HowTo: Expected value

Found at Autoblog, via Opit:

Could Detroit be exporting cars to Europe soon?

zafria

With a weakening US dollar and more competitive union contracts, exporting vehicles to Europe from the US is looking more and more plausible with each passing day.

… Automobilwoche in Europe is reporting that Opel worker’s council head Klaus Franz called a US-built Zafira a “distinct possibility”

Many things are a distinct possibility. A strong holiday sales period over thanksgiving is a distinct possibility. I’d still keep my money under my mattress, though. In Euros.

If GM can pull off building a vehicle in the States destined for Europe, it would strengthen its plant utilization in North America while also increasing European capacity. While there is only a slight chance this will happen, we think it would be a huge stride towards profitability in the General’s largest market. While there is only a slight chance this will happen, we think it would be a huge stride towards profitability in the General’s largest market.

So. GM may pull this off, or it might not. It might make loads of money, or it might lose loads of money (although we’re talking about a company that can post a USD39bn loss and pretend it’s just a tax ‘thing’, no big problem). It’s also the company whose European arm had, last year, posted 6 years and USD4bn worth of straight losses.

GM’s auto profits, like most, are the poor cousin of its various income streams. Hell, they apparently lost USD2,311 per vehicle in 2004, with an average cost per vehicle of USD18,348. So these cars of theirs may (a) sell for a profit, (b) sell for a loss, or (c) not sell at all in Europe. Apparently there’s only a slight chance that they’ll sell.

Let’s assume, then, that GM will not manufacture cars specifically for the EU market, only to have them not sell. They’ll either manufacture-and-sell these cars or not: i.e., they will make some profit in Europe on these cars, or they will make zero profit because they won’t make the cars. This is probably a naive assumption, but it’s a nice conservative one.

Profit per vehicle? They apparently sold a little over 2 million vehicles in Europe, last year. They have 12 brands; those brands carry 42 models, between them. Clearly some brands and models are better sellers, but it’s late and I already don’t care that much. I’m going to call it around 50,000 sold per model (rounding makes my – admittedly abstracted, already – example easier), and a profit of who the hell knows, if they don’t make profits on their cars? Let’s give them Ford’s USD620 profit per vehicle (Ford had the highest for American firms – is it even worth making the damn things?).

If GM’s plan comes through, they’ll make π1 = 50000 x 620 = USD31m; if it does not, they make π2 = 0 (as opposed to making and not selling the cars, in which case π3 = negative USD115.5m to negative USD916bn – though that’s clearly ridiculous).

The expected value, then, is the one in which we’re actually interested. When this is guaranteed to happen, we can become excited. Until then, we need to weight the payoff by the likelihood that it will occur, as well as weight the loss by the likelihood with which it will occur (in this case there is no loss). The expected value of GM’s deal is given by

EV(GM Zafria in Europe) = Pr(Zafria happens) x π1 + Pr(Zafria does not happen) x π2

EV(GM Zafria in Europe) = Pr(Zafria happens) x USD31m + Pr(Zafria does not happen) x 0

EV(GM Zafria in Europe) = Pr(Zafria happens) x USD31m

Now – what is Pr(Zafria happens)? A rule of thumb in statistics is that 5% is significant: a probability of 5% is small, but significant (unless it’s a risk of accident or cancer – then a probability of 0.005% is important). So I’ll split the difference and say that “slight chance” = 2.5%. Then

EV(GM Zafria in Europe) = 0.025 x USD31m

EV(GM Zafria in Europe) = USD775,000

Now, as I said, GME has posted losses of hundreds of billions for 6 straight years. A profitable car being sold would be good news indeed – it would be good news to any company (although it would absolutely blow the minds of companies that actually manufactured, say, plastic straws). Until those cars are wanted in – and/or get purchased in – Europe, we should work with our expected payoffs, accommodating the probability that there will be any payoff at all.

My numbers aren’t likely to be terribly accurate, but I also think I made kind assumptions, along the way, so I would not be surprised if my expected value was actually generous.

It certainly doesn’t seem like all that much about which to get excited.

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