Prescriptive Analytics Company Case Study
Description
The Jogger Shoe Company is trying to decide whether to make a
change in its most popular brand of running shoes. The new style would cost the
same to produce and be priced the same, but it would incorporate a new kind of
lacing system that (according to its marketing research people) would make it
more popular.
There is a fixed cost of $300,000 for changing over to the new
style. The unit contribution to before-tax profit for either style is $8. The
tax rate is 35%. Also, because the fixed cost can be depreciated and will
therefore affect the after-tax cash flow, a depreciation method is needed. You
can assume it is straight-line depreciation.
The current demand for these shoes is 190,000 pairs annually.
The company assumes this demand will continue for the next three years if the
current style is retained. However, there is uncertainty about demand for the
new style, if it is introduced. The company models this uncertainty by assuming
a normal distribution in year 1, with mean 220,000 and standard deviation
20,000. The company also assumes that this demand, whatever it is, will remain
constant for the next three years. However, if demand in year 1 for the new
style is sufficiently low, the company can always switch back to the current
style and realize an annual demand of 190,000. The company wants a strategy
that will maximize the expected net present value (NPV) of total cash flow for
the next three years, where a 10% interest rate is used for the purpose of
calculating NPV.
Realizing that the continuous normal demand distribution doesn’t
lend itself well to decision trees that require a discrete set of outcomes, the
company decides to replace the normal demand distribution with a discrete
distribution with five “typical” values. Specifically, it decides to use the
10th, 30th, 50th, 70th, and 90th percentiles of the given normal distribution.
Why is it reasonable to assume that these five possibilities are equally
likely? With this discrete approximation, how should the company proceed?
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