This is the first post I’ve written, which is rather technical in nature (not really, but it’s the most technical I’ve ever written on my blog anyway). It is about deriving an expression for how changes in leverage, profitability, sales, and firm value multiples affects value creation, and by how much. The reason for writing this post was that I couldn’t find anything on the web, which satisfied me in explaining the derivation—so I did it myself.

We can look at value creation in companies in many ways—however, generally, we define value creation as the value created for shareholders from one point in time (t) to another (t+1), as follows (where S is equity value):

We are often interested in analysing exactly how this value came about, i.e. which factors influenced the value creation. As mentioned, there are several ways of looking at this and of breaking it down—here, I will focus on the very popular break-down into debt reduction, multiple expansion, and growth in earnings. The latter can again be divided into sales growth and margin expansion.

In other words, we want to arrive at an expression that groups value creation into what was created from debt reduction, multiple expansion, sales growth, and margin expansion.

Let us first realise that (1) total enterprise value is equal to the sum of equity (S) and debt value (B), and (2) that enterprise value is equal to earnings before interest, tax, depreciation, and amortisation (EBITDA) multiplied by (EV/EBITDA), as follows:

We can then write our valuation creation equation (the first equation) from before as:

We have now isolated the effect of debt reduction on value creation—the two terms on the far right. We still need to regroup the remainder of the equation in order to find expressions for the development in the (EV/EBITDA)-multiple, sales growth, and EBITDA-margin, as follows:

Thus, we arrive at the following expression, where EBITDA is shortened to E to save space (equivalent to the last line in the derivation above):

That is, value creation can be attributed to earnings growth, when holding the multiple constant, multiple arbitrage, when hold earnings constant, and, finally, debt reduction.

As mentioned in the beginning of the post, earnings growth can be further disaggregated into sales growth and earnings margin expansion. The derivation of that is similar to the above, and the result is, as follows (EBITDA is again shortened E, and sales is shortened R, to save space):

So the first part of the equation tells us how much of the value can be attributed to sales growth, when holding the earnings margin constant; the second part tells us how much can be attributed to earnings margin expansion when holding sales constant; the remainder of the equation has already been explained.

Final notes:

• Substitute EBITDA for your favourite earnings measure.
• You can convert the absolute figures into percentages and then compare across companies. Be sure to get the signs right.

This entry was posted on Tuesday, July 11th, 2006 at 7:14 am and is filed under Business. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.