1. Financial analysts often use the following model to
characterize changes in stock prices:
Pt = P0
P0 = current stock price
Pt = price at time t
m = mean (logarithmic) change of the stock price
per unit time
s = (logarithmic) standard deviation of price
Z = standard normal random variable
This model assumes that the logarithm of a stock’s price
is a normally distributed random variable (see the discussion of the lognormal distribution and note that the
first term of the exponent is the mean of the lognormal
distribution). Using historical data, one can estimate values for m and s. Suppose that the average daily change
for a stock is $0.003227, and the standard deviation is
0.026154. Develop a spreadsheet to simulate the price
of the stock over the next 30 days, if the current price
is $53. Use the Excel function NORMSINV(RAND( ))
to generate values for Z. Construct a chart showing the
movement in the stock price.
6. Using the generic profit model developed in the section Logic and Business Principles in Chapter 9 , develop a financial simulation model for a new product proposal and construct a distribution of profits under the following assumptions: Price is fixed at $1,000. Unit costs are
unknown and follow the distribution.
Implement your model using Crystal Ball to determine
the best production quantity to maximize the average
profit. Would you conclude that this product is a good
investment? (Data for this problem can be found in the
Problem 6 worksheet in the Excel file Chapter 10 Problem
7. The manager of the apartment complex in Problem 9
of Chapter 9 believes that the number of units rented
during any given month has a triangular distribution
with minimum 30, most likely 34, and maximum 40.
Operating costs follow a normal distribution with mean
$15,000 and a standard deviation of $300. Use Crystal
Ball to estimate the 80%, 90%, and 95% confidence intervals for the profitability of this business.
a. What is the probability that monthly profit will be
b. What is the probability that monthly profit will
c. Compare the 80%, 90%, and 95% certainty ranges.
d. What is the probability that profit will be between
$1,000 and $3,000?
8. Develop a Crystal Ball model for the garage band in
Problem 11 in Chapter 9 with the following assumptions. The expected crowd is normally distributed with
a mean of 3,000 and a standard deviation of 400 (minimum of 0). The average expenditure on concessions
is also normally distributed with mean $15, standard
deviation $3, and minimum 0. Identify the mean profit,
the minimum observed profit, maximum observed
profit, and the probability of achieving a positive profit.
Develop and interpret a confidence interval for the
mean profit for a 5,000-trial simulation.
|Due By (Pacific Time)||05/01/2014 11:00 pm|
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