Session 5
Stock Valuation and the Cost of Capital
Lecture Material
Introduction
This session represents the close of the first half of the course. This session is designed to tie the past three sessions (3,4, and 5) together and provide a basis for moving into the second half of the class, which focuses on valuation and corporate financial policy. This session will seem to be a bit shorter than most others to this point, and this is by design.
Stock Valuation
We finished the last session with a discussion of stock pricing, and you have been working through material in Chapter 10 of the textbook, which covers the technical aspects of pricing a stock quite thoroughly. The pricing model we dealt with in the lecture notes for Session 4 looks like this:
P = (*eps1)/ (k – g)
What this represents is that fact that stock price is some function of earnings discounted by a growth-adjusted rate. The growth-adjusted discount factor is also referred to as a capitalization rate. Therefore, stock prices may be looked at as a form of capitalized earnings.
The meaning of the coefficient is at the same time both significant and elusive. For example, in the prior session, it was noted that if the company whose stock is being valued pays a consistent dividend, the coefficient takes the form of the dividend payout ratio, and the numerator becomes the expected dividend payout. The resulting model is referred to as the constant growth (or Gordon growth) model.
The elusiveness of the meaning of the coefficient is evident, however, when we consider the fact that a large number of companies do not pay dividends to shareholders. Most of these companies tend to be higher growth companies which, by financial logic, should not be paying dividends. The reason for this is that, for these high growth companies, the high rate of return on invested capital typically exceeds the investors required rate of return. In these cases, it makes sense for the company to retain its investors’ capital and reinvest it into the new products and service projects. In other words, the company can do more with than the shareholders could with the money, and it benefits the shareholders to leave their money with the company. As soon as the return on invested capital falls below the investor required rate of return, a company should no longer invest those extra funds, but rather, should distribute them in the form of dividend payments (or repurchases of stock). In this case, the company can not do better than the investors can do for themselves (at least at that risk level), and therefore, investor money should be returned to them,
For this reason it is logical to see that most companies that pay higher dividends are NOT high growth companies. Further, when a company announces a dividend payment for the very first time, its stock value usually declines. With the initial dividend the company is essentially announcing that the days of high growth are over and that they are going to start distributing the benefits of that growth back to investors in the form of dividends. At this point, the investors who were interested in high growth and capital gain returns will not cash out by selling their stocks (they don’t want to hold low growth, dividend paying stocks), which makes the price fall on the market. The lower capital gain yield is compensated for by the higher dividend yield thereafter.
In the case of a non-dividend paying company, then, what does the coefficient represent? It could represent a factor that converts current into future earnings, but it could also measure something else. The problem is that we don’t really know exactly how stocks are valued.
Estimating the Cost of Capital
The cost of capital for any form of capital, be it debt or equity, is determined by an interaction of supply and demand in the capital markets. Essentially, the cost of capital is ultimately investor determined, and it is based on the return they demand as compensation for risk. The most accurate way to estimate the cost of capital, therefore, is to observe it in the market.
The cost of debt capital is fairly easy to observe because bond yields in the market can be measured. Given a bond’s interest, principle, term and price, a yield can be mathematically determined. Required stock returns, on the other hand, are much more difficult to observe in the market process.
As you can see from looking at the stock equation, the fact that the true meaning of the coefficient is unknown makes it much more difficult to estimate the cost of equity capital (ke) by observing market data. If we solve the equation for ke, we get the following:
ke = [( * eps)/P] + g
If the company pays a dividend and is the dividend payout ratio, then the first part of the equation represents the dividend yield. If, however, the company does not pay a dividend and we do not know the true meaning or value of , then we can’t specifically identify Ke by using such a formula. This is one reason why P/E multiples are so important. Using the stock pricing equation again, this time dividing P by eps, yields:
P/eps = / (k – g)
Using the P/eps multiple, I only need to know the earnings in order to value the stock. I simply apply the multiple to come up with the price, and I don’t have to worry about calculating the cost of equity capital. This is very often done for IPO stocks.
The problem this creates for companies, however, will ultimately be seen when it comes time to determine a discount factor to be used in valuing assets in the capital budgeting and other processes. This process relies on the fact that we do, in fact, have an estimate for the cost of equity capital.
The CAPM Approach
Other than directly observing stock pricing data in the market, it is also theoretically possible to estimate the cost of equity capital by using a market model such as the CAPM. In this case, you would have to estimate three factors correctly. These are the risk free rate of return, the expected rate of return on the market portfolio, and beta.
The difficulty with estimating the market return is twofold. First, it is forward-looking, and therefore only a forecast. Second, you need to identify just what makes up the market portfolio. For example, the Dow Jones Index is supposed to represent the market, but it only contains 30 stocks! Then there is the S&P 500 (not to mention the S&P 100 and 400). What about the Wilshire 5000? Compounding the problem is the fact that any of these indices can be calculated by either equally weighting the importance of each stock in the index or by weighting according to the total value of each as a percentage of the total value of the entire portfolio, which gives higher weight to the companies with larger capitalization.
Ibbotson and Sinquefeld
Instead of having to estimate the market return, many investors and analysts rely on data that has been produced by two researchers by the names of Ibbotson and Sinquefeld. Studying stock and bond market returns over the past 75 years, they have concluded that the market risk premium (the difference between the risk free rate and the expected market return) has averaged 6.5% to 7.0% over that time period. Rather than trying to estimate the expected market return, therefore, most analysts simply assume that the market risk premium will be within that range.
Problems Estimating Beta
The CAPM, and its basic component, beta, have been the subject of more debate than any other in the history of modern finance. One of the most basic problems is simple: beta is measured from historical data, yet, the CAPM measures a required return that is to be used to discount future earnings and cash flows (e.g., dividends or cash from investment projects). The problem here is that the true underlying beta for a company may change from time to time, and there is no guarantee that the beta for a company over the past five years is a good estimate for what the beta will be over the next five years, or even one year at that! Companies restructure, change product lines and management strategies, all of which may affect the way the company relates to the market. The overall market can change as well, having a similar effect on beta, which captures the relationship between company and market returns.
Another problem with the CAPM is referred to as the “joint test” problem. This problem is described by the fact that when you test the accuracy of the CAPM by comparing returns as measured by the model to actual returns in the market, you are testing two hypotheses at the same time. The first is that the behavior of all returns in the market will be explained by one model, and the second is that the CAPM is that model. The CAPM may appear to be right, but for the wrong reasons. It may be right but appear wrong. We can’t however, design two separate tests, however, so that creates a limitation in our ability to understand behavior in the investment markets.
In spite of the tremendous volume of criticism of the CAPM and its use in financial modeling, the beta coefficient is still widely reported and the model is taught as a foundation principle. Whether or not it is, in fact, 100% accurate, the theory underlying the model is logical and provides excellent insights into financial decision-making.
The textbook describes several different methods of estimating the cost of equity capital in detail. You will note that many of these require the use of measurable cash flows such as dividend payments. As stated earlier, many firms do not pay dividends, which would invalidate the use of those models. You may read about those methods and ask any questions you have on the discussion board over the next week.
Average Historical and Marginal Cost of Capital Estimates
If someone were to ask: “What is the cost of capital for this company?” the answer would depend upon whether one was interested in the cost of capital based on funds already raised in the capital markets or funds to be raised in the capital markets. In the case of debt capital, once a company issues bonds at a certain price, the yield that it pays on those bonds is constant over the life of the bonds, and the cost of raising funds with those bonds is therefore fixed by the historical price. The exception here would be the case of floating rate bonds, which have become more popular since the early 1980’s.
Such a yield or return that is locked in by a security price can be considered as a historical cost of capital. If a firm were to issue new securities in the open markets, the cost of capital for those issues may or may not be the same as the historical cost. The fact that markets change makes it more likely that the marginal cost of capital will differ from the historical average. The cost of new capital can be considered as a measure of the marginal cost of capital.
The differences between historical and marginal cost of capital are more pronounced for debt issues than equity issues. This is true because issuing stock at a certain price does not lock in a yield. Stockholders are residual claim owners and will demand that a certain level of return be provided. If such return is not provided, the stock price will adjust downward until such a return is earned. If the stock value falls too much, management is in danger of being replaced, either by a shareholder action or a market transaction such as a leveraged buyout.
The Weighted Average Cost of Capital
The weighted average cost of capital (WACC) is the answer to the question: What is the overall cost of capital to the firm? The overall cost of capital to the firm is obviously going to be based on an average of the cost of each instrument it uses to raise money in the financial markets. In the case of the WACC, the individual component cost of capital values making up the overall cost are weighted by the value each represents as a percentage of the total value of the firm’s financial capital.
The weighting scheme is usually based on a set of book value weights, where outstanding amounts for each type of capital security issued are obtained from the balance sheet. In the case of debt, the book value is closer to the market value than it is for equity. The market value of equity, on the other hand, changes frequently. The basis for using book values as weights for equity returns is that book equity represents the amount of capital that stockholders have invested in the company. That total includes all paid-in-capital (the value of stock that investors have purchased directly from the company as opposed to purchasing from other investors) and retained earnings (profits that have been reinvested rather than distributed as a dividend).
For example, suppose we have the following amounts from the balance sheet:
Capital ComponentAmount
Ten year notes payable$25MM
Twenty year notes payable$40MM
Preferred Equity$10MM
Common Equity$80MM
The total capital base is obtained by adding the amounts issued of each type together. In this case total capital (total capitalization if you are talking about long term bonds and equity) is $155MM. Ten year notes represent 16.12% of that total (i.e. $25/$155). Common equity represents 51.61%. The twenty-year notes and preferred stock represent 25.81% and 6.45% respectively. Note that all weights sum up to 100% or 1.00.
To calculate the weighted average cost of capital, you also need to determine the cost of each component of capital and the tax rate for the company. The tax rate is important because interest payments on debt are tax deductible, and this lowers the cost of debt itself by providing a subsidy to interest payments. The calculation is as follows, assuming that the company pays a 40% tax rate:
(1) / (2) / (3) / (4) / (1)*(3)*(4)Capital Component / Component Cost / Value / Weight / Tax Factor / Wtd. Component
Ten year Notes / 7.50% / $25.00 / 16.13% / 0.60 / 0.726%
Twenty Year Notes / 9.85% / $40.00 / 25.81% / 0.60 / 1.525%
Preferred Equity / 11.00% / $10.00 / 6.45% / 1.00 / 0.710%
Common Equity / 14.50% / $80.00 / 51.61% / 1.00 / 7.484%
Totals / $155.00 / 100.00% / 10.445%
As can be seen, the weight is the value of each component divided by the total capitalization of the company. Each component cost is multiplied by the weight and then the tax adjustment factor. The sum of the four weighted components becomes the WACC for the company.
As is evident, the WACC can be changed by either changing the relative weights of each component, or by changing the cost of each component. Generally, firms want to see the WACC minimized, and changes in corporate debt and equity policy can help achieve this goal. When we get to the unit on capital structure, we’ll speak more of this.
At this point you should read through your textbook and continue book problems as you go. Additional questions for thought and discussions will be posted in the discussion board this week. As always, use the board to ask questions about the material.