# Articles

**UNDER THE HOOD OF THE CASH FLOW MULTIPLE**

*By Larry Gerbrandt, Principal, Media Valuation Partners*

Among the many tools available for valuing assets is the cash flow multiple, which in the last decade has often been specifically defined as the EBITDA multiple (earnings before interest, taxes, depreciation and amortization). It is easy to understand its attraction: the math is simple. Simply multiply it by an asset’s cash flow and you have a value that gets the investor or analyst into the ballpark.

Equally as important, cash flow multiples can be calculated for other companies and deals and these benchmarks become useful as comparables. What is less often discussed is what a cash flow multiple actually measures or why certain categories of assets may command high cash flow multiples (often in the high teens) and others routinely sell for single digit multiples.

In theory, two variables determine what a cash flow multiple should be for any business: the discount rate (sometimes also referred to as a company's cost of capital) and how fast a company's cash flow is growing (it can even be a negative number). The two variables act in countervailing ways: the higher the cash flow growth rate, the higher the cash flow multiple that can be justified; higher discount rates push the multiple down.

It's easier to understand--and calculate--the relationship if it is assumed the business is mature and cash flow growth can be projected and sustained over a very long term horizon. This is precisely the assumption made in discounted cash flow (DCF) valuations which employ a terminal value. The notion of the terminal or residual value is that it captures all the value of the asset into perpetuity.

In DCF valuations that use terminal values, cash flow is projected over a discrete time horizon, typically five and sometimes as many as 10 years, discounted back to present value and then a multiple is applied to the*n*th year's cash flow to create a terminal value.

The formula for the terminal value, also known as the Gordon Growth Model (proposed by Gordon and Shapiro in 1956) is Value = CF/(k-g), where k is the discount rate and g is the long-term sustainable cash flow growth rate (technically, into perpetuity). Since a cash flow multiple is Value divided by year-ahead Cash Flow, the formula becomes CF Multiple = 1/(k-g).

The table on the following page illustrates the relationship between the long-term growth rate (g) and the discount rate (k). Higher cash flow growth rates naturally yield higher multiples while higher discount rates (which in effect are an estimate of the marketplace risk that the asset will continue generating the cash flows) push the cash flow multiple downwards. Inherent in the math is that the discount rate must be higher than the cash flow growth rate.

Using this matrix, a company with a long-term cash flow growth rate of 5% could justify a 10x cash flow multiple at a 15% discount rate. It is actually possible to test out if a cash flow multiple really does capture the value of future cash flows.

Let’s assume a company is generating $1 million in cash flow. At a 10x cash flow multiple, the implied valuation would be $10 million. In this case, how long does it take for a company that is generating 5% cash flow growth to generate $10 million in future cash flows, discounted back to the present at 15%? To answer this proposition a simplified discounted cash flow model was created, where each future year’s cash flow was discounted back to present value (in this case at 15%) and then each year’s present valued cash flow was cumed (or added to the prior year’s cf).

In this example, a 10x multiple is essentially capturing the next 22 years of cumulative cash flows, discounted back to present value at 15%. Different cash flow growth rates and discount rate combinations will produce different time lines. For instance an asset valued at 10x but growing its $1 million in cash flow at 10% year on year but discounted back at 20% would cume to $10 million in about 20 years.

While we've proven that the math works, in the real world few companies can predictably sustain steady cash flow growth indefinitely and economic conditions--such as the period we are currently in--can cause even the most stable media company to slow down or even temporarily have negative cash flow growth. One way to adjust for some of this risk to raise the discount rate, which,as we've shown, would cause the cash flow multiple to decline.

In fact, the proper calculation of the discount rate is a relatively complex issue and generally reflects not only a company's capital structure but also prevailing interest rates, historic stock market returns, a company's stock beta and sector specific adjustments, among other things.

It is for this reason cash flow multiples, as *primary* valuation metrics, are approximations--though a good shorthand language which allows different kinds of deals within a sector to be compared and analyzed.

Nonetheless, in a transaction, a buyer is generally willing to pay a higher multiple for an asset which has the potential to grow cash flow at rapid pace over a significant period of time than one in a sector where there is either an uncertain economic outlook or in a sector where the ability to grow cash flow is limited by technology or capital restraints.