Project Risk Analysis: Techniques for Measuring Stand-Alone Risk 319
Then those values are combined, and the project’s NPV is calculated and stored in
the computer’s memory. Next, a second set of input values is selected at random, and
a second NPV is calculated. This process is repeated perhaps 1,000 times, generat-
ing 1,000 NPVs. The mean and standard deviation of the set of NPVs is deter-
mined. The mean, or average value, is used as a measure of the project’s expected
NPV, and the standard deviation (or coefficient of variation) is used as a measure of
risk.
Using this procedure, we conducted a simulation analysis of RIC’s proposed proj-
ect. As in our scenario analysis, we simplified the illustration by specifying the distri-
butions for only four key variables: (1) sales price, (2) variable cost, (3) Year 1 units
sold, and (4) growth rate.
We assumed that sales price can be represented by a continuous normal distribu-
tion with an expected value of $3.00 and a standard deviation of $0.35. Recall from
Chapter 3 that there is about a 68 percent chance that the actual price will be within
one standard deviation of the expected price, which results in a range of $2.65 to
$3.35. Put another way, there is only a 32 percent chance that the price will fall outside
the indicated range. Note too that there is less than a 1 percent chance that the actual
price will be more than three standard deviations of the expected price, which gives us
a range of $1.95 to $4.05. Therefore, the sales price is very unlikely to be less than
$1.95 or more than $4.05.
RIC has existing labor contracts and strong relationships with some of its suppli-
ers, which makes the variable cost less uncertain. In the simulation we assumed that
the variable cost can be described by a triangular distribution, with a lower bound of
$1.40, a most likely value of $2.10, and an upper bound of $2.50. Note that this is not
a symmetric distribution. The lower bound is $0.70 less than the most likely value, but
the upper bound is only $0.40 higher than the most likely value. This is because RIC
has an active risk management program under which it hedges against increases in the
prices of the commodities used in its production processes. The net effect is that RIC’s
hedging activities reduce its exposure to price increases but still allow it to take advan-
tage of falling prices.
Based on preliminary purchase agreements with major customers, RIC is certain
that sales in the first year will be at least 15,000 units. The marketing department be-
lieves the most likely demand will be 20,000 units, but it is possible that demand will
be much higher. The plant can produce a maximum of 30,000 units in the first year, al-
though production can be expanded in subsequent years if there is higher than ex-
pected demand. Therefore, we represented Year 1 unit sales with a triangular distri-
bution with a lower bound of 15,000 units, a most likely value of 20,000 units, and an
upper bound of 30,000 units.
The marketing department anticipates no growth in unit sales after the first year,
but it recognizes that actual sales growth could be either positive or negative. More-
over, actual growth is likely to be positively correlated with units sold in the first year,
which means that if demand is higher than expected in the first year, then growth will
probably be higher than expected in subsequent years. We represented growth with a
normal distribution having an expected value of 0 percent and a standard deviation of
15 percent. We also specified the correlation between Year 1 unit sales and growth in
sales to be 0.65.
We used these inputs and the model from Ch 08 Tool Kit.xls to conduct the sim-
ulation analysis. If you want to do the simulation yourself, you should first read the
instructions in the file Explanation of Simulation.doc. This explains how to install an
Excel add-in, Simtools.xla, which is necessary to run the simulation. After you have
installed Simtools.xla, you can run the simulation analysis, which is in a separate
318 Cash Flow Estimation and Risk Analysis
