1. Example 12.14 A Market Share Model

2. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Background Information n Sweetness and IceT are the two dominant companies in the bottled iced tea market. n Each currently possess 49% of the total iced tea market, with three smaller companies splitting the remaining 2%. n At the beginning of any year, a random number of new small companies enter the iced tea market. n The actual number of new entries is assured to be Poisson distributed with mean 1.

3. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Background Information -- continued n After the new entries enter the market, there is a random shift in market share among all competitors. n Essentially, all competitors lose a random percentage of their market share to other competitors. n We will assume that each of these percentages is triangularly distributed with the parameters given in the table on the next slide. n Therefore, the more small companies there are in the market, the more of its market share Sweetness will tend to lose to them.

4. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Background Information -- continued Parameters of Lost Market Share Percentages MinimumMost LikelyMaximum From Sweetness To IceT1.0%5%10% To each small company0.5%1%3% From IceT To Sweetness1.0%5%10% To each small company0.5%1%3% From Small Companies To Sweetness5.0%10%15% To IceT5.0%10%15%

5. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Background Information -- continued n At the end of each year, each of the small companies has a 50% chance of exiting the ice tea market. n Each small company that exits will lose its market share to Sweetness or IceT. n The percentage of this marketshare that goes to Sweetness is triangularly distributed with parameters 40%, 50%, and 60%; the rest goes to IceT. n The dominant companies, Sweetness and IceT, want to use simulation to see how their market share is likely to change over the next 10 years.

6. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Solution n At the beginning of the year we observe the market shares of Sweetness, IceT, and the small companies (combined). n Next, we simulate the number of new entrants. Then we simulate the shifts in market share during the year. n Next, we simulate the number of small companies that exit at the end of the year, and we simulate the market shares that go to Sweetness and IceT. n Finally, we tally the total market share at the end of the year for all competitors.

7. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 ICETEA.XLS n This file provides the setup to develop the model seen on the next two slides.

8. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17

9. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17

10. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model n The model can be formed with the following steps: –Inputs. Enter the inputs shown in shaded ranges. –Beginning market shares. For year 1 the beginning market shares are inputs. For example, find the beginning market share for Sweetness in cell B35 with the formula =B5. For every other year, the beginning market shares are the ending market shares from the previous year. For example, find the beginning market share for Sweetness in year 2 by entering the formula =B66 in cell C35. Then copy this to the range C35:K37 for all the competitors over the remaining years.

11. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model -- continued –Entries to the market. In year 1 find the number of small companies before entries, the number of new entries, and the number of small companies after entries by entering the formulas =B9, =RISKPOISSON(MeanEntries), and =SUM(B40:B41) in cells B40, B41, and B42, respectively. Note that the RISKPOISSON function, which takes a single argument, generates the number of new entrants in a single year. For year 2 the number of small companies before entries is the remaining number from year 1. Therefore, enter the formula =B58 in cell C40. Then copy the formulas in cells C40, B41 and B42 across the rows.

12. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model -- continued –Market shares lost during the year. Generate the percentage of its market share Sweetness loses to IceT and to the small companies (combined) in year 1 by entering the formulas =RISKTRIANG($B$24,$C$24,$D$24)*B35 and =RISKTRIANG($B$25,$C$25,$D$25)*B35*B42 in cells B46 and B47 and then copy these across rows 46 and 47. Next, enter similar formulas in rows 49, 50, 52 and 53 for market share lost by IceT and the small companies. For example, the formula in cell B53 is =RISKTRIANG($B$31,$C$31,$D$31)*B37.

13. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model -- continued –Exiters. Rows 56-59 contain information about small companies before and after exiting. To calculate this information, enter the formulas =SUM(B37, B47,B50)- SUM(B52:B53), =IF(B42>0,RISKBINOMIAL(B42,$B$13),0), =B42-B57, and =IF(B42>0,(B57/B42)*B56,0) in cells B56, B57, B58, B59. The copy these across rows 56-59. The formula in B56 simply tallies the market shares lost and gained for the small companies before exiting takes place. The formula in B57 uses the RISKBINOMIAL function to generate the number of small companies and the probability that any company exits. Finally, the formula in B59 finds the amount of market share possessed by the exiting companies under assumption that all small companies have an equal market share.

14. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model -- continued –Market share gained by exiters. The assumption of the model is that the market share of the exiters in row 63 is split randomly between Sweetness and IceT. To generate the split, enter the formula =RISKTRIANG($B$20,$C$20,$D$20) and =B59-B62 in cells B62 and B63. Then copy these across rows 62 and 63. –Year-end market shares. Calculate the year-end market shares of Sweetness, IceT, and the small companies (combined) by entering the formulas =SUM(B35,B49,B52,B62)-SUM(B46:B47), =SUM(B36,B46,B53,B63)-SUM(B49:B50), and =B56-B59 in cells B66, B67, and B68. Then copy these across rows 66-68. If you like, you can check that the year-end market shares sum to 100% for each year, as they should.

15. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 Developing the Model -- continued –@Risk outputs. We have not yet designated any cells as @Risk output cells. There are at least two possibilities. If we are interested in only the final market shares after 10 years, we should designate cells K66, K67, and K68 as output cells. –Alternatively, if we want to see how market shares move through time, we can specify whole ranges as output ranges. When you do this, the formulas change slightly. For example, the formula in cell B66 becomes =RISKOUTPUT(,”Sweetness”,1)+SUM(B35,B49,B52,B62) -SUM(B46:B47) to indicate that this is the first cell in the Sweetness output range.

16. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 @Risk Results n We set the number of iterations to 1000 and the number of simulations to 1. n After running @Risk, we obtain histograms of market share after 10 years. The histograms can be seen on the next two slides. n We see that the final IceT market share is essentially symmetric around its original value of 49%, although there is considerable variability. n In contrast, the final market share for the small companies has a good chance of being 0, although there is a small probability that it could be considerably larger – up to 8%, say.

17. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17

18. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17

19. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17 @Risk Results -- continued n Assuming that we designate whole rows as output ranges, such as row 66 for Sweetness, we can obtain a summary chart of the company’s market share though time as shown on the next slide. n This chart shows that the mean market share for Sweetness remains approximately constant through time. n However, as we stand at the beginning of year 1 and try to predict the future, there is more uncertainty the farther out we look. n This is a general rule. It is almost always harder to make long-range forecast than short-range forecasts!

20. 12.112.1 | 12.2 | 12.3 | 12.4 | 12.5 | 12.6 |12.7 | 12.8 | 12.9 | 12.10 | 12.11 | 12.12 | 12.13 | 12.15 | 12.16 | 12.1712.212.312.412.512.612.712.812.9 12.1012.1112.1212.1312.1512.1612.17