Super Bowl
Tanya was always happy whenever uncle Jim came home for a visit. This time she was thrilled because they would watch the Super Bowl together. She knew enough about football to enjoy it, and because Tinku and Peter always talked about it. She asked uncle if they could also watch the game with them. After all, they did have a large screen TV. Uncle, her parents and the parents of Tinku and Peter all agreed it was a good idea.
They were all sitting and chatting and the commercials came before the game. Tanya’s grandfather told them that the TV channels have great commercials during the Super Bowl.
Great commercial
Tanya: How can you have a great commercial? They are boring and always selling things.
Granpa: If I can remember a commercial from more than 30 years ago, it must have been great. In 1980 Super Bowl, there was an advertisement called “Hey Kid Catch”. An actor played the famous football player “Mean Joe” Green and a kid gave him a bottle of coke. The player drank the coke in one sip and tossed the kid his game-worn jersey as repayment and says, “Hey kid, catch”. The commercial became so famous that in 2011 (thirty one years after it aired), it was voted as the best Super Bowl commercial of all time. If you want, you can see the commercial on the you tube at https://www.youtube.com/watch?v=FmbHkR-9PZs.
Cost of a commercial
Uncle Jim: They have to make good commercials because it costs them a lot of money to air them. I think this year, one 30 second commercial in Super Bowl costs about 5 million dollars.
Tanya: 5 million dollars is a lot of money.
Grandpa: Yes, that’s more than I made during in my whole life.
Tinku: I think, large companies can afford them because they have a lot of money.
Peter: Yes, I heard the company Amazon is very rich.
Tanya: How rich?
Big money
Uncle Jim had already opened a financial page on the internet, and said: Yesterday, at the time of market closing Amazon traded at $1350 per share.
Tanya: That’s a lot of money. It is more than my whole year’s allowance. Who can afford to buy them?
Uncle Jim: Many rich investors buy them but it is mostly pension plans and insurance companies.
Peter: You told us that one share was $1350. How many shares are traded in one day?
Uncle Jim: A million is 1 followed by 6 zeros like 1,000,000. Average trading volume is 4,522,080 which is more than 4.5 million shares per day.
Tinku: What is the dollar amount of the shares traded like 1350 x 4,522,080?
Uncle Jim: You are right. The number you came up would be 6,104,808,000. A billion is 1 followed by 9 zeros. So this would be like 6.1 billion dollars but it is different for each day.
Tanya: Do they even have that many shares?
Uncle Jim: It says that the market cap for Amazon is roughly $648,5100,000,000 which is more than 648 billion dollars. It is only $6,104,808,000 worth shares which trade hands in one day. You know 1 percent of 648 billion is 6.48 billion. So this daily trade of about 6.1 billion dollars is less than 1% of the total value of the company.
Tanya: Uncle, are all big companies that rich?
Uncle Jim: Actually, APPLE is even richer. It is worth $793.6 billion which is just short of eight hundred billion dollar. Pepsi cola company is worth over $150 billion. So the big companies usually have their market values in billions of dollars.
Tanya: Uncle, you said that it costs about 5 million dollars for a 30 second commercial in the Super Bowl. How many commercials can they air in this time?
Tinku: I think about 60 and that would mean that they charge 60 x 5,000,000 which is about 300 million dollars for airing the commercials. Who keeps all the money?
NFL’s monetary worth
Uncle Jim: The money gets divided because the TV companies have to pay NFL (National Football League) which is a franchise consisting of about 30 teams.
Peter: The league must be rich because they also charge you for watching each game. You have to pay for their jerseys and everything too.
Uncle Jim: Don’t forget that the League has to pay the teams which has to pay the players and their other staff. Still the league is worth more than six billion dollars ($6,000,000,000) today.
Grandpa: I know you are saying that the cost of a 30 second commercial during Super Bowl is about 5 million dollars. It used to be much less when I was in school. I remember it cost only $44,000 in 1967.
Uncle Jim was fidgeting with his smart phone and said: You are right Grandpa. I have the costs of all the years here. I will give them to Tanya and her friends.
Challenge
Uncle Jim gave Tanya the table with the cost of a 30 second commercial in different years. On a graph paper plot with the number of years after 1967 as the independent variable (horizontal axis) and the actual cost as a dependent variable (vertical axis).
| Historical Cost of a 30 second Super Bowl Commercial in dollars | ||||
| Year | Years after 1967 | Actual Cost | Linear Model | Exponential Model |
| 1967 | 0 | 44000 | 44000 | 44000 |
| 1972 | 5 | 86000 | 495936 | 70493 |
| 1977 | 10 | 125000 | 947873 | 112937 |
| 1982 | 15 | 324000 | 1399809 | 180938 |
| 1987 | 20 | 600000 | 1851745 | 289883 |
| 1992 | 25 | 850000 | 2303682 | 464424 |
| 1997 | 30 | 1200000 | 2755618 | 744059 |
| 2002 | 35 | 1900000 | 3207555 | 1192065 |
| 2007 | 40 | 2600000 | 3659491 | 1909820 |
| 2012 | 45 | 3500000 | 4111427 | 3059742 |
| 2017 | 50 | 5020000 | 4563364 | 4902045 |
The best fit for the cost in linear model is:
Cost = $44,000 + $90387 x Number of years after 1967.
They can also fitted best into an exponential model:
Cost = $44,000 x 1.09885(Number of years after 1967). This corresponded to an average of 9.885% increase over a previous year. On the same graph plot the costs based on linear and exponential models given in the Table. Which model do you think is better?
Solution: Picture of the Graph for linear and exponential models shows that the exponential model better explains the rise in the cost.
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