Principles of Corporate Finance_ 12th Edition

(lu) #1

Chapter 22 Real Options 583


bre44380_ch22_573-596.indd 583 09/30/15 12:08 PM


Flexible production means the ability to vary production inputs or outputs in response to fluc-
tuating demand or prices. Take the case of CT (combustion-turbine) generating plants, which
are designed to deliver short bursts of peak-load electrical power. CTs can’t match the thermal
efficiency of coal or nuclear power plants, but CTs can be turned on or off on short notice.
The coal plants and “nukes” are efficient only if operated on “base load” for long periods.
The profits from operating a CT depend on the spark spread, that is, on the difference
between the price of electricity and the cost of the natural gas used as fuel. CTs are money-
losers at average spark spreads, but the spreads are volatile and can spike to very high levels
when demand is high and generating capacity tight. Thus a CT delivers a series of call options
that can be exercised day by day (even hour by hour) when spark spreads are sufficiently high.
The call options are normally out-of-the-money (CTs typically operate only about 5% of the
time), but the money made at peak prices makes investment in the CTs worthwhile.^10
The volatility of spark spreads depends on the correlation between the price of electricity
and the price of natural gas used as fuel. If the correlation were 1.0, so that electricity and
natural gas prices moved together dollar for dollar, the spark spread would barely move from
its average value, and the options to operate the gas turbine would be worthless. But in fact
the correlation is less than 1.0, so the options are valuable. In addition, some CTs are set up to
give a further option, because they can be run on oil as well as natural gas.^11
The top panel of Figure 22.5 shows a histogram of electricity prices for the U.K. between
January 2013 and January 2015. Prices are set every half hour, so there are about 35,000
prices plotted. Prices are quoted as pounds per megawatt-hour (£/MWH). Notice how strongly
the histogram is skewed to the right. Although the average price was only £53 per MWH,
prices above £100/MWH crop up regularly when electricity demand peaks. The highest price
was £429/MWH. The occasional high prices are hardly visible in the top panel of Figure 22.5.
The bottom panel plots only the prices above £60/MWH.
Suppose you have a CT generating plant in the U.K. that is profitable only at prices above
£60/MWH. Of course you will exercise your option to operate if prices are above £60 and leave
the plant idle otherwise. The payoff from operating equals the price minus £60. Although the
plant would have been idle for nearly three-quarters of the time, it would have reaped an aver-
age profit of over £17 per MWH when it was producing. The possible payoffs are plotted in
the bottom panel of Figure 22.5. The payoff line exactly matches the payoff diagrams for call
options with an exercise price of £60. The only difference is that your plant has about 17,500
options every year, one for each half hour in the year.
The payoff line in Figure 22.5 assumes that the plant’s operating cost is constant at £60.
This is accurate only if the cost of natural gas is constant. Otherwise the payoff to the option
to operate depends on the spark spread. Often the cost of gas is locked in by contract between
the generator and the gas supplier. But if the cost of gas is sufficiently volatile, you would
replot Figure 22.5 in spark spreads rather than electricity prices. You would operate when the
spark spread is positive.
In this example, the output is the same (electricity); option value comes from the ability to
vary output. In other cases, option value comes from the flexibility to switch from product to
product using the same production facilities. For example, textile firms have invested heavily


22-4 Flexible Production and Procurement


(^10) Here we refer to simple CTs, which are just large gas turbines connected to generators. Combined-cycle CTs add a steam generator
to capture exhaust heat from the turbine. The steam is used to generate additional electricity. Combined-cycle units are much more
efficient than simple CTs.
(^11) Industrial steam and heating systems can also be designed to switch between fuels, depending on relative fuel costs. See
N.  Kulatilaka, “The Value of Flexibility: The Case of a Dual-Fuel Industrial Steam Boiler,” Financial Management 22 (Autumn
1993), pp. 271–280.

Free download pdf