Question

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 $3700, and the average first-year commission for each new account opened is $5400. 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	0
   4	0
   5	0
   6	0
   7	1
   8	0
   9	1
   10	0
   11	0
   12	0
   13	2
   14	0
   15	0
   16	0
   17	0
   18	1
   19	0
   20	0
   21	1
   22	0
   23	0
   24	1
   25	1

   
   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 × $5,400 ) – $3,700

(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)

в | DE Simulation Trial New Accounts Total commission Profit 0 0 Average profit =AVERAGE(G3:G27) No. of times profit <0 =COUNTIF(G3:G27,"<"&0) Probability of loss =34/25 Fixed cost 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 3700 Commission per new account 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 5400 =C3*E3 =C4*E4 =C5*ES =C6*E6 =C7*E7 =C8*E8 =C9*E9 =C10*E10 =C11*E11 =C12*E12 =C13*E13 =C14*E14 =C15*E15 =C16*E16 =C17*E17 =C18*E18 =C19*E19 =C20*E20 =C21*E21 =C22*E22 =C23*E23 =C24*E24 =C25*E25 =C26*E26 =C27*E27 =F3-D3 =F4-D4 =F5-D5 =F6-D6 =F7-D7 =F8-D8 =F9-D9 =F10-D10 =F11-D11 =F12-D12 =F13-D13 =F14-D14 =F15-D15 =F16-D16 =F17-D17 =F18-D18 =F19-D19 =F20-D20 =F21-D21 =F22-D22 =F23-D23 =F24-D24 =F25-D25 =F26-D26 =F27-D27 1

Result:

Simulation Trial	New Accounts	Fixed cost	Commission per new account	Total commission	Profit
1	0	$3,700	$5,400	$0	($3,700)		Average profit	($1,972)
2	0	$3,700	$5,400	$0	($3,700)		No. of times profit < 0	18
3	0	$3,700	$5,400	$0	($3,700)		Probability of loss	0.72
4	0	$3,700	$5,400	$0	($3,700)
5	0	$3,700	$5,400	$0	($3,700)
6	0	$3,700	$5,400	$0	($3,700)
7	1	$3,700	$5,400	$5,400	$1,700
8	0	$3,700	$5,400	$0	($3,700)
9	1	$3,700	$5,400	$5,400	$1,700
10	0	$3,700	$5,400	$0	($3,700)
11	0	$3,700	$5,400	$0	($3,700)
12	0	$3,700	$5,400	$0	($3,700)
13	2	$3,700	$5,400	$10,800	$7,100
14	0	$3,700	$5,400	$0	($3,700)
15	0	$3,700	$5,400	$0	($3,700)
16	0	$3,700	$5,400	$0	($3,700)
17	0	$3,700	$5,400	$0	($3,700)
18	1	$3,700	$5,400	$5,400	$1,700
19	0	$3,700	$5,400	$0	($3,700)
20	0	$3,700	$5,400	$0	($3,700)
21	1	$3,700	$5,400	$5,400	$1,700
22	0	$3,700	$5,400	$0	($3,700)
23	0	$3,700	$5,400	$0	($3,700)
24	1	$3,700	$5,400	$5,400	$1,700
25	1	$3,700	$5,400	$5,400	$1,700

So,

The expected profit from a seminar is $ -1972 and there is a 0.72 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*5400 > 3700
or, n > 3700 / (5400*0.01)
or, n > 68.5

So,

The answer should be 69 attendees and we do not need trial and error for this.