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# What is the Value of a Monopoly?

If you've played a board game, odds are that you've played Monopoly. And as you know, bargaining and trading properties is a huge part of the game. Today, we use economics and math to try and figure out how much money a Monopoly is actually worth!

The following was a reproduction, and was originally posted on May 12, 2018. The original article, and many others, can be found at RemptonGames.com

Hey everybody! A few months ago I wrote an article that compared the different colored monopolies on the monopoly board (you can find it here). In that article I used math and statistics to examine several different aspects of the Monopoly board game, but there is one aspect of these games that I didn’t really deal with – trading.

Trading is a huge part of Monopoly strategy, and making good trades can easily be the difference between victory and defeat. And of all the different trades that can be made in a game of Monopoly, the most important trades are when you are trying to complete a Monopoly.

Perhaps it’s just the people that I play with, but I have found that when I am trying to trade with somebody to complete a Monopoly I end up paying through the nose. On the one hand, this makes sense – Monopolies are key to winning the game, because without them you cannot build houses, hotels, or maintain a reasonable income.

On the other hand, it can be difficult to know if you are getting a good trade or not. If you complete the Monopoly but don’t have any money left, you can end up in a far more dangerous position than you were previously. And without at least a few houses, it can be difficult to earn enough income to make up for your initial purchase.

In a game where paying too much can spell death for a player, it is important to make sure that you are not overextending yourself. Today, I am going to look at various business valuation techniques to try and answer the question – how much should you actually pay for that last property in your Monopoly?

Let us Count the Ways

According to Investopedia, there are a number of different ways of measuring the value of a business, including Market Capitalization, Times Revenue Model, Earnings Multiplier, Discounted Cash Flow, Book Value, and Liquidation Value. In this section, I want to go through these different methods and determine if any of them would be applicable to the game of Monopoly.

Market Capitalization is a way of measuring the value of a business through its share value. Basically, if your business has 100 shares, and each is valued at \$100, then this would give you a market capitalization of 100 * 100 = \$10,000 dollars. While this method is relatively simple to calculate, it doesn’t really apply to Monopoly.

The Times Revenue Method is a way of analyzing the value of a business by looking at how much it can earn over a given period of time, and multiplying it by some constant factor which is dependent upon the type of business. These multipliers usually lie somewhere between 0.5x and 2x, depending on how profitable the business is. This method seems like a promising area to look into for this question.

The Earnings Multiplier method is a way of determining the value of a business based on it’s profit and earnings, rather than just based on revenue. Generally this method compares the annual returns on a given stock to the purchase price of the stock, and uses this to compute a ratio known as the P/E ratio. While it may be possible to modify this method to make it apply to Monopoly, as is it doesn’t really seem like a reasonable metric for determining the value of a Monopoly.

Discounted Cash Flow estimates are made by estimating the future earnings of a company, adjusting them for predicted inflation rates, and using these adjusted earnings to estimate the present value of the company. I don’t think that this method would be ideal for Monopoly because there is no inflation, and the income potential of every property is always known.

Finally, there are the Book Value and Liquidation values of the company, which are both calculated by taking the company’s total assets and subtracting their total liabilities. The difference between these two is that Liquidation value assumes that you are liquidating all assets due to bankrupcy, which means that you are generally going to be getting lower than market value for your assets. These methods are extremely easy to calculate for Monopoly pieces, but are not great at evaluating the value of a Monopoly because they don’t take intangible assets into account – having all the pieces of a Monopoly is worth far more than the pieces are worth separately.

Examining Our Options

Based on the above, it seems like the most appropriate method for determining the value of a Monopoly would be the Times Revenue method. This method is usually based upon the annual income of a business but, while games of Monopoly can last a very long time, I don’t think actually figuring out how much a property can earn during a year is going to be the best way to value it’s income potential. Instead we have to determine what the equivalent of a year would be within a game of Monopoly.

We actually have a number of different options to choose from – a year could be represented as a single turn, a round (each player gets a turn), a single rotation around the board, or even an entire game. For this article, I am going to be using the metric of 1 complete circuit around the board = 1 year. This metaphor seems to be implied by the board itself – you collect a Salary every time you complete the circuit, and have to pay annual taxes.

The board is 40 squares around, and the average roll for two dice is a 7. This means that it would take a little under 6 rounds for a player to make a circuit around the board, on average. However, because you get to roll again if you roll doubles, and the odds of rolling doubles are 1 in 6, this brings the number of rounds down to around 5. This number is further affected by things such as the “Go to Jail” square, as well as Chance and Community Chest cards, but for this article I will be using the metaphor of 5 rounds = 1 circuit = 1 year.

The next thing we have to look at is the actual earning potential of these different Monopolies. However, calculating this is actually quite tricky, because it relies on a number of factors such as the number of players at the table and how much you can afford to improve the Monopoly.

First off, lets look at how the number of players affects the price of a Monopoly. First of all, the more other people are on the board, the more chances there are for people to land on your property every “year”. It also means that there is more total cash to go around, since each person gets the same starting amounts. Finally, more players simply means more competition for the same amount of resources, which will drive the prices up. Therefore, I propose that the estimated prices should have a “Opponent multiplier” (N) , which multiplies the income potential of a Monopoly by the number of other players on the board.

Secondly, the total value of a Monopoly is also related to how much you can do with it. The expected income for a Monopoly increases based on how many houses or Hotels you have on it, and if you are unable to improve the property then it’s value to you is actually much lower.

Finally, we need to figure out what our actual multiplier should be. In general, the multiplier used in these calculations is based on expected rates of growth and recurring revenue. In general, when buying a Monopoly you would expect the potential for growth to be relatively high. However, the recurring business is relatively low. At most, each player will only be landing on your property once every “year”, and usually not even that. Based on this, I am going to be choosing a multiplier of 2.

The Price is Right

Based on the above, we can finally complete the Times Revenue value of a Monopoly. Using calculations from this article by Truman Collins, we can determine the average earnings of each property per opponent dice roll. Then, we will multiply this number by 5 due to our calculation of 5 rolls per complete navigation of the board, and then multiply it by 7/6 due to the additional 1/6 change of rolling doubles each turn. We will then add up the earning potential of all properties that are part of a single monopoly, and multiply by our Times Revenue multiple of two. Finally, we will perform this calculation for each possible number of houses.

When performing these calculations, we also need to keep track of the up-front costs of actually constructing the houses and hotels. The cost of building the houses will significantly reduce the expected income of the first year, but will have little to no effect on the expected income of following years. Therefore, I propose to depreciate the construction costs of those buildings over the expected lifespan of the monopoly, which I would estimate to be around 10 years.

• Example Calculation

Suppose we were looking at completing the Orange Monopoly and putting 3 houses on it, and there are 4 people at the table. The expected income per roll for each of these spaces with three houses on them is 50.015. We then multiply this number based on our multiples of 5 * 7/6 * 2 = 583.5. Because there are 3 opponents, this gets further multiplied by 3 and becomes \$1750.53 (which I will round to \$1751, because there are no coins in Monopoly). Because houses cost \$100 each, and you must buy a total of 9 houses for each property to have 3, (depreciated over 10 years),  this gets reduced to \$1661 for the whole Monopoly.

Suppose that I had already purchased Tennessee Avenue and St. James Place, and am thinking about trading for New York Avenue. I have already paid \$360, out of the total value of \$1661, which means that the maximum I am willing to pay to complete this Monopoly is \$1301 – quite a bit higher than the face value of \$200! Keep in mind that if you are willing to pay this price, you must also have enough cash left over after purchasing to actually buy the houses as well (and probably even a little more above that).

The Results!

After performing this calculation on all the different Monopolies, and every number of houses, I came up with the following table:

(The table only lists one member of each Monopoly per row, which represents the whole Monopoly)

 0 Houses 1 House 2 Houses 3 Houses 4 Houses Hotel New York Avenue \$91 \$197 \$578 \$1661 \$2247 \$2834 Connecticut Avenue \$32 \$65 \$195 \$630 \$944 \$1290 Illinois Avenue \$115 \$242 \$732 \$2066 \$2558 \$3050 Virginia Avenue \$56 \$111 \$362 \$1140 \$1594 \$1958 Boardwalk \$146 \$278 \$854 \$2008 \$2397 \$2786 Marvin Gardens \$126 \$271 \$858 \$2142 \$2689 \$3029 Pennsylvania \$145 \$554 \$998 \$2366 \$2852 \$3292 Mediterranean \$9 \$13 \$48 \$173 \$322 \$477

As you can see, the value generally increases significantly the more renovations the player can afford to place on it. In addition, most Monopolies don’t actually produce enough income to offset their costs until you are able to build the second or third houses.

Until Next Time!

That is all I have for this week! I hope you enjoyed this article about Monopoly strategy! If you did, check out the rest of the blog and subscribe on Facebook, Twitter, or here on WordPress so you will always know when I post a new article. If you didn’t, let me know what I can do better in the comments down below. I will be taking a bit of a break next week because I am going to be traveling, but I will be back the week after that with another Game Design article! See you then!

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