Via LinkedIn : Perhaps the most rigorous way to calculate the value of a firm is by using discounted cash flow (DCF) analysis. When we use DCF analysis, we build a detailed forecast of the firm’s sales, costs and expenses, and long term capital investments. We then use those forecasts to calculate the “free cash flow”, or the cash that will be available to the firm’s investors, over the life of the firm.
I prefer using DCF analysis to estimate firm value, because it allows for a deeper understanding of the drivers of performance within the firm. A sound DCF valuation provides significant strategic insight to firm owners on how to maximize the value of the firm. Owners can estimate the impact to firm value of increasing or decreasing prices, of stimulating firm growth, or of postponing capital investment.
But DCF analysis requires us to make a somewhat tricky calculation. What is the value of the firm at the “end” of the forecast? If you think about it, forecast projections are always finite. The weather forecast is for a five day period (with a wild guess about the next week, which no one takes seriously). Outlooks on the U.S. economy generally range from one to five years. In the same way, valuation analysts forecast the firm’s free cash flows for a finite period. At some point, it becomes impractical to forecast the firm’s cash flow, say, 98 years in the future. In general, valuation analysts forecast the firm’s free cash flow until the firm reaches a steady state of performance. Then we embark on a related, but significantly different analysis.
Unless firm owners have a plan to close down shop, we assume that firms live forever. Even a firm that is acquired continues to “live on” as part of the firm that acquired it. Therefore, if we forecast a firm’s free cash flow for 10 years (until the firm achieves steady state performance), we must ask ourselves “What will the firm be worth at the end of the 10 year forecast period?”
The best way to find that answer is to calculate a “continuing value” for the firm. This value represents the value of that last year’s free cash flow, growing at a steady state into perpetuity, but valued in “today’s” dollars.
American economist Myron Gordon, a Ph.D. out of Harvard, invented a tidy formula for calculating this. It is:
Continuing value = FCF * (1 + g) ÷ (WACC – g),
where FCF is the firm’s free cash flow in the last year of the forecast period, g is the rate at which we expect the firm’s cash flow to grow in steady-state, and WACC (weighted average cost of capital) is the required rate of return on investment that the firm’s owners demand.
So the numerator, or the top part of the fraction, represents the free cash flow that the firm generates for its owners in the “first year of perpetuity”. The denominator, or the bottom of the fraction, modifies that value in two ways. First, we all value a dollar received today more than a dollar received next year. How do we quantify the difference between the value of a dollar received today and the value of a dollar received in the future? We use the investor’s expected rate of return.
Let’s say that you ask me to loan you $100, and you promise to pay it back a year from today. If I’m a rational business person, I will ask you to return to me more than $100 this time next year. How much more? I will ask you to compensate me for the investment income I could have otherwise generated with that $100. That’s my “required rate of return.” If I know I can generate 5% return with that $100, then I will ask you to return $105 to me next year. Investors in a firm have a required rate of return. That’s what the WACC represents – the rate of return that the investors of the firm require in order to defer receiving that income.
So now we have a good estimate of the value of the free cash flow of the firm from the end of the forecast period, into perpetuity. But most firms will grow into perpetuity, right? Firms don’t remain the same size year after year. We can conveniently adjust the denominator of this formula by subtracting g, or the firms’ long-term expected growth rate, from WACC (Isn’t algebra great? And we all hated it in high school.)
Let’s say we forecast the free cash flow of a private restaurant business for ten years. At the end of ten years, we are comfortable that the firm has achieved a steady state of performance. The free cash flow forecast in year ten is $750,000. Firm owners require a 20% return on this investment (why so high? Because owning a private restaurant business is fairly risky – much more risky than investing in the stocks of publicly traded companies). We believe the firm can grow at 3% per year in the steady state. What is the value of the firm into perpetuity?
Continuing value = $750,000 * (1 + 0.03) ÷ (0.20 – 0.03) = $4,544,118.
We now have the value of the firm’s free cash flow, growing at a constant rate, accounting for the investors’ required rate of return for deferring this income, from the end of the forecast into perpetuity. Pretty sharp.
How do we interpret that? One way is to say that in 10 years, the business could be reasonably sold for $4.54 million.
$4.54 million is a lot of money; how do we know this calculation yields a reasonable estimate? A good valuation analyst will do a few sanity checks on this value. One good sanity check is to compare the estimate of continuing value to the value of publicly traded firms in similar lines of business. Let’s say that we identify three companies that have been recently sold that are roughly comparable to the firm we are valuing. We can compare those firms’ cash flows (approximated by earnings before interest taxes depreciation and amortization, or EBITDA, right off the firms’ income statements) to the purchase prices.
When we observe the comparable companies that have been sold recently, we note that the ratio of firm’s sale price to the firm’s EBITDA range from 6.0 to 8.0. That means that comparable restaurant businesses are selling for about six to eight times their EBITDA. That’s called an EBITDA multiple. Let’s compare that to our estimate of continuing value for the business we are valuing.
Implied EBITDA multiple = $4,544,118 ÷ $750,000 = 6.05.
I like that answer. It tells me that my estimate of continuing value for my client’s business is in line with “real life” sales. It also tells me that since my implied EBITDA multiple is on the low side; perhaps I’ve been appropriately conservative.
We glossed over many other issues today, such as required rates of return, reasonable long-term growth rates, and the actual process of forecasting free cash flow. Perhaps we can return to those another time.