11: Risk and Capital BudgetingexampleImagine that Greene Transportation Incorporated
(GTI) has developed a new skateboard equipped with
a gyroscope for improved balance. GTI estimates that
this project has a positive NPV of $236,000 under the
following base-case assumptions:
1 The project’s life is five years.
2 The project requires an up-front investment of $7
million.
3 GTI will depreciate the initial investment on a
straight-line basis for five years.
4 One year from now, the skateboard industry as a
whole will sell 500,000 units.
5 Total industry unit volume will increase by 5% per year.
6 GTI expects to capture 5% of the market in the first
year.
7 GTI expects to increase its market share by one
percentage point each year after year 1.
8 The selling price will be $200 in year 1.
9 The selling price will decline by 10% annually after
year 1.
10 All production costs are variable and will equal 60%
of the selling price.
11 GTI’s tax rate is 30%.
12 The appropriate discount rate is 14%.Under the base-case assumptions, the project has a
small (relative to the $7-million investment) but positive
NPV ($236,000), so GTI’s managers may want to explore
how sensitive the NPV is to changes in the assumptions.
Analysts often begin a sensitivity analysis by developing
both pessimistic and optimistic forecasts for each of the
model’s important assumptions. These forecasts may
be based on subjective judgements about the range of
possible outcomes, or on historical data drawn from the
company’s past investments. For example, a company
with historical data available on output prices might set
the pessimistic and optimistic forecasts at one standard
deviation below and above their expected price.
Table 11.4 shows pessimistic and optimistic
forecasts for several of the NPV model’s key
assumptions. Next to each assumption is the project
NPV that results from changing one (and only one)
assumption from the base-case scenario. For example,
if GTI can sell its product for $225 rather than $200
per unit the first year, the project NPV increases to
$960,000. If, however, the selling price is less than
expected – say, $175 per unit – then the project
NPV declines to –$488,000. A glance at Table 11.4
reveals that small deviations in assumptions about
market share generate large NPV changes whereas
assumptions about market size have less impact.TABLE 11.4 SENSITIVITY ANALYSIS OF THE GYROSCOPE SKATEBOARD PROJECT (BASE-CASE NPV = $236)NPV Pessimistic Assumption Optimistic NPV
–$558 $8,000 Initial investment $6,000 $1,030
–343 450,000 units Market size in year 1 550,000 units 815
–73 2% per year Growth in market size 8% per year 563
–1,512 3% Initial market share 7% 1,984
–1,189 0% Growth in market share 2% per year 1,661
–488 $175 Initial selling price $225 960
–54 62% of sales Variable costs 58% of sales 526
–873 –20% per year Annual price change 0% per year 1,612
–115 16% Discount rate 12% 617
Note: all dollar values in thousands, except initial selling price.11-2c SCENARIO ANALYSIS
Scenario analysis is a variation of sensitivity analysis. Rather than adjusting a single assumption up or down,
analysts conduct scenario analysis by calculating the project’s NPV when a whole set of assumptions
changes in a particular way. For example, what if consumer interest in GTI’s new skateboard is low,LO11.4
scenario analysis
A variation of sensitivity
analysis that provides for
calculating the decision
variable, such as net present
value, when a whole set of
assumptions changes in a
particular way