Question

To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3700, and the average first-year commission for each new account opened is $5300. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.

1. Determine the equation for computing Gustin’s profit per seminar, given values of the relevant parameters. Round your answers to the nearest dollar.
   
   Profit = (New Accounts Opened × $  

   ) – $  

   
   
   

2. What type of random variable is the number of new accounts opened? (Hint: Review Appendix 12.1 for descriptions of various types of probability distributions.)
   
   The number of new accounts opened is a 

   binomial 

    random variable with 

    trials and 

    probability of a success on a single trial.
   
   

3. Assume that the number of new accounts you get randomly is:
   
   

   Simulation Trial	New Accounts
   1	0
   2	0
   3	0
   4	0
   5	0
   6	2
   7	2
   8	1
   9	1
   10	0
   11	1
   12	2
   13	1
   14	2
   15	0
   16	0
   17	0
   18	0
   19	1
   20	0
   21	1
   22	0
   23	1
   24	0
   25	0

   
   Construct a spreadsheet simulation model to analyze the profitability of Gustin’s seminars. Round the answer for the expected profit to the nearest dollar. Round the answer for the probability of a loss to 2 decimal places. Enter minus sign for negative values.
   
   The expected profit from a seminar is $  

    and there is a 

    probability of a loss.
   
   Would you recommend that Gustin continue running the seminars?
   
   Gustin 

   should consider discontinuing 

    the seminars in their current format.
   
   

4. How large of an audience does Gustin need before a seminar’s expected profit is greater than zero? Use Trial-and-error method to answer the question. Round your answer to the nearest whole number.
   
   

    attendee

( Note: Please show the excel output and formulae used.)

Answer 1

We are assuming that Gustin must have conducted 100 seminars in a year with 25 individuals each.

So we are simulating 100 times.

According to the simulation the total number of new accounts opened are 24.

This means that out of the 2500 individuals attending the seminars only 24 have opened a new account which is close to the probability of 0.01.

The total cost of the seminars is 3700*100 = $370000

The total revenue earned is 5300*24 = $127200

The expected profit is 127200 - 370000 = -$242800 which is a considerable loss.

A loss will occur when total cost exceeds the total revenue.

Probability that an individual will open an account is 0.01. The probability that out of 25 individuals one opens an account is 0.01*25 = 0.25

The probability of having zero loss is 3700/5300 = 0.698113

Thus, the probability of a loss is 1 - 0.25/0.698113 = 0.6419

In order for the seminar to be successful Gustin needs the difference between the cost and revenue to be zero.I would not recommend Gustin to run the seminar since the probability of loss is very high.

i.e. the expected return from the seminar should atleast be 3700

So the probability of success is 3700/5300 = 0.698113

This means that Gustin would need atleast 0.698113/0.01 = 69.8113 individuals attending the seminar to make up the cost and more to get some profit.

The minimum number of attendees required for the seminar are 70.

Answer 2

Answer:-

Given That:-

Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3700, and the average first-year commission for each new account opened is $5300.

We are assuming that Gustin must have conducted 100 seminars in a year with 25 individuals each.

So we are simulating 100 times.

According to the simulation the total number of new accounts opened are 24.

This means that out of the 2500 individuals attending the seminars only 24 have opened a new account which is close to the probability of 0.01.

The total cost of the seminars is 3700 * 100 = $ 370000

The total revenue earned is 5300* 24 = $ 127200

The expected profit is 127200 - 370000 = - $ 242800 which is a considerable loss.

A loss will occur when total cost exceeds the total revenue.

Probability that an individual will open an account is 0.01. The probability that out of 25 individuals one opens an account is 0.01 * 25 = 0.25

The probability of having zero loss is 3700/5300 = 0.698113

Thus, the probability of a loss is 1 - 0.25/0.698113 = 0.6419

In order for the seminar to be successful Gustin needs the difference between the cost and revenue to be zero.I would not recommend Gustin to run the seminar since the probability of loss is very high.

i.e. the expected return from the seminar should atleast be 3700

So the probability of success is 3700/5300 = 0.698113

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