Look, I know, I have forgotten about the blog for a while. And I am pretty rubbish at writing regurlary. But I have come across a topic which I can actually say something about.

The lawsuit between Constantin Medien and Bernie and Co in London is a pretty interesting thing to observe. Some people say some things that are pretty fascinating. One of such things that ended up in the press is Donald Mackenzie’s statement regarding the valuation of the business.

**DM:** No, they, I think they put it in because, well, the client asked them to and because they *could make the numbers work*. They made all sorts of *ridiculous assumptions* in that document. That the Concorde Agreement would stay in place for ever. That earnings would go up endlessly for ever. And the risk of the whole business was as low as you could imagine. So they got it wrong. I think they had something like 70% of the value, the value that they put in that document, relating to the Concorde period after 2012. And we hadn’t even signed Concorde from 2008 to 2012. So it was a very pie in the sky valuation, in my opinion.

— Pitpass

The assumptions sound rather bold, but the thing is that this is industry standard. What E&Y did was a simple Discounted Cash Flows Valuation, which requires all sorts of ridiculous assumptions. To value a company you need two sorts of things: cash flow forecasts into infinity and a discount rate.

Usually 3 stage model is used:

- 1st stage is a detailed forecast of the firm’s cash flows for the next 5 years. You analyse your strategic position, the value drivers, you forecast revenues and costs making most of the assumptions based on the analysis of your previous periods and the management’s plans
- 3rd stage is so-called perpetuity stage, where you assume that your revenues will continue into infinity. The logic behind this is that you expect the firm to be there forever, but making forecast for the next 5 years is hard enough, to forecast anything that happens in 100 years is pretty much impossible. What you need for this stage is the perpetual growth rate, which we’ll discuss later.
- 2nd stage – which E&Y probably have just left out – is the normalization phase. This is the period in which the yearly growth rate of revenues converges towards the perpetual growth rate from the 3rd stage. Usually it is assumed that the growth rate decreases linearly, but usually the functional form of the transition is not that important.

At the first sight an assumption about perpetual revenues growth is ridiculous, but actually it’s more than logical. The cash flow forecasts are made in nominal terms, they don’t take into account an inflation rate. This means that if you want to assume constant revenues in real terms you still need your nominal cash flows to grow. The industry standard is to take the GDP growth rate in the country of operations and add the inflation on top. In this case you assume that the cost increases induced by inflation can be charged from the customers. Oh and there is a mathematical shortcut to calculate the Present Value of a perpetuity. The thing is called Gordon Growth Model and looks like this: FCF / (r-g) where FCF is free cash flow of the first period, r – cost of capital and g – growth rate. Doesn’t look like rocket science.

One could argue, that there is no guarantee that F1 is worth anything without the Concorde Agreement, and one should only take into account the cash flows for the years for which the agreement is in place. The problem is that the company has all the possibilities and plans to extend the contract, and this possibility has to be paid for. To assume that the new agreement will be signed is very logical.

This is the first part. Now the question is how risky the whole thing is, how much the investors want to be paid for the risk and for time value of money.

The industry standard to calculate the cost of capital is the Capital Asset Pricing Model (CAPM), which is composed of the following components:

- the risk free interest rate
- the so-called beta (the measure of the company’s systematic risk)
- and the Market Risk Premium calculated as the difference between the return on the market and the risk free rate

The model is based on a bunch of assumptions that don’t really hold, for once for CAPM to work you need the interest rate at which you can borrow money be equal to the rate at which you can lend money – which is kinda not true. Another assumption is that capital markets are efficient, that all the information is reflected in the stock prices and there are no information asymmetries between the management and the investors. Further the model is based on the assumption that there are no transaction costs and no taxes. This is what I call a pie in the sky. The problem is that the alternatives are not really applied in the industry, and they have other sorts of assumptions, which are not really any better.

The risk free rate is the easy bit. You usually take the the yield curve of the government bonds of the countries with high credit rating. The yield curve gives you the interest rate of the bond with different maturities. Then you have a choice: either you discount each cash flow at the corresponding interest rate, or you use the interest rate of about 9 year bond for all cash flows (which maturity you choose depends on the growth rate you’ve assumed before). The difference is minimal and the latter approach is more popular for complexity reduction reasons.

Beta is a complicated thing. As I said above it measures the systematic risk of the company. Systematic risk is everything you can’t diversify like general state of the economy. If the risk is diversifiable that’s what a rational investor would do, so the company doesn’t have to pay for it. The companies that produce luxury goods are more reactive to the market conditions and have higher than 1 betas, the companies that produce essential stuff usually have lower than 1 betas.

For traded companies beta is calculated using a linear regression of stock returns on the market returns for the past 5 years. The market in the model is assumed to be a perfectly diversified portfolio of all investment opportunities. Such thing simply doesn’t exist, that’s why people usually take a big national index. There is a bunch of problems: is the 5 year period representative for the future eternity? is the market and your stock liquid enough to provide a reliable estimate? which index do you take: DAX, Eurostoxx, MSCI World? do you take monthly data or weekly?

But what if your company isn’t listed? You can use the beta of comparable companies, the firms from the same industry, which have the same risk profile. But F1 doesn’t really have comparable companies, let alone listed comparable companies. You know that the beta for the entertainment industry is about 1.31 (calculated as a weighted average of the regression betas in the entertainment industry), but it doesn’t mean that F1 has the same risk as the entertainment industry. It would be logical to assume beta higher than 1, yes, but how much higher?

The market risk premium is another ingredient of the pie. It is the difference between the risk free return and the market return. The problem is that you don’t know what the market return is going to be in the future. So you usually take the historical data, calculate average and assume it’s going to stay the same. Nice assumption. The question is how far back in time you go: 20, 30, 70, 150 years? do you include crisis years? do you take geometric or arithmetic average? The latter choice gives you a difference of approximately 4% (based on German data, I’m sure UK or US aren’t that different).

You put all the things together and get the cost of capital = risk free rate + beta * market risk premium. And this is the number you use into infinity. Needless to say that it’s fairly easy to *make the numbers work *by just varying the components of the CAPM.

Did E&Y do something wrong? Methodically probably no. But the methods aren’t really robust, so that any value you get can be questioned, which both sides are now trying to do.