Question

1. Problem 16-05

   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 $3100, and the average first-year commission for each new account opened is $5800. 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 16.1 for descriptions of various types of probability distributions.)
      
      The number of new accounts opened is a   random variable with  trials and  probability of a success on a single trial.
      
   3. Assume that the number of new accouts you get randomly is:
      

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

Answer 1

(a)

Profit = (New Accounts Opened × $5800) – $3100

(b)

The number of new accounts opened is a binomial random variable with 25 trials and 0.01 probability of success on a single trial.

(c)

Simulation Trial	New Accounts	Fixed Cost	Commission per new account	Total Commission	Profit
1	0	3100	5800	0	-3100
2	0	3100	5800	0	-3100
3	1	3100	5800	5800	2700
4	0	3100	5800	0	-3100
5	0	3100	5800	0	-3100
6	0	3100	5800	0	-3100
7	0	3100	5800	0	-3100
8	1	3100	5800	5800	2700
9	0	3100	5800	0	-3100
10	2	3100	5800	11600	8500
11	0	3100	5800	0	-3100
12	0	3100	5800	0	-3100
13	0	3100	5800	0	-3100
14	2	3100	5800	11600	8500
15	1	3100	5800	5800	2700
16	0	3100	5800	0	-3100
17	0	3100	5800	0	-3100
18	0	3100	5800	0	-3100
19	1	3100	5800	5800	2700
20	0	3100	5800	0	-3100
21	0	3100	5800	0	-3100
22	0	3100	5800	0	-3100
23	0	3100	5800	0	-3100
24	0	3100	5800	0	-3100
25	0	3100	5800	0	-3100

Average Profit	-1244
No of time profit< 0	19
Probability of loss	0.76

So,

The expected profit from a seminar is $ -1244 and there is a 0.76 probability of a loss.

Gustin should not conduct the seminars in their current format.

(d)

The average number of new accounts = n.p (binomial distribution property) where p = 0.01 and 'n' is unknown.

The profit is greater than zero when the commission is greater than the cost. So,

n.p*5800 > 3100
or, n > 3100 / (5800*0.01)
or, n > 53.44

The answer should be 53  attendees and we do not need trial and error for this.