Chapter 10 Stock Valuation

10.1 Common and Preferred Stocks

Equity in a public corporation is divided into shares of stock. Typically, shares of stock have some key features. The first is the right to receive dividendsPayouts (usually in cash) to the owners of a company proportional to their ownership of the company., which are payouts (usually in cash) to the owners of a company proportional to their ownership of the company. Dividends are typically paid quarterly, though exceptions are not uncommon. The company’s board of directors decides when dividends are to be issued and how much they are to be. The board of directors is elected by the shareholders, as determined by the company’s corporate charter.

Shares of stock can be divided into different classes, and these can have different features. For example, one class of shares might have more voting power than a second class. Each class of stock will trade separately (or some might not trade at all) and, potentially, have a different price. The most common division of equity is between preferred shares of stock and common stock.

Preferred stockA type of equity that acts as hybrid of bonds and common stock, with no maturity date and fixed dividend payments. is equity, but behaves as almost a hybrid between bonds and common stock. In fact, at many investment banks, the fixed income traders handle bonds and preferred stock, and the equity traders only work with common stock. Preferred stock usually doesn’t have a maturity date, and, like a bond, has a dividend that is at a fixed. Preferred stock has a nominal par value (typically $100 per share), and the annualized dividend is quoted as a percentage of this par value. Thus, one share of 5% preferred stock will pay $5 total in dividends over a year. Like a bond, if these dividends are insufficient to provide the required return to investors, the stock will trade at a price below the nominal par value. Unlike a bond, if the dividend isn’t paid, stockholders can’t send the company into bankruptcy. If, however, the full dividend isn’t paid to the preferred shareholders, than no dividend is allowed to be paid to the owners of the common stock until all missed payments are paid in full. If the company is driven into bankruptcy and liquidation by the bondholders, the preferred shareholders have a superior claim to the assets compared to common shareholders (though both are subordinate to the bondholders). Typically, preferred shareholders get no votes for the board of directors.

Many corporations don’t issue preferred stock, so the bulk of equity issues are called common stockThe bulk of equity issues, representing a residual claim on firm assets.. Common stock also has a nominal par value, but it is mostly an accounting/legal relic and has no bearing on the dividends or price of the stock. Since dividends on common stock are determined by the board, their cash flows are the most uncertain of the financial instruments discussed so far. Shareholders have a residual claimThe value of assets leftover after all other claims have been paid. on the firm’s assets, which is the value leftover after all other claims have been paid. Thus, any earnings remaining after all other obligations are met, are either paid out in dividends or retained by the firm, ostensibly to be used as capital for the firm’s growth. These retained earnings increase the residual claim, potentially increasing the value of stock shares.

When a firm is doing poorly, and liabilities are larger than the value of the assets, the residual claim is zero and share prices understandably drop. If the company isn’t driven into bankruptcy and can increase the assets to an amount more than liabilities, the residual claim grows and share prices rise. Since liabilities are relatively fixed but asset prices are potentially unbounded, the equity share similarly has unbounded growth potential.

From the company’s perspective, it is important to note that equity only directly raises cash when the shares are issued. After the initial issue, trading occurs in the secondary markets, so any increase in value of the shares will be captured by the owners of the stock. It the company has positive earnings but chooses not to pay out all of those earnings as dividends, then the company is able to retain those earnings for use as capital. This is an indirect way of raising equity capital, though it does not come without a cost: the retained earnings should lead to an expectation of increased earnings in the future, allowing for an eventual increase in dividends. If this is the case, the share price should rise in anticipation of the expected higher future dividends.

Increasing the value of those outstanding shares is one of the primary goals of management, for a few key reasons. First, shareholders have voting power, and if they aren’t receiving the returns they desire, they might replace the board with the intention of replacing senior management. Second, any additional offerings of equity will benefit from the increased share price, so the company will have access to a larger source of capital, if necessary. As an additional incentive, senior management will often receive a portion of their compensation tied to the value of equity, through stock grants, restricted shares, or stock options.

10.2 Dividend Discount Model

The financial value of anything is the present value of all future cash flows. If we knew with certainty what the future dividends of a stock will be, we should be able to determine the value of a share of stock. Hence the dividend discount model (DDM). It is useful for us to consider this method of valuing securities, since, ultimately, this is the driver of value in stock ownership. In practice, however, the uncertainty of future dividend payments, especially with common stock, limits the usefulness of using this method. For preferred stock, where the dividend is fixed when it is paid, this method has a bit more accuracy.

Constant Dividend Stream

If our dividend stream is constant, we can use the perpetuity formula from chapter 7 to arrive at the financial value:

Figure 10.1 Constant Dividend Timeline

Equation 10.1 Perpetuity Equation

$$PV=\frac{PMT}{r}$$

Since the dividend payments are constant, the value of a share of preferred stock should be inversely proportional to our required rate of return.

Equation 10.2 Preferred Stock Price

$$P_{pref}=\frac{D}{r}$$

D and r should be in matching time units, so if dividends are quarterly, a quarterly rate of return needs to be used. Note that if the required rate of return doesn’t change, then this implies that the stock price should likewise never change. The corollary to this is: if the dividends are a known constant, then any changes in the stock price must be due to changes in the required rate of return!

Suppose we have a 5% preferred stock and investors require a 6% rate of return. Since par is assumed to be $100, our stock pays $5 in dividends per year. Our expected price would be (.05 × $100) / .06 = $83.33.

Dividend Stream with Constant Growth

If our dividend stream isn’t constant, as is more likely with common stocks, but is growing steadily with a constant growth rate, then we can use another formula from chapter 7:

Figure 10.2 Constant Dividend Growth Timeline

Equation 10.3 Perpetuity with Constant Growth

$$P{V}_n=\frac{PM{T}_{n+1}}{(r-g)}=\frac{PM{T}_n(1+g)}{(r-g)}\{for g<r)$$

Equation 10.4 Stock Price with Constant Dividend Growth

$$P_n=\frac{D_{n+1}}{(r-g)}=\frac{D_n(1+g)}{(r-g)}\{for g<r)$$

Again, D, r, and g should all be in matching time units. Typically we are interested in the price now (that is, at time 0), but this equation could be used to find our expected stock price in a future year by calculating the expected dividend for that year. Also note that D₀ is the dividend that was just paid, and thus is no longer factored into the stock price.

If a company’s most recent dividend (D₀) was $0.60, dividend growth is expected to be 4% per year, and investors require 10%, we can find the expected current stock price (P₀). $0.60 × (1 + .04) / (.10 − .04) = $10.40.

If we use the current price (P₀) and rearrange our equation to solve for returns, we find an interesting result:

Equation 10.5 Components of Stock Returns

$$\begin{array}{l}P0=\frac{D_1}{(r-g)}\{for g<r\}\\ \left(r-g\right)=\frac{D_1}{P_0}\\ r=\frac{D_1}{P_0}+g\\ r=dividend yield+capital gains yield\end{array}$$

With this result, we can clearly see the tradeoff between dividends now and growth (which should lead to future dividends). If expected return is steady over time, then a constant capital gains yield (g) implies a constant dividend yield. A constant dividend yield means that the stock price must grow proportionally to the dividends; that is, both should grow by g.

Dividend Stream with Varied Dividends

Without constant growth, determining the present value of the stock requires finding the present value of each of the future cash flows. While the most flexible and realistic, this also is the most difficult to execute properly. The best way to think about this method is to imagine holding the stock for a specific number of years, with the intention of selling the stock at the end of the period.

Figure 10.3 Varied Dividends Timeline

If we know the dividends and have an expectation for the future stock’s price, we can discount everything to find the price today. The difficulty, of course, is in getting an accurate expectation for the future stock price. The traditional solution is to assume that, at some point in the future, dividend growth will be steady, and to use the constant dividend growth formula to calculate an expected future price.

Equation 10.6 Stock Price with Constant Dividend Growth

$$\begin{array}{l}P0=PV of Future Dividends+PV of Future Price of Stock\\ P0=\frac{D_1}{{(1+r)}^1}+\frac{D_2}{{(1+r)}^2}+\dots +\frac{D_n}{{(1+r)}^n}+\frac{P_n}{{(1+r)}^n}\end{array}$$

A common mistake is to neglect the discounting on the future price of the stock. Once the cash flows are found, the discounting can also be accomplished using NPV functions on a calculator or spreadsheet, as discussed in chapter 7.

Suppose our stock will pay out $0.50 flat per year for 4 years, and then dividends are expected to grow at 5% afterwards. If investors expect a 9% return, we can find the expected price of the stock:

Figure 10.4 Varied Dividends Example Timeline

Our terminal value (P₄) should be $0.50 × (1 + .05) / (.09 − .05) = $13.13. Once we add this to the above cash flows and discount appropriately, we arrive at a stock value of $10.92.

We can use this to method value a corporation that is not a going concern (that is, going out of business) or expected to be acquired. In this case, we should use the liquidation value of the shares or the acquisition price as our P_n.

10.3 Market Multiples Approach

If we try to compare two companies that are in the same line of buisness and approximately the same size, we would expect them to have certain features in common and, perhaps, behave in similar ways. This is the basis for a popular approach to stock valuation based called the market multiples approach.

“Market multiples” is a generic term for a class of many different indicators that can be used to value a stock. Probably the most familiar is using the price to earnings (P/E) ratio (first discussed in chapter 4), and it is used in the following manner: if we know that the average P/E ratio for companies in our sector is 25, and we know the expected earnings (that is, net income) per share of our company is $2 per year, then an appropriate valuation for our stock should be $2 × 25 = $50.

Of course, we can use a competitor’s P/E ratio, if we think it more appropriate than an industry average. Or we can use our company’s historic P/E ratio. Or a trending average over years. This approach is both versatile and simple to use, which might explain its popularity with the financial press.

But what do we do if earnings are expected to be negative? Does this imply that our stock price is also negative? Of course not! Many companies have emerged from negative earnings (perhaps due to a slumping economy) only to skyrocket in value. The simplicity of ratio analysis is its major weakness, as it is impossible to capture everything about a company in one ratio. Other ratios and metrics can be used, if we believe them to be a good indicator of the company’s value. Common ratios (many are mentioned in chapter 5) are price to book, price to EBIT, price to EBITDA, price to sales, etc. but virtually anything can be used if it is justifiable (price to headcount, price to watermelons…). It is important, however, that we don’t attempt to use ratios solely because they are convenient or only because they support the result we desire; we should try to use reason to explain why a given metric is useful, and examine the data to determine if a meaningful relationship exists to aid is in our valuation efforts.

10.4 Free Cash Flow Approach

The free cash flow (FCF) approach for valuing a company is very much related to the dividend discount model explained in section 2. The key difference is that we look at all of the cash flows available for distribution to the investors and use them to arrive at a value for the entire company. Since we are using the cash flows for all investors, we need to discount them not using just our expected return on equity, but on the weighted average cost of capital (WACC)An average of the returns required by equity holders and debt holders weighted by the company’s relative usage of each.. As the name implies, this is an average of the returns required by equity holders and debt holders weighted by the company’s relative usage of each. Arriving at the WACC will be the topic of a later chapter.

Finding the terminal value for a company has some of the same headaches as finding the future expected stock price. A common method is to assume a long-term growth rate for FCF, and use a variation of the perpetuity with growth formula:

This method can be extremely sensitive to the assumption used for the long-term growth rate. Once the value of the entire company is determined, we need to subtract the market values of our debt and preferred stock to arrive at the value of the residual due to common shareholders:

Once the value of the common stock is obtained, dividing by the number of shares outstanding should lead to an appropriate price per share.

Of course, a company might have a negative FCF currently but still be a good investment, if FCF is expected to turn positive in the future. This can happen particularly with corporations that are experiencing rapid growth, necessitating a large investment in capital to support future revenues. Since FCF for such companies tends to turn positive well before dividends are paid, this approach typically provides a superior estimate for stock value over the DDM.

10.5 The Bigger Picture

Like bonds, selling stock allows the issuer to raise capital for new or ongoing projects. Unlike bonds, selling shares of common stock is effectively selling a “piece” of the company. Equity financing tends to command a higher risk premium, so the expected returns by investors is higher. If a company is considered risky, particularly in its early stages, equity financing might be the only reasonable way to raise the necessary funds, even if it entails possibly losing voting control over the board.

Through the election of board members, shareholders can exercise their power to approve or disapprove of the company’s actions. This exercise of corporate governance, combined with the effect of the cost of financing, causes managers to have multiple reasons to consider the desires of shareholders when taking action.

Investors must understand what drives stock prices if they are to properly assess the risk and return of adding stocks to their portfolios.

10.6 End-of-Chapter Problems