Download Instructions on the Write-Up

COLUMBIA
BUSINESS
SCHOOL
B6015: Decision Models
Spring 2007
Simulation Homework
This assignment is to be done in groups. In your write-up, answer all the questions and
provide a thorough description of your models. Each question must be answered in words and
also must include a printout of the spreadsheet (as described below).
Instructions on the Write-Up
Try to limit your write-up to one page of text with support exhibits attached. The exhibits
should include, for each problem, a printout of your spreadsheet, including the relevant Crystal
Ball Results (on one page if possible). Please make sure that: all important formulas are
described and all important parts of the spreadsheet are labeled. Of course, the labeling can be
handwritten. Another option is to use the comments feature in Excel.
 To write a comment: either right-click on a cell (and choose “Insert Comment”) or from the
menu choose “Insert|Comment”.
 To get the comments to print: go to File|Page Setup and then pick the Sheet tab and pick
“Comments: as displayed on sheet.” Click OK or Print.
 To get the file to print with row and column headings: go to File|Page Setup and pick the
Sheet tab and check off “row and column headings.” Click OK or Print.
Problem 1: Competitive Bidding (50 points)
Two partners have decided to sell the manufacturing business they have been running. They have
lined up 5 prospective buyers and have hired a consultant to help them with the bidding and the
sale. The consultant has told the partners that the business is worth $10 million.
The consultant has obtained indications that the prospective buyers would be willing to
participate in a sealed-bid auction to determine who will buy the business and at what price.
Under the rules of the auction, the sales price would be equal to the highest bid.
Possessing only limited information about the business, the bidders may overestimate or
underestimate what the business is actually worth. After listening to their preliminary thoughts,
the consultant has concluded that each buyer’s bid for the business is equally likely to be
anywhere between $8 million and $12 million (i.e., each buyer’s bid is uniformly distributed on
the interval from $8 million to $12 million) and that there is no correlation between the buyers’
bids.
a) (20 points) Set up and run a simulation model with n=10,000 trials and an arbitrary
seed to determine an estimate for the expected price that the partners will receive for
their business. How accurate is your estimate? (Give a 95% confidence interval for the
true value of the expected price.) How many trials would be needed in order to ensure
that the width of the 95% confidence interval for the expected price does not exceed
$1000?
b) (10 points) Suppose that the partners would also like to know the probability that they
will receive at least $10 million for their business. Estimate, with 95% confidence, this
probability with a precision of 0.001 (i.e., run a sufficient number of trials to ensure that
the width of the 95% confidence interval for this probability does not exceed 0.001).
c) (20 points) Suppose the consultant asks for a $300,000 fee in order to identify 5 more
bidders to participate in the auction. Assume that each new bidder is equally likely to
bid anywhere between $8 million and $12 million and that their bids are not correlated
with each other, or the bids of the first 5 bidders. Use a simulation with n=10,000 trials
and an arbitrary seed to estimate the expected value of the net revenue (= extra revenue
as compared to the case of 5 bidders, net of the consulting fee) that the partners will
obtain through this new arrangement. What is the probability that the actual net revenue
will be positive?
Problem 2: Pharmaceutical Capacity Management (50 points)
Lang Drug needs to determine the proper level of production capacity for a new drug,
Niagara. The company’s goal is to maximize the expected NPV earned from the drug during
the years 0-15, assuming an annual discount rate of 10%. It costs $10 to build enough annual
production capacity to produce 1 unit of the drug. All construction costs are incurred during
year 0. Once built, the capacity is available for years 1-15. In addition, it costs $1 per year to
maintain a unit of annual production capacity for each year 1 through 15. For example, if
Lang Drug builds capacity to produce 100,000 units of Niagara per year and maintains this
capacity for 15 years, its total capacity cost will be 100,000×$10 + 100,000×($1/(1+0.1)+
$1/(1+0.1)2+…+$1/(1+0.1)15) = $1,760,608.
In year 1, the demand for Niagara will amount to160,000 units. For each of the subsequent
years 2-15, the annual rate, at which demand grows, is equally likely to fall anywhere
between 10% and 20% (i.e., in each year the rate at which demand grows, is a different
realization from a uniform random variable with a minimum value of 10% and a maximum
value of 20%). It is assumed that the growth rates of the product’s demand, in different
years, are uncorrelated. Assume also that, every year, Lang Drug produces up to capacity,
and because of the drug’s perishability, no units can be carried over from one year to the
next. At the same time, in each year, any demand in excess of the chosen capacity is lost.
During year 1, each unit of Niagara sells for $8. Lang Drug will increase the price of Niagara
at a rate of 5% per year. The variable cost of production is known to be 40% of the sales
price, in each year.
a) (25 points) Lang Drug is evaluating all five capacity levels from 300,000 to 700,000
units in increments of 100,000 units. Build and run a simulation model to determine
which of these capacity levels maximizes the expected NPV from Niagara in years 015.
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Simulation Homework
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b) (25 points) Lang Drug is developing an alternative capacity strategy. After building
the capacity up to the level determined in part a), the company is reserving an option to
add an extra 400,000 units of annual capacity in year 6, after observing the actual
demand levels in years 1 through 5. Lang Drug projects that it would cost $12 to build
1 additional unit of capacity in year 6. In addition, a regular annual maintenance fee of
$1 per unit of capacity will apply to the extra capacity in years 6-15. The company has
decided that the extra capacity should be added if the ratio of demand in year 5 to the
initial capacity level exceeds a certain cut-off point C. Lang Drug considers the
following cut-off values: C=50%, 60%, 70%, 80%, 90%, 100%, 110%. Which one
should the company choose to maximize the expected NPV from Niagara in years 015? According to your simulation results, what is the expected value of this capacity
strategy?
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Simulation Homework
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