General Ford (GF) Auto Corporation is developing a new type of compact car. This car is
assumed to generate sales for the next 10 years. GF has gathered information about the
following quantities through focus groups with the marketing and engineering departments.
• Fixed cost of developing car. This cost is assumed to be normally distributed with mean and
standard deviation $2.3 billion and $0.5 billion. The fixed cost is incurred at the beginning of
year 1, before any sales are recorded.
• Variable production cost. This cost, which includes all variable production costs required to
build a single car, is assumed to be normally distributed during year 1 with mean and
standard deviation $7800 and $600. Each year after year 1, the variable production cost is
the previous year’s variable production cost multiplied by an inflation factor. Each year this
inflation factor is assumed to be normally distributed with mean 1.05 (a 5% increase) and
standard deviation 0.015. All production costs are assumed to occur at the ends of the
• Selling price. The price in year 1 is already set at $11,800. After year 1 the price will increase
by the same inflation factor that drives production costs. Like production costs, revenues
from sales are assumed to occur at the ends of the respective years.
• Demand. The demand for the car in year 1 is assumed to be normally distributed with mean
100,000 and standard deviation 10,000. After year 1 the demand in a given year is assumed
to be normally distributed with mean equal to the actual demand in the previous year and
standard deviation 10,000. For example, if the observed demand in year 3 is 105,000, then
the demand distribution in year 4 has mean 105,000. An implication of this assumption is
that demands in successive years are not probabilistically independent. For example, if the
demand in one year is large, the mean demand for the next year is also large, so that the
actual demand for the next year will tend to large.
• Production. In any particular year GF plans to base its production policy on the probability
distribution of demand for that year – before the actual demand for that year is observed.
In particular, if the expected demand in year t is μ and standard deviation of demand is σ,
then GF’s policy is to produce μ + k * σ cars, where k is a multiple that GF will have to select.
For example, if it chooses k = 1, then its production quantity in any year will be one standard
deviation above the mean of demand. From the properties of the normal distribution, using
k = 1 implies that the chances are approximately 5 out of 6 of meeting demand for the year.
(This is because a normal random variable has approximate probability 5/6 of being no more
than one standard deviation above the mean.) If demand in any year is greater than
production, the excess demand is lost. However, if production in any year is greater than
demand, GF will sell the excess cars at an end-of-year discount of 30%.
• Interest rate. GF plans to use a 10% interest rate to discount future cash flows. This means,
for example, that a cash flow of $1 at the beginning of year 1 is equivalent to a to cash flow
of $1.10 at the end of year 1.
Given these assumptions, develop a simulation model with Excel + @RISK that will evaluate
the net present value (NPV) for this new car over the 10-year time horizon.
Considerations to be included:
• An analysis of pros and cons of various k multiples that have been considered for the
• A recommendation to GF with respect to which value of k multiple should be in the
production policy; and
• Assuming demands for the new car over the 10 years are independently normally
distributed with mean 100,000 and standard deviation 10,000:
o Please comment on differences with respective to relevant aspects associated with
the new car business analysis, between this demand scenario and the previous
scenario in which demands in successive years are not probabilistically independent;
o Recommend a k multiple for the production policy under this demand scenario.