000 x PVIFA(6%, 20) = 1,000,000 + 50,000 x 11.4699

= 1,000,000 + 573,495 = 1,573,495

BCR = 1,433,738 / 1,573,495 = 0.91

Since BCR < 1, project is not acceptable.

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