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Appendix
B: Details
of Present Net Value Calculation
Economics of New Combined-Cycle Generator
This appendix describes in more detail the calculations
of net present value (NPV) reported in Chapter 2. The combined-cycle
(CC) generator example is particularly relevant because the technology
is less capital intensive than other technologies, such as coal, nuclear,
and renewable electricity plants. In addition, Energy Information Administration
projections show natural-gas-fired generation increasing from 16 percent
of total U.S. electricity generation in 2000 to 32 percent of the total
in 2020, overtaking nuclear power as the Nation’s second-largest
source of electricity by 2004.150 Moreover, a growing number of refineries, petrochemical plants, and
other industrial facilities that use natural gas to generate electricity
for their own needs are becoming cogenerators, selling excess electricity
to local utilities and power marketers. Those firms rely on stable natural
gas supplies and prices; volatile gas prices can have considerable impact
on their earnings, as noted in Chapter 2.
Capital Budgeting for a Power Generator
In the example shown in Chapter 2, an independent power
producer faces a capital budgeting project (e.g., building a gas-fired
plant) and uses NPV methodology to evaluate the project. The simple
rule often given for choosing investment projects is the NPV rule: choose
only projects with positive NPVs. The NPV methodology implicitly assumes
that the incremental cash flows from a project will be reinvested to
earn the firm’s risk-adjusted required rate of return throughout
the life of the project. The NPV of a project reveals the amount by
which its productive value (present value of net cash flows) exceeds
or is less than its cost. Naturally, investors choose only those projects
whose productive values exceed or at least equal their costs. If the
NPV of a project is positive (NPV > 0), the amount of the NPV is
the amount by which the project will increase the value of the firm
making the investment.
The assumptions underlying the capital investment example
shown in Chapter 2, Table
4, are summarized in Table
B1.151 Table
B2 shows the detailed annual cash flow calculations based on the
assumptions and the price projections shown in Chapter 2, Table
4. Because the plant has a positive NPV of $2,118,017, it is profitable
and should be built.
NPV Distributions with Simulation
In fact, the future output and input prices for the project
are uncertain, and it may become unprofitable if the actual input and
output prices vary much from their expected means. Therefore, a Monte
Carlo simulation was used to estimate the distribution of the project’s
NPV when both electricity and natural gas prices are varied.152 For the simulation analysis, lognormal distributions were defined for
both electricity and natural gas prices, and the prices were varied
by plus and minus 77 percent and 47 percent, respectively, as a standard
deviation, from the expected prices.153 The price variations were based on daily historical data on NYMEX spot
prices from March 1999 through March 2002. A historical positive correlation
of 0.88 between the average electricity spot price and Henry Hub natural
gas spot price was specified for each year of the project’s life.154 The NPV distribution generated by the simulation is shown Figure
6, and the statistical results and summary are shown Table
5, in Chapter 2.155 The simulation results indicate that there is about a 17-percent chance
that the investment will be unprofitable (i.e., that it will have a
negative NPV).
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Because the investor faces some probability of loss as
a result of price fluctuations, he may have an incentive to mitigate
the risk by hedging with such tools as long-term contracts, futures,
options, and swaps. It was assumed for the analysis that the power producer’s
maximum risk tolerance for the price volatilities was plus or minus
one standard deviation from their means, or 77 percent and 47 percent
of the mean price for electricity and natural gas, respectively. This
assumption led to triangular distributions for both prices (Table
B3).
When it was assumed that the price volatility would be
hedged, the probability of positive NPV increased from 83 percent to
99 percent with a coefficient of variation (CV) of 0.42. Without hedging
the price volatility, the CV was 1.09. The distribution is shown in Figure B1.
The summary of statistical results and a statistical comparison of the
simulations are shown in Table
B4. As shown, a hedged project has less probability of negative
NPV, smaller standard deviation of NPV, and a smaller risk measurement
(CV).
Appendix B - Tables 
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