Question

Consumer Energy Corp. is an electric utility that uses natural gas to produce electricity. If the firm does not hedge its exposure to natural gas prices, it will have taxable income in the coming year of $80,000,000 if the market price of natural gas is “low” and -$20,000,000 if the market price of natural gas is “high.” The probability of each outcome is 50%. The firm has a corporate tax rate of 40% and cannot carry its losses forward.

The firm has decided to hedge a portion of its natural gas exposure by entering into futures contracts that will provide a gain of $20,000,000 if the market price of natural gas in the coming year is “high” and a loss of $20,000,000 if the market price of natural gas is “low.” The firm has to pay transaction costs of $1,000,000 to enter into the futures contracts. What is the firm’s expected net (after-tax) income for the coming year, after undertaking this hedge?

Answer 1

firm’s expected net (after-tax) income for the coming year with hedging = [((taxable income if price of natural gas is low*probability) + (taxable income if price of natural gas is high*probability))*(1 - tax rate)] + (gain from futures contract if price of natural gas is high*probability) - (loss from futures contract if price of natural gas is low*probability) - transaction costs of futures contracts

probability of gain and loss from futures contracts is 50% each because only one of the event can happen.

firm’s expected net (after-tax) income = [(($80,000,000*50%) + (-$20,000,000*50%))*(1-0.40)] + ($20,000,000*50%) - ($20,000,000*50%) - $1,000,000

firm’s expected net (after-tax) income = [($40,000,000 - $10,000,000)*0.60] + $10,000,000 - $10,000,000 - $1,000,000 = ($30,000,000‬*0.60) + $10,000,000 - $10,000,000 - $1,000,000 = $18,000,000 + $10,000,000 - $10,000,000 - $1,000,000 = $17,000,000‬

the firm’s expected net (after-tax) income for the coming year, after undertaking this hedge is $17,000,000‬.