Question: A power plant that produces emissions of sulfur dioxide (SO2). Annual

Question

Question: A power plant that produces emissions of sulfur dioxide (SO2). Annual emissions are 1,000 tons per year in perpetuity and it currently faces an emissions tax of $20 per ton of SO2. The power plant can install a scrubber with a capital cost of $50,000. If it uses the scrubber, it incurs a one-time cost of $250,000 and the plant will not emit any SO2 for the remainder of its operational life. The plant faces a discount rate of 10%. There is no marginal cost to using the scrubber. We can thus view the scrubber as an option to control SO2 emissions in the future.

(A, 10 points): Should the power plant install the scrubber and commit to using it?

(B, 20 points): There is a 50% probability that the emissions price will increase to $35 per ton next year. Calculate the value of the option to control SO2 pollution. Should the power plant install the scrubber?

Explanation / Answer

Power Plant cost $50000 is incurred whether or not use scrubber

One time cost $250000 is relevant for decison making

A) Annual emissions are 1,000 tons per year in perpetuity and it currently faces an emissions tax of $20 per ton of SO2

Present value of benefits from scrubber = 1000tons X $20

= $20000/0.10

=$200000

Not incur one time cost, if emission tax $20 per ton

B) If there is a 50% probability that the emissions price will increase to $35 per ton next year

expected emission tax in next year = $35 X 50% + $20 X 50%

=$ 27.5

PV of benefits from scrubber = $20000(in year 1) + PV of perpectuvity

   perpectuvity(year 2) =1000 tons x $27.5/.10

= $275000

PV of perpectuvity =275000 X .9091 = 250000

Total Benefits =20000 + 250000 =270000

PV of benefits more than cost incure one time cost of $250000 and save $20000

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