Southwestern University: (B) * Southwestern University (SWU), a large state coll

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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

Explanation / Answer

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

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