1. Financial analysts often use the following model to

characterize changes in stock prices:

Pt = P0

e

1m- 0.5s

2

2t +sZ2t

where

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

change

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

Data. )

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

positive?

b. What is the probability that monthly profit will

exceed $4,000?

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.

Subject | General |

Due By (Pacific Time) | 05/01/2014 11:00 pm |

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