Sample Exam Problems

Policy uncertainty and power plant construction.

Suppose an electric power producer is interested in building a new 500 MW power plant.  It is considering three technologies: (1) advanced pulverized coal (APC); (2) combined cycle natural gas (NGCC); and (3) combined cycle natural gas with carbon capture and sequestration (NG CCS). More information on the technologies is given in the table below.  In all cases the company expects the plant to last for 40 years and expects to be able to sell electricity for $60 per MWh (in all years). The firm uses 5% as the real interest rate when doing present value calculations.

Table 1: Technology Characteristics

Variable APC NGCC NG CCS
Construction cost, $/MW $3,167,000 $980,000 $1,060,000
Capacity factor 0.9 0.8 0.8
Annual fixed cost, $/MW $36,000 $14,000 $30,000
Variable cost except fuel, $/MWh $4 $3 $6
Heat rate, million BTU/MWh 8.8 7.05 7.525
CO2 rate, metric tons/million BTU 0.093 0.053 0

The table shows fixed and variable costs except fuel, which needs to be taken into account separately. For power production, fossil fuels are often measured by the amount of heat they generate when burned rather than as tons (coal) or cubic feet or cubic meters (gas).  The heat rate of a fossil fuel power plant is the amount of fuel (measured in millions of BTUs of heat content) needed to produce a given amount of electricity.   For example, an advanced coal plant needs 8.8 million BTU of coal to produce 1 MWh of electricity.  

The prices of coal and gas are quoted per million BTU as well and in this case the company believes that throughout the life of the plant the price of coal will be $2.25 per million BTU and the price of natural gas will be $4.25 per million BTU.  (It would be interesting to relax this assumption and consider varying prices but you don't need to do that in this exercise).

The company also believes that a carbon tax on CO2 emissions might be imposed in the near future.  The amount of CO2 produced per unit of fuel is shown in the last line of the table, with 0 for the NG CCS plant since it would emit no CO2.  The firm believes there is a 50% chance that a tax will be announced in year 5 to take effect beginning in year 6.  If the tax is imposed, it will be $50 per ton of CO2. However, there's also a 50% chance no tax will be imposed.  Whatever tax is announced in year 5 will remain in effect for the life of the plant.

The company is only going to build one plant, but it can choose whether to build immediately (t=0) or in year 5 (t=5) after the tax has been announced.  In either case, you may assume that the plant can be built in a single year; that it will begin producing electricity in t=1 or t=6; and that it will last for 40 years (1-40 or 6-45).  Just to be clear, if a carbon tax is imposed, the first year the firm will have to pay it is t=6.

  1. Please calculate the NPV of building each plant at t=0 using the expected value of the carbon tax.  Which plant is the best option?
  2. Please calculate the expected NPV in year 0 of waiting until the tax (or lack of tax) is revealed at t=5 and then building the optimal plant given the actual tax.  
  3. What is the firm's best alternative?  Briefly explain the intutition behind why it's best.  If option value is involved, please calculate it.
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/26/2016