Homework SourseSouthwestern University B Southwestern University SWU a larg
Southwestern University: (B)*
Southwestern University (SWU), a large state college in Stephenville, Texas, enrolls close to 20,000 students. The school is a dominant force in the small city, with more students during fall and spring than permanent residents.
Always a football powerhouse, SWU is usually in the top 20 in college football rankings. Since the legendary Phil Flamm was hired as its head coach in 2006 (in hopes of reaching the elusive number 1 ranking), attendance at the five Saturday home games each year increased. Prior to Flamm’s arrival, attendance generally averaged 25,000 to 29,000 per game. Season ticket sales bumped up by 10,000 just with the announcement of the new coach’s arrival. Stephenville and SWU were ready to move to the big time!
The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in 1953, has seating for 54,000 fans. The following table indicates attendance at each game for the past 6 years.
One of Flamm’s demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head-on. Flamm had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.
SWU’s president, Dr. Joel Wisner, decided it was time for his vice president of development to forecast when the existing stadium would “max out.” The expansion was, in his mind, a given. But Wisner needed to know how long he could wait. He also sought a revenue projection, assuming an average ticket price of $50 in 2013 and a 5% increase each year in future prices.
Discussion Questions
1.
Develop a forecasting model, justifying its selection over other techniques, and project attendance through 2014.
2.
What revenues are to be expected in 2013 and 2014?
3.
Discuss the school’s options.
Southwestern University Football Game Attendance, 2007–2012
2007
2008
2009
GAME
ATTENDEES
OPPONENT
ATTENDEES
OPPONENT
ATTENDEES
OPPONENT
1
34,200
Rice
36,100
Miami
35,900
USC
2a
39,800
Texas
40,200
Nebraska
46,500
Texas Tech
3
38,200
Duke
39,100
Ohio State
43,100
Alaska
4b
26,900
Arkansas
25,300
Nevada
27,900
Arizona
5
35,100
TCU
36,200
Boise State
39,200
Baylor
2007
2008
2009
GAME
ATTENDEES
OPPONENT
ATTENDEES
OPPONENT
ATTENDEES
OPPONENT
1
41,900
Arkansas
42,500
Indiana
46,900
LSU
2a
46,100
Missouri
48,200
North Texas
50,100
Texas
3
43,900
Florida
44,200
Texas A&M
45,900
South Florida
4b
30,100
Central Florida
33,900
Southern
36,300
Montana
5
40,500
LSU
47,800
Oklahoma
49,900
Arizona State
a
Homecoming games.
bDuring the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance.
please try to show steps thanks!!!!!
| 2007 | 2008 | 2009 | ||||
|---|---|---|---|---|---|---|
| GAME | ATTENDEES | OPPONENT | ATTENDEES | OPPONENT | ATTENDEES | OPPONENT |
| 1 | 34,200 | Rice | 36,100 | Miami | 35,900 | USC |
| 2a | 39,800 | Texas | 40,200 | Nebraska | 46,500 | Texas Tech |
| 3 | 38,200 | Duke | 39,100 | Ohio State | 43,100 | Alaska |
| 4b | 26,900 | Arkansas | 25,300 | Nevada | 27,900 | Arizona |
| 5 | 35,100 | TCU | 36,200 | Boise State | 39,200 | Baylor |
Solution
Forecasting Techniques
When historical data is involved we use \'Time series method\' to forecast for the prevailing time periods. Three types of time series methods are available for forecasting;
1. Smoothing
2. Trend Projection
3. Trend projection with seasonal adjustment
As per the given data, there are seasonal factors present in the historical figures and hence we will use 3rd method for the forecasting revenues for the period of 2013 and 2014.
Since the table for 2010, 2011 and 2012 is not mentioned, assuming that the last three tables are for these years.
Step 1: Calculate Centred moving averages
Tthere are 5 different weeks in each year hence taking 5 season moving average to eliminate seasonality and issregular factors.
1st Week Moving Average = (34200 + 39800 + 38200 + 26900 + 35100) / 5
Step 2:
Associate this value with centre of the series, that is for week 3. Similarly follow the same for all the remaining weeks and arrange in the table.
Step 3: Determine seasonal and irregularity factors (StIt)
StIt = Yt / Moving average of period t
Step 4: Determine average seasonal factors
Week 1: (1.017 + 0.96 + 1.053 + 1.034 + 1.044)/5 = 1.022
Similarly, calculate the average of seasonal factors for remaining 4 weeks.
Week 2 = 1.154
Week 3 = 1.071
Week 4 = 0.738
Week 5 = 1.006
Step 5: Scale the seasonal factors (St)
Average of seasonal factors = (1.022 + 1.154 + 1.071 + 0.738 + 1.006)/5 = 0.998
Now, divide all the weekwise seasonal factors by average seasonal factor.
Week 1 = 1.022/0.998 = 1.0234
Week 2 = 1.156
Week 3 = 1.073
Week 4 = 0.739
Week 5 = 1.008
The sum of all above factors should be equal to 5 (for 5 different seasons)
Step 6: Determine deseasonalized data
Divide Yt by St
Step 7: Determine trandline of deseasonlized data
Tt = b0 + b1t
where,
b1 = (n * sum(t * Yt) - sum(t) * sum(Yt)) / (n * sum(t2) - (sum(t))2)
b0 = average(Yt) - b1 * average(t)
Lets put all the values in the table to get the equation;
The time series equation is;
T = 33242.76 + 418.53t
Step 8: Determine deseasonlized predictions
Substitute t = 31 to 40 to determine the forecasted revenues for all 5 weeks for the year 2013 and 2014;
Step 9: Embrace the seasonality index
Multiply each deseasonalized prediction by its respective seasonality factor;
Week 1 (2013) = T31 * 1.0234 = 47302
Similarly, calculate for the remaining weeks of the year 2013 and 2014.
We get the following result;
The decision:
The School has to increase the capacity of the stadium by the year 2014 since the attendees expected in the week 2 are more than the capacity of the stadium.
| Year | Week | Opponent | Attendees (Yt) | Centred Moving average | St.It | Weekwise average | St | Yt/St |
| 2007 | 1 | Rice | 34,200 | 1.022 | 1.023482 | 33415.33 | ||
| 2a | Texas | 39,800 | 1.154 | 1.156108 | 34425.84 | |||
| 3 | Duke | 38,200 | 34840 | 1.096 | 1.071 | 1.072999 | 35601.16 | |
| 4b | Arkansas | 26,900 | 35220 | 0.764 | 0.738 | 0.739335 | 36384.05 | |
| 5 | TCU | 35,100 | 35300 | 0.994 | 1.006 | 1.008076 | 34818.81 | |
| 2008 | 1 | Miami | 36,100 | 35480 | 1.017 | 1.023482 | 35271.73 | |
| 2a | Nebraska | 40,200 | 35160 | 1.143 | 1.156108 | 34771.83 | ||
| 3 | Ohio State | 39,100 | 35380 | 1.105 | 1.072999 | 36439.93 | ||
| 4b | Nevada | 25,300 | 35340 | 0.716 | 0.739335 | 34219.95 | ||
| 5 | Boise State | 36,200 | 36600 | 0.989 | 1.008076 | 35910 | ||
| 2009 | 1 | USC | 35,900 | 37400 | 0.960 | 1.023482 | 35076.32 | |
| 2a | Texas Tech | 46,500 | 37920 | 1.226 | 1.156108 | 40221.15 | ||
| 3 | Alaska | 43,100 | 38520 | 1.119 | 1.072999 | 40167.8 | ||
| 4b | Arizona | 27,900 | 39720 | 0.702 | 0.739335 | 37736.62 | ||
| 5 | Baylor | 39,200 | 39640 | 0.989 | 1.008076 | 38885.97 | ||
| 2010 | 1 | Arkansas | 41,900 | 39800 | 1.053 | 1.023482 | 40938.66 | |
| 2a | Missouri | 46,100 | 40240 | 1.146 | 1.156108 | 39875.16 | ||
| 3 | Florida | 43,900 | 40500 | 1.084 | 1.072999 | 40913.38 | ||
| 4b | Central Florida | 30,100 | 40620 | 0.741 | 0.739335 | 40712.27 | ||
| 5 | LSU | 40,500 | 41040 | 0.987 | 1.008076 | 40175.55 | ||
| 2011 | 1 | Indiana | 42,500 | 41100 | 1.034 | 1.023482 | 41524.9 | |
| 2a | North Texas | 48,200 | 41860 | 1.151 | 1.156108 | 41691.6 | ||
| 3 | Texas A&M | 44,200 | 43320 | 1.020 | 1.072999 | 41192.97 | ||
| 4b | Southern | 33,900 | 44200 | 0.767 | 0.739335 | 45852.02 | ||
| 5 | Oklahoma | 47,800 | 44580 | 1.072 | 1.008076 | 47417.07 | ||
| 2012 | 1 | LSU | 46,900 | 44920 | 1.044 | 1.023482 | 45823.94 | |
| 2a | Texas | 50,100 | 45400 | 1.104 | 1.156108 | 43335.04 | ||
| 3 | South Florida | 45,900 | 45820 | 1.002 | 1.072999 | 42777.31 | ||
| 4b | Montana | 36,300 | 0.739335 | 49098.18 | ||||
| 5 | Arizona State | 49,900 | 1.008076 | 49500.25 |
