Re-estimating an NHL team's Picasso value

Sports franchises are different from "regular" businesses in one important way -- they're a lot more fun. If you own a team, you get any profit it makes, but you get lots of perks in addition to that. You get to be on TV a lot. You get the best seat in the house. You get to hire and fire staff. You get quoted in the paper any time you want. You get to be a hero in your local community. And so on.

Because of this, you'd expect team owners to be willing to pay more for a team than its future earnings are worth; they want the "consumption value" in addition to the investment value. You can call this the "Picasso effect," because owning an expensive sports team is a bit like owning an expensive painting; you do it partly for the pride of ownership.

In the previous post, I tried to estimate the Picasso value this way: I ran a regression to predict team market value from team earnings (both values as estimated by Forbes). The equation came out

Market Value = 4 * annual earnings + $200 million

From that, I suggested that Picasso value was $200 million: that is, since the $200MM term didn't have anything to do with the success of the business, it must be the value that owners are willing to pay just to own the team.

But, following a post by Dackle over at "The Book" blog, I realized that isn't quite right.

The problem is that team value -- at least that portion that has to do with earnings -- is based on *future* prospects. And future prospects don't correlate 100% with current prospects. In effect, some of today's earnings is random noise -- the economy might be good in that particular city, or a promotion works well, or the team is just having a good year.

The more random noise, the higher the Picasso estimate. For instance, suppose that profits were completely random, and had nothing to do with any particular attribute of the team. Then, all teams would be valued equally, and the equation would be

Market Value = 0 * annual earnings + $220 million

And it would look like the entire value was Picasso, when, in reality, it could be that the value is driven entirely by earnings.

So to do the calculation right, you have to remove the noise from the earnings.

To try to figure out how to do that, I started by running a regression on Forbes 2008 earnings vs. 2007 earnings. If earnings were completely random, the correlation coefficient would be zero. Of course, it wasn't zero; the Leafs were profitable not because they were lucky that year, but because there are millions of loyal idiots like me who worship the team even though it continues to suck. The correlation coefficient was actually a very high .93. I'll put that in courier font:

One-year earnings correlation coefficient = .93

An r of .93 doesn't suggest a lot of noise, so it won't change things much. But maybe the .93 is still too high. Remember, the economic value of the team is the present value of *all* future earnings, not just next year. And earnings might change more in future years. For instance, between one year and the next, team performance is usually similar. Good teams stay good teams, and poor teams stay poor teams. Maybe that all evens out after, say, five years.

If we take .93 to the fifth power, in effect "compounding" the regression to the mean, we get about .70. This seems reasonably generous to me; a correlation of .7 is an r-squared of .5, which implies that the "fixed" component of a team's earnings has the same variance as the "variable" component.

That means that to get a team's "true" earnings from its 2008 earnings, we regress the number 30% towards the mean. To take one example: the Rangers had earnings of $30.7MM in 2008. The mean is $4.7MM. Regressing $30.7MM thirty percent towards $4.7MM gives $22.9 MM. So we assume that the expected value of the Rangers' "real" earnings was $22.9MM, and the remaining $7.8MM was due to random factors specific to that season.

If we do that for all 30 teams, and rerun the analysis using our regressed estimates of earnings, we now get

Market Value = 5.6 * annual earnings + $193 million

Not much different ... but better, I think. I'm more comfortable with a higher earnings multiple (5.6, in this case, rather than 4.0), since, for publicly traded securities, ratios (I think) tend to range between 7 and 11.

So this reduces our estimate of "Picasso value" from $200 million to $193 million. Not much. And it's easy to see why not much: according to the Forbes data, the money-losing teams are worth an average of about $160 million. If you believe these teams will continue to lose money, then, obviously, the Picasso value must be at least $160MM, since they're worth zero as a going concern.

I believe some of the $193 million is Picasso value, and some of it is hopes that the team will eventually be profitable: either by moving it to a city where it can make money, or by making more money in other ways (like a better TV deal).

Anyway, getting back to the Zimbalist/Balsillie question of how much more a team is worth in Hamilton ... if we run the revised numbers, we get an even bigger difference -- which makes sense, since the more profits matter, the more a team is worth in a money-making city as compared to a money-losing city.

The regressed estimate for Phoenix earnings is a loss of $5.4MM. For Hamilton, we continue to use Balsillie's own estimate of $11MM (we don't regress that since it's an estimate and not an actual observation).

That means, by this method,

$163MM market value for Phoenix
$255MM market value for Hamilton

Still, about the same as in the previous analysis. The benefit to the move is around $90MM, and three-quarters of the value of the Hamilton franchise is Picasso value.

(Thanks again to Dackle for the comment that led to this post.)

Is a Hamilton NHL team worth as little as Andrew Zimbalist thinks?

I've just finished reading Andrew Zimbalist's sworn submission to the courts with regard to the Phoenix Coyotes situation (hat tip to blogger James Mirtle for posting the entire legal document), and there's lots in it I don't agree with. It could be that I don't understand the antitrust or economics issues, which, of course, are Zimbalist's specialties. I'll list my issues and maybe someone can explain.

First, a quick summary of the situation, as I understand it.

The Phoenix Coyotes are bankrupt. Jim Balsillie wants to buy the team and move it to Hamilton, Ontario, a hockey-mad city 45 miles from Toronto. The NHL doesn't like the idea. First, it believes that it, not the courts, have the right to decide where a team plays. Second, it seems to want to protect the Toronto Maple Leafs from competition. And, third, it doesn't like Balsillie, who is being combative with the NHL rather than cooperating with it.

Zimbalist's written testimony, written at the request of the Balsillie team, argues that

(a) a franchise in Hamilton is worth only $12 million more than if the bankrupt franchise was left in Phoenix, at $175 million versus $163 million;

(b) the effect on the Toronto Maple Leafs would be minimal;

(c) the price Balsillie is offering to pay for the team, $212 million is therefore more than the team is worth, and the difference is "Picasso value," the price Balsillie is willing to pay for the consumption pleasure of owning the team;

(d) the Hamilton expansion opportunity does not "belong" to the NHL.

Maybe there's something about the economics I don't understand, but I don't see it the same way. I'll deal with (b) and (d) in a future post, but for now, let me concentrate on (a) and (c). I think the team is worth substantially more than $175 million, and I think the "Picasso value" is huge, much more than the $37 million that Zimbalist thinks it is.

First, doesn't it seem strange that a hockey team in Hamilton, so close to the best hockey market in the world, would be worth only 7 percent more than the same, bankrupt team in a non-hockey market in the desert? The way Zimbalist gets his numbers is to multiply gross revenue by 2.4. That's based on Forbes Magazine's estimates of team revenue and market value (Zimbalist doesn't justify the 2.4 figure separately).

That seems strange to me, valuing a team by its revenues rather than its profits. It would kind of make sense in comparing "normal" businesses, companies of different sizes in the same industry. Suppose you have two widget manufacturers; Acme sells $10 million worth of widgets a year, and Consolidated sells $100 million worth. You'd expect Consolidated to be worth about 10 times as much as Acme. After all, Consolidated probably has 10 times as many employees, and 10 times as many machines, and 10 times the bill for raw materials, and 10 times the shipping costs, and so on. All else being equal, Consolidated should make 10 times the profit.

But that's not the case in the NHL. With the salary cap, you could argue that team expenses are roughly the same, whether the team is in Glendale or Hamilton. Most of the expense is salaries, and those are now fixed in the range of $41 to $57 million. Forbes has the Coyotes at revenue of $68 million, meaning that if they paid $50 in player salaries, that would leave only $18 million for other expenses and profit. On the other hand, a team like Vancouver, with $107 million in revenue, has $57 million left for other expenses and profit.

For both teams, it looks like those "other expenses" are around $30 million: because Forbes has Vancouver turning a profit of $19 million, whereas Phoenix *lost* $10 million. Vancouver is a profitable enterprise, whereas Phoenix would struggle just to break even. Profits are much less proportional to revenues in hockey than they are in a "regular" business. So why use revenues as your measure?

As a verification, I ran a regression to predict team value based on revenues. The results:

Market Value = 3.2 * annual revenue - $73 million

or, rephrased,

Market Value = 3.2 * (annual revenue - $22.8 million)

The correlation coefficient was .965.

So the value of a team isn't a multiple of revenues: it's a multiple of revenues *above $22.8 million*. Suppose the Coyotes make $68 million revenue, and the Hamiltons twice that. Hamilton won't be worth twice Phoenix, then: it'll be worth two-and-a-half times. Apparently you need at least $22.8 million in revenue to make the team desirable even at $0. Only revenue after that translates into market value.

If you look at Forbes' chart, you can see that: the top 6 teams have a little less than twice the revenues of the Coyotes: and they're worth a little less than 250% as much.

Anyway, if you use this formula for the Coyotes instead of just 2.4 times revenue, you get $145 million, not $163 million. That makes sense, since the regression was based on Forbes data, which values the Coyotes at $142 million. However, Zimbalist did consider subsidies from the city of Glendale, which might make up part of the difference.

As for Zimbalist's Hamilton estimate ... well, he takes Balsillie's own estimate, which assumes revenues would be $73 million. That, to me, seems *way* too low. It would put Hamilton last among the other Canadian teams:

$160MM Leafs
$139MM Habs
$107MM Canucks
$ 96MM Senators
$ 97MM Flames
$ 85MM Oilers

I think an estimate of $100 million would be much more appropriate, given the size of the market. Based on the results of the regression, that would make the new Hamilton franchise worth $247 million -- not $175 million.


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Now, Zimbalist also calculates team value another way, a better way: by estimating actual future profits, and calculating their present value. He doesn't do that for Phoenix, which I think is because he can't predict the Coyotes to ever make a profit in the future (in which case, shouldn't its value by this method be zero? But I digress). However, he does it for the proposed Hamilton franchise. Here's how: he starts with Balsillie's own projections of earnings the first five years of the franchise. Then, he assumes earnings will grow steadily for the next 25 years. He then discounts all 30 years' profit into today's dollars.

Zimbalist performs this calculation for five different 25-year growth rates (from 3 to 7 percent) and for three different discount rates (from 8 to 12 percent). He winds up with a franchise value ranging from $70 million to $177 million, with a typical value of $150 million.

This is all quite reasonable, although you have to keep in mind that Balsillie is probably being very conservative in his earnings projections in order to keep his price down. Still, it doesn't seem like this is how other teams are valued, probably because of the "Picasso factor." Looking at the Forbes chart, the market value of teams is much, much flatter than their earnings. The top three teams (Leafs, Rangers, Habs) make an average of about $45 million a year, and their market value is about $400 million -- an earnings/price ratio of about 11%. But the teams in the middle, who look like they make an average of about $3 million a year, are worth about $200 million -- an earnings/price ratio of about 1.5%. And the teams at the bottom are all losing money -- but their market values are still around $160 million.

Why are the values so flat relative to profits, where a team that makes $1 million a year is worth almost half as much as a team that makes $40 million a year? It could be the Picasso effect. I ran a regression to predict market value based on earnings. The results, rounded:

Market value = $200 million + 4 times annual earnings

The correlation coefficient? 0.88. Not as high as for revenues, but still huge.

What that tells us is that, regardless of earnings, there's a value of $200 million dollars to owning a team, even if it only breaks even every year. That might be Picasso value. Or, it might partially reflect the value of the right to move the team if it starts losing money. It might reflect the fact that owners think that earnings will jump soon -- maybe they think a new TV contract will someday be worth a present value of $30 million each, and that's part of the $200 million. But I think it's consumption value, Picasso value.

$200 million does seem reasonable in terms of consumption value. At today's low interest rates of (say) 4%, the opportunity cost of locking up $200 million is only $8 million. Most of these owners are billionnaires -- what's a tiny $8 million a year? Jim Balsillie's own willingness to pay is no doubt much more than $8 million. He likes publicity. He's making much of the fact that he wants to bring the NHL to more Canadian cities, making him something of a hero in some circles. He might have some ambitions beyond NHL owner, ambitions which being in the limelight will further.

Using the regression results puts the Coyotes at $161 million, which is about where Zimbalist has them in his revenue model (he can't use the earnings model because the Coyotes have negative earnings).

So, let's say we use this same regression equation to value the Hamilton team. Balsillie claims that five years from now, the team will be making $11 million. That means it'll be worth about $244 million then. Discounting that to today's dollars, at 4%, gives $209 million today. Adding in $35 million of Picasso value ($40 million discounted) for the next five years takes us back to $244 million.

And, again, that's conservative because it uses Balsillie's own estimates of his profits. Here are the earnings of the six Canadian teams last year, according to Forbes:

$66.4 million (Leafs)
$39.6 million (Canadiens)
$19.2 million (Canucks)
$ 4.7 million (Senators)
$ 7.4 million (Flames)
$11.8 million (Oilers)

Judging by this, I'd say that, for a Hamilton franchise, $11 million five years from now is pretty conservative. Even so, the Picasso value drives so much of franchise valuation that it doesn't matter much: even if the Hamiltons made as much as the Canucks, it would only raise the franchise value from $244 million to $276 million.

So I think the team in Hamilton is worth about $250 million. Not only is this substantially higher than its worth in Phoenix, but it's even more than Balsillie has offered. So I bet Balsillie is willing to spend a whole lot more than his $212 million offer, if necessary, to achieve his dream of a team in Hamilton.

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So, a summary of our respective market value estimates:

Zimbalist thinks:

-- Phoenix $163MM by revenues
-- Hamilton $175MM by revenues (based on $78MM in revenues)
-- Hamilton $150MM by earnings

I think:

-- Phoenix $145MM by revenues, plus government subsidies
-- Phoenix $161MM by earnings
-- Hamilton $247MM by revenues (based on $100MM in revenues)
-- Hamilton $250MM by earnings

Zimbalist thinks the difference between Phoenix and Hamilton is maybe $12 million at most. I think the difference is close to $100 million.

Am I missing something?