Thoughts on Company Valuation

Since I graduated college I’ve taken quite a bit of interest in the stock market. I’ve done so primarily because I felt I owed it to myself to be financially educated. I’ve gone through a number of hair-brained and hackneyed theories about how to cash-in on the market during this time. For awhile I was enamored with the idea of quick money in the currency markets and loved using Excel to back test every technical indicator one could imagine.

Eventually, however, you fall back to earth. And when you do, names like Benjamin Graham and Warren Buffett start to float around with greater frequency. What is the intrinsic value of a company? How is the market valuing the company differently from it’s intrinsic value. Well, it turns out that this is calculated by a little method called discounted cash flow analysis. Basically this involves plugging in a few known (and unknown) company variables into an equation to produce the fair value that the company ought to be trading for.

Discounted cash flows are based on a principle called the “time value of money.” It’s the notion that the value of something now is higher than the value of that something in the future. So, for instance, (most rationally self-interested) people would prefer to have $1000 now than $1000 a year from now. So, if we are going to loan that $1000 now, we expect to be compensated by more than that amount a year from now. Depending on how badly the owner of the money wants to give it up and how badly the borrower needs it, they will eventually come to an agreed upon amount of future repayment a year from now. Let’s say this is $1050. We therefore now have what’s popularly called an interest rate of 5%.

Companies, according to discounted cash flow analysis, are worth the present value of the stream of future income that the company will produce. How you know what this future stream will be, of course, is a good question. This is why discounted cash flow analysis is necessarily an imprecise matter. However, it is possible to lock in certain assumptions in the equation to yield a fair value for the company identical to the prevailing market price. In other words, we can ask ourselves, “if the market price was decided by a consensus on discounted cash flow, what variables would the market be plugging in?” In other words, if market price was always identical to intrinsic value, how would the market be determining intrinsic value right now? We can then ask the more important question, “were those assumptions correct?”

Moneychimp.com has a discounted cash flow calculator. There are five variables one needs to plug in to produce intrinsic value: annual earnings, annual growth rate for the forecast period, length of forecast period, perpetuity growth rate, and the discount rate. Let’s break these down. Earnings are simple. It is how much the company profited the last year. It is generally recommended to use cash flows instead of earnings in the equation, but generally they converge over the long run. Company growth is divided amongst a forecast period and a perpetuity period (in other words, the entire time after the forecast period). If you wanted, you could plug projected earnings for each individual upcoming year into the equation. This particular calculator simplifies matters by asking for an average growth over a certain period of time, followed by a general prediction of the growth thereafter. Typically, this perpetuity growth will be assumed to be very modest.

The last component is the discount rate. This is the minimum required rate of return. A good way to think about how the discount rate works is by assuming 0% growth and running the calculations. You find that for a constant earnings stream of $10, a discount rate of 10% will produce a value of $100. $10 being 10% of $100, the discount rate indicates a baseline for what earnings should be in relation to value. If you were dealing with 5% interest on treasury bonds, you would expect that that $10 “earnings” to produce a bond worth $200 ($10/$200 = 0.05 = 5%). You expect stock to produce at least the same return (if not greater) as a bond, which is presumably risk free.

As a matter of fact, you should expect more than that. You should expect a company to return at least the same as its Weighted Average Cost of Capital (WACC). This is the amount it costs to finance the company through debt and equity. Cost of debt is the rate the company can borrow at. Cost of equity is more complex. It includes not only dividends, but also expected appreciation on share values. Because of this, cost of equity is generally higher than cost of debt. The higher the WACC (and by extent, the higher the discount rate), the more conservatively you are valuing the company. A 10% WACC on $10 earnings means a $100 company. 20% WACC means a $50 company.

At this point, it is safe to start introducing some of the assumptions I am going to put into the equation. For forecast period, I chose 10 years. Basically this is the period for which one would desire to hold the stock. Perpetuity growth rates are assumed to be 3%, roughly the rate that GDP expands. The discount rate I am using is 15%. I arrived at this figure by basing it totally on the higher cost of equity, which was calculated according to the Capital Asset Pricing Model. The primary company specific variable involved is the Beta coefficient, a measure of share volatility. The equation is R = Rf + B( Rm – Rf ). R is rate of return (cost of equity), Rf is the risk-free rate of return (treasury bond yield), Rm is the market rate of return (historic S&P500 growth rates), and B is the Beta Coefficient. So R= 5% + B (11%-5%). For R=15%, B is roughly 1.67, which is a fairly high amount, resulting in a conservative value estimate. According to Yahoo’s stock screener, only about one fifth of the securities in the S&P500 have a Beta higher than 1.5.

This leaves forecast period growth and earnings. Earnings have been normalized to $1. The reason for this is that ultimately I am looking to compare price/earnings ratios. The major concern is not so much to gauge company value directly as it is to estimate how much company value there is for each dollar of earnings, whatever actual earnings figure may be. Therefore, earnings have been put at $1 so as to produce a price/earnings ratio in the final value solution.

This leaves growth rate as the only remaining independent variable. Zero growth in the forecast period means a P/E of 7.14. There is an upward limit on acceptable P/E, governed by maximum sustainable growth. Return on equity (ROE) caps the growth rate, since growth higher than that requires borrowing more money or floating new shares. Because ROE is affected by leverage, and because we want to look at companies will lower debt, we will cap the debt/equity ratio at 1, so at most ROE can be twice Return on Assets (ROA.) Only 1% of the S&P500 has a reported ROA higher than 25% (hypothetical ROE of 50%).This would yield a P/E of over 179! A more reasonable upper limit seems like 30% ROE, which yields just over 50 P/E. Anyhow, we can produce a table correlating various P/E ratios to expected growth rates:


Growth P/E
0 7.14
1 7.59
2 8.07
3 8.58
4 9.14
5 9.73
6 10.36
7 11.05
8 11.78
9 12.56
10 13.40
11 14.30
12 15.26
13 16.29
14 17.40
15 18.58
16 19.85
17 21.21
18 22.66
19 24.21
20 25.87
21 27.64
22 29.54
23 31.56
24 33.73
25 36.04
26 38.50
27 41.13
28 43.94
29 46.93
30 50.12

Then there’s the final question: is the market right? I screened for companies with P/Es below 7 but had historical growth rates above 10%, the assumption being that there will likely not be a steep drop in growth over the coming period, and it produced a few results. There are other factors to consider of course, but this seems like an interesting and promising angle on P/E ratios. Perhaps more on that to come.