Question

Assume that a coal fired power plant has just had its license to operate expire. This company holds $50 million in a fund to cover the costs of shutting down its power plant. The government has offered the company a new 10-year license. Due to a new carbon tax on coal use, the company’s costs have gone up, to the point where the company will lose $2 million per year simply by operating the plant and selling electricity. They will then have to pay the $50 million to decommission in ten years. The firm has to decide whether it wants to renew its license. If it refuses a new license, then all of the $50 million in the fund must be used immediately to shut down the plant. The interest rate is 4%. Advise the company on whether it should accept or reject the new 10-year license. Please show your work.

Answer 1

To decide whether to accept or reject the new 10-year license, we compare the present value of operating the plant for 10 years with the present value of decommissioning the plant immediately.

Step-by-step explanation:

To advise the company on whether it should accept or reject the new 10-year license, we need to compare the present value of operating the plant for 10 years with the present value of decommissioning the plant immediately.

The present value of operating the plant for 10 years and paying $2 million per year is calculated as follows:

-PV = -C x((1-(1+r)^-n)/r) where C is the annual cost, r is the interest rate, and n is the number of years.
PV = -2 million x ((1-(1+0.04)^-10)/0.04) = -15.786 million

The present value of decommissioning the plant immediately is $50 million. Since the present value of operating the plant for 10 years (-15.786 million) is greater than the present value of decommissioning the plant immediately (-50 million), the company should reject the new 10-year license.