Question

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

Tully Tyres
Data
Probability	Cumulative Prob	Demand	Selling price	$160	$180
0.05		100	Monthly fixed cost	$2000
0.10		120	Profit margin	20%	30%
0.20		140
0.30		160
0.25		180
0.10		200
1
Model
Month	RN1	Demand	Selling price	RN2	Profit margin	Fixed cost	Profit
1	0.23297	#N/A	$180	0.227625	0.2

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

Answer 1

a)Model sheet and Formula Sheet

Model
Month	RN1	Demand	Selling price	RN2	Profit margin	Fixed cost	Profit	Cost price	profit per piece
1	0.94557728	200	171	0.45306216	0.24530622	2000	6736.87521	137.3156	33.68438
2	0.86504377	180	163	0.86540213	0.28654021	2000	6534.64988	126.6964	36.30361
3	0.75401736	180	167	0.31171716	0.23117172	2000	5644.23443	135.6431	31.35686
4	0.84764454	180	161	0.04897888	0.20489789	2000	4928.1693	133.6213	27.37872
5	0.01798387	100	179	0.74707744	0.27470774	2000	3857.56551	140.4243	38.57566
6	0.11064554	120	160	0.55468882	0.25546888	2000	3906.90889	127.4424	32.55757
7	0.65084945	180	176	0.09396328	0.20939633	2000	5485.11312	145.5271	30.47285
8	0.82800777	180	162	0.24019748	0.22401975	2000	5336.85494	132.3508	29.64919
9	0.51640536	160	167	0.38647226	0.23864723	2000	5148.07908	134.8245	32.17549
10	0.08969567	120	175	0.27855721	0.22785572	2000	3897.01335	142.5249	32.47511
11	0.9398299	200	165	0.94256129	0.29425613	2000	7502.72843	127.4864	37.51364
12	0.13051547	120	169	0.50122161	0.25012216	2000	4057.5854	135.1868	33.81321
					Average profit =		5252.98146

Formula
Month	RN1	Demand	Selling price	RN2	Profit margin	Fixed cost	Profit	Cost price	profit per piece
1	=RAND()	=VLOOKUP(B14,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E14	2000	=J14*C14	=D14*100/(100+(F14*100))	=D14-I14
2	=RAND()	=VLOOKUP(B15,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E15	2000	=J15*C15	=D15*100/(100+(F15*100))	=D15-I15
3	=RAND()	=VLOOKUP(B16,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E16	2000	=J16*C16	=D16*100/(100+(F16*100))	=D16-I16
4	=RAND()	=VLOOKUP(B17,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E17	2000	=J17*C17	=D17*100/(100+(F17*100))	=D17-I17
5	=RAND()	=VLOOKUP(B18,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E18	2000	=J18*C18	=D18*100/(100+(F18*100))	=D18-I18
6	=RAND()	=VLOOKUP(B19,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E19	2000	=J19*C19	=D19*100/(100+(F19*100))	=D19-I19
7	=RAND()	=VLOOKUP(B20,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E20	2000	=J20*C20	=D20*100/(100+(F20*100))	=D20-I20
8	=RAND()	=VLOOKUP(B21,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E21	2000	=J21*C21	=D21*100/(100+(F21*100))	=D21-I21
9	=RAND()	=VLOOKUP(B22,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E22	2000	=J22*C22	=D22*100/(100+(F22*100))	=D22-I22
10	=RAND()	=VLOOKUP(B23,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E23	2000	=J23*C23	=D23*100/(100+(F23*100))	=D23-I23
11	=RAND()	=VLOOKUP(B24,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E24	2000	=J24*C24	=D24*100/(100+(F24*100))	=D24-I24
12	=RAND()	=VLOOKUP(B25,$L$4:$M$9,2,TRUE)	=RANDBETWEEN(160,180)	=RAND()	=0.2+(0.3-0.2)*E25	2000	=J25*C25	=D25*100/(100+(F25*100))	=D25-I25
					Average profit =		=AVERAGE(H14:H25)

b)Average monthly profit over 12-month period is 5252.9816