**Sports Market Outcomes** Here we look at some details of a sports league.

**Single Entity Cooperation** Single entity cooperation defines the actions that owners must take to make league play happen. These actions include: 1) Setting the schedule, including the season length, 2) Setting the rules of play, with officials, and 3) Determining how a champion is determined. This includes how many teams are involved, how many rounds are involved, etc…

**Joint- Venture Cooperation** All cooperative actions that do not make play happen are called joint ventures. Joint venture activity includes 1) Leagues have been allowed to grant exclusive territories to their members, typically through franchise agreements (a contract between league and owner that specifies what it means to be an owner). 2) Leagues limit the number of teams in the league.

**Expansion of the League** Economic idea – expansion will occur if the current team owners in the league will be better off because of the expansion. Expansion team owners pay an expansion fee that is distributed to the existing owners. Before considering some ideas here, let’s explore a finance idea. Here We will use the idea of present value.

**Single Payment Ideas** A single payment really means an individual receives funds once and gives up funds once. There are two payments, but there is a closing of a loop in that money comes in and then goes out (or vice versa.) Between the two points in time interest is considered.

**Single Payment Future Amount ** If you have $1 today and can earn an interest rate of 10% by the end of the first year then you will have $1.10. The$1.10 is calculated as the amount you start the period with plus the product of what you start the period with times the rate of interest that period – the 1.10 = 1 + 1(.1). If F is the amount at the end of the period, P is the amount at the beginning of the period and i is the rate of interest during the period, then in general we have F = P + Pi = P(1 + i).

**Growth in general** If you start out with P and wait one period at rate i we just saw you have F = P(1 + i). Now, if you again earn i, by the end of the second period you would have F = P(1 + i) + P(1 + i )i (start period with + start period with times i) = P(1 + i)(1 + i) = P(1 + i)2. In general, at the end of n periods, you have F = P(1 + i)n.

**The formula** F = P(1 + i)n, can be called the single payment future value (sometimes called the single payment compound amount) formula. Notice if we know or have specific numerical values for -the present amount P, -the constant interest rate each period i, and -the number of periods n, then we can solve for the future amount. Example: Say your grandmother gives you $10 and wants you to pay her back in 2 years and she will charge you 8% interest each year. How much do you pay her back at the end of two years? Let’s look at a time line on the next slide.

**10 – you received $10** 0 1 2 3 … n ? – How much do you pay back? F = 10(1 + .08)2 = 10(1.1664) = 11.66

**The Future Value Factor** We saw on the last page that the amount to be paid back was F = 10(1 + .08)2 = 10(1.1664) = 11.66. Remember in general we know F = P(1 + i)n. (1 + i)n is called the interest factor by which we multiply the present amount to get the future amount. The interest factor is part of the formula and includes the interest rate.

**I want to show you how Microsoft Excel can be used to get** single payment future value interest factors. On the next slide I have put into the first column time with values from 0 to 10. In the second column I have the future value interest factors for time 0 to time 10. If you clicked the mouse in cell B3 you see the value 1.1. But if you look up in the Excel spreadsheet area formula bar you see the formula =(1 + .1)^A2. I typed it in. The (1 + .1) looks familiar. The ^ is how you raise to a power in Excel. A2 refers to the cell A2. Where we see the value is 1. So (1 + .1)^A2 = 1.1 The reason I put A2 into the formula is because when I am done typing it I can drag the cell down to the 10th time period and the A2 will change to A3, A4 and so on as I drag down. This way, repetitive equations can be entered quickly.

**Single Payment Present Value** The present value concept uses the growth process we just studied, but the focal point is the present. As an example, what amount do you need today if you want $1.10 at the end of the period and you can earn 10% during the period. You need P = F / (1 + i) = 1.10 / (1 + .1) = $1.00 In general if you want to have F n periods from now and you can earn i each period , then today you need P = F / (1 + i)n. Note, the present value of an amount today would mean n = 0 and so P = F because anything raised to the power zero equals 1.

**The single payment present value factor** In the formula P = F / (1 + i)n the interest factor is 1 / (1 + i)n. We could use Excel to get the factor. In the third column of the Excel slide I had before I typed the equation =1/(1 + .1)^A3 in column C3. Then I was able to drag down the rest of the way. Let’s do an example. Say on your 21st birthday you want to have $100 so you can go out on the town and buy you and your friends some stuff, you know, pizza and soda and the like. The bank is currently paying 4% a year in interest each year. How much do you have to put into the bank on your 18th birthday so that you have the $100 on your 21st birthday?

**100** 0 1 2 3 … n 18 19 20 21 P = 100/(1 + .04)^3 = 100(.8890) = 88.90

**Discount Rate or Internal Rate of Return** The present value P of a future amount F n periods from now at interest rate i is P = F / (1 + i)n. The interest rate i in this context is often called the discount rate. It is the rate at which we “discount” future values to place them in terms of today’s value. Do not confuse this with the discount rate in the context of monetary policy. The Federal Reserve charges banks the “discount rate” when those banks borrow from the Fed.

**Example** Say you buy a stock for $50 and 3 years later the stock sells for $87.50. How much did you earn on the stock on an annual basis? Remember the general formula F = P(1 + i)n connects F, P, i, and n. If we fill in what we know we get 87.50 = 50(1 + i)3. So (1 + i)3 = 87.50/50, or 1+ i = (87.50/50)1/3, or i = (87.50/50)1/3 - 1 = 1.2051 – 1 = .2051 or 20.51% The internal rate of return on the stock over the 3 years was 20.51%.

**The rule of 70** The rule of 70, sometimes called the handy rule of 70, is an approximation rule to answer the question of how long it will take a dollar amount to double. Remember the formula F = P(1 + i)n ? If F = 2 and P = 1 the formula becomes 2 = (1 + i)n. Taking the natural log of both sides gives, after some arrangement ln 2 = n ln (1 + i), Or n = ln 2/ln (1 + i). Now, using this formula will tell you exactly how long it will take some dollar amount to double. I bet you like this formula, right? A few people do not like it so an approximation was found that works fairly well when interest rates are around 5 to 12%.

**The approx rule is** Years to double (n) = 70/interest rate. Note, in the approximation rule 12%, for example, is 12, while in the exact formula on the previous slide we use 12% as .12. So, at 12% approx rule says a dollar amount will double in 70/12 = 5.83 periods. The exact formula would have n = ln 2 / ln(1 + .12) = 6.12 periods.

**Summary** Here we have seen the financial arrangements known by the umbrella phrase of single payment formulas. Whenever we compare dollars across time we incorporate interest. Now, back to considering an expansion of a league. Let’s note 2 ways that current owners can be impacted by expansion. 1) Revenues in the local market could be lower for a while because when the expansion team comes to town folks may not want to go because it will be seen as an easy win. 2) More teams in the league may mean that the total broadcast rights to the league will be expanded.

**Expansion Fee** Let’s define F as the expansion fee charged for a new team, E as the net present value of the expansion team to the new owner, and C as the change in the net present value added up across all the existing teams. The logic of using the net present value is that the value of owning a team occurs over many periods of time. The actual expansion fee is determined after negotiation. The current owners would like to make the expansion fee F = E. This means that the current owners would like the expansion team to pay now for all the money the expansion team will make in the future.

**Expansion Fee** The expansion team would like to make the fee lower and the expansion team will claim that by expansion the current owners gain C and so the expansion fee should reflect this so the fee should be F = E – C. The actual fee will move toward E if there are many people interested in an expansion spot, and will move toward E – C if there is a single entity interested in expansion. If a single entity is interested in being the expansion team the it will be argued that they are the reason the existing owners get C and thus that should be taken off the fee. If there are many potential buyers then the existing owners will claim C is really due to their existence and the expansion team has no claim on that value.

**Notes on Expansion** 1) The expansion fee is typically paid over time, like a loan or mortgage, 2) Owner viability – of 2 or more potential expansion owners, the league doesn’t likely want a maverick owner (although they do end up with some) because of the potential instability that results, 3) Expansion teams use the expansion draft and typically choose cheaper and younger players and fill out the roster with free agents and trades, 4) Expansion clubs may not national TV money for several years, 5) Imputed expansion fee – with the expansion fee the new owner now has to make enough revenue to cover both the operations of the team and cover the expansion fee.

**Strategy on expansion/relocation** 1) Believable threat location - -Current owners would like to have some economically viable locations (cities) open without a team so that if their current city doesn’t meet their demands for subsidies that they can threaten to leave for the other location. Tampa Bay served that purpose for several years in MLB while the White Sox, Giants and Mariners wanted new stadiums. 2) Rival League - The author notes that if a current league has some interested cities without a team, then maybe these cities can have a new league formed. This works against the believable threat idea. A real problem for the current league would be that the new league gains momentum. The established league could then have both reduced revenues and higher costs due to bidding wars for players. The author does note, though, that in the US we have a single league eventually dominate a sport.