Financial planning is a logical process from the general to the specific. It starts with de- termining financial goals and prioritizing investment objectives, followed by analyzing the individual’s available resources. Then the funds are allocated among various assets to construct a diversified portfolio designed to meet the individual’s financial objectives.
Fundamental securities analysis and valuation also follows a logical process from the general to the specific. The valuation of a stock starts with the economic environ- ment, including estimates of economic growth, employment, inflation, and the geopo- litical environment in which firms operate. The analyst then proceeds to more specific
questions such as regulatory issues and the impact of government policy and interven- tion. The incursion of government, of course, is not limited to regulation, since subsi- dies and tax policy are often designed to stimulate demand for specific products such as more fuel-efficient cars. Public policy often shifts the demand and supply for specific goods and services and may also affect pricing and funds that firms divert to invest- ments in specific products and services.
After considering the macroeconomy and regulatory environment, the analyst moves to the various sectors of the economy. Sectors are broad divisions of the econ- omy such as energy or technology or health. The economic impact on the various sec- tors will differ. Firms classified as producing consumer staples (e.g., H.J. Heinz) may be less affected by the economic environment than firms producing consumer discretion- ary products (e.g., Ford). Sectors are subdivided into industries. For example, “health”
includes pharmaceuticals, health providers such as hospitals, and producers of medical devices. “Energy” encompasses oil and natural gas drillers, refiners, distributors, and re- tailers. Within each industry the analyst needs to be aware of the degree of competition, cost structures, the pricing environment, and anticipated growth. Such background is necessary prior to analyzing an individual firm.
After taking into account the macroeconomy, the sector, and the industry, the se- curities analyst progresses to consider specific firms. The product mix, management, sources of funds, measures of performance such as return on assets and equity, and the capacity to generate cash are all part of the process of valuing a company. Ultimately the purpose of the analysis is to determine if the firm’s securities (i.e., its stocks and bonds) are undervalued and should be purchased for inclusion in an individual’s or investment company’s portfolio. That valuation process constitutes the remainder of this chapter.
THE INVESTOR’S ExPECTEd RETURN
Investors purchase stock with the anticipation of a total return consisting of a dividend yield and a capital gain. The dividend yield is the flow of dividend income paid by the stock. The capital gain is the increase in the value of the stock that is related to the growth in earnings. If the firm is able to achieve growth in earnings, then dividends can be increased, and over time the shares should grow in value.
The expected return on an investment, which was discussed in Chapter 5 and expressed algebraically in Equation 5.1, is reproduced here:
E1r2 5E1D2
P 1E1g2.
The expected return, E(r), is the sum of the dividend yield, which is the expected divi- dend E(D) divided by the price of the stock (P) plus the expected growth rate E(g). If a firm’s $0.93 dividend is expected to grow at 7 percent to $1.00 and the price of the stock is $25, the anticipated annual return on an investment in the stock is
E1r2 5 $1
$25 10.0750.11511%.
For an investment to be attractive, the expected return must be equal to or exceed the investor’s required return. (Specification of the required return will be discussed later in this chapter.) If an individual requires an 11 percent return on investments in common stock of comparable risk, then this stock meets the investor’s requirement. If, however, the investor’s required rate of return is in excess of 11 percent, the anticipated yield on this stock is inferior, and the investor will not purchase the shares. Conversely, if the required rate of return on comparable investments in common stock is 10 percent, this particular stock is an excellent purchase because the anticipated return exceeds the required rate of return.
In a world of no commission fees and in which the tax on dividends is the same as on capital gains, investors would be indifferent to the composition of their return. An investor seeking an 11 percent return should be willing to accept a dividend yield of zero if the capital gain is 11 percent. Conversely, a capital growth rate of zero should be acceptable if the dividend yield is 11 percent. Of course, any combination of growth rate and dividend yield with an 11 percent return should be acceptable.
However, because of commissions and taxes, the investor may be concerned with the composition of the return. To realize the growth in the value of the shares, the inves- tor must sell the security and pay commissions. This cost suggests a preference for divi- dend yield. In addition, capital gains occur in the future and may be less certain than the flow of current dividends. The uncertainty of future capital gains versus the likelihood of current dividends also favors dividends over capital appreciation.
Prior to the changes in the federal tax laws in 2003, dividends were taxed at a higher rate than long-term capital gains. As of 2012, the highest rate on both is 15 per- cent. (The rate on short-term capital gains is the individual’s marginal tax rate. This dif- ference in the taxation of short-term and long-term capital gains is an obvious incentive to hold the stock for at least a year and a day.) The 15 percent tax rate on dividends and long-term capital gains certainly levels the playing field. However, there remains a tax argument favoring long-term capital gains. The tax may be deferred until the gains are realized; the tax on dividends cannot be deferred. (The frequent changes in the federal income tax laws points out the need to keep abreast of tax regulations and to recon- sider their impact on the composition of your portfolio.)
STOCk VALUATION: THE PRESENT VALUE OF dIVIdENdS
Value investing focuses on what an asset is worth—its intrinsic value. Discounted cash flow methods value a stock by bringing future cash inflows (e.g., dividends) back to the present at the appropriate discount factor. For the individual investor, that discount fac- tor is the required return, which is the return the investor demands to justify purchas- ing the stock. This return includes what the investor may earn on a risk-free security (e.g., a Treasury bill) plus a premium for bearing the risk associated with investments in common stock.
The process of valuation and security selection is similar to comparing expected and required returns, except the emphasis is placed on determining what the investor believes the security is worth. Future cash inflows are discounted back to the present at the required rate of return. The resulting valuation is then compared with the stock’s
current price to determine if the stock is under- or overvalued. Thus, valuation com- pares dollar amounts. The dollar value of the stock is compared with its price. Returns compare percentages. The expected percentage return is compared to the required re- turn. In either case, the decision will be the same. If the valuation exceeds the price, the expected return will exceed the required return.
The process of valuation and security selection is readily illustrated by the simple case in which the stock pays a fixed dividend of $1 that is not expected to change. That is, the anticipated cash inflow is
Year 1 2 3 4 . . .
Dividend $1 $1 $1 $1 . . .
The current value of this indefinite flow of payments (i.e., the dividend) depends on the discount rate (i.e., the investor’s required rate of return). If this rate is 12 percent, the stock’s value (V) is
V5 $1
1110.12211 1
1110.1222 1 1
1110.1223 1 1
1110.12241# # #,
V5$8.33.
This process is expressed in the following equation in which the new variables are the dividend (D) and the required rate of return (k):
V5 D
111k211 D
111k22 1# # # 1 D
111k2`, 9.1
which simplifies to
V5 D
k. 9.2
If a stock pays a dividend of $1 and the investor’s required rate of return is 12 percent, then the valuation is
$1
0.125$8.33.
Any price greater than $8.33 will result in a yield that is less than 12 percent. Therefore, for this investor to achieve the required rate of return of 12 percent, the price of the stock must not exceed $8.33.
There is, however, no reason to anticipate that common stock dividends will be fixed indefinitely into the future. Common stocks offer the potential for growth, both in value and in dividends. For example, if the investor expects the current $1 dividend to grow annually at 6 percent, the anticipated flow of dividend payments is
Year 1 2 3 . . .
Dividend $1.06 $1.124 $1.191 . . .
The current value of this indefinite flow of growing payments (i.e., the growing divi- dend) also depends on the discount rate (i.e., the investor’s required rate of return). If this rate is 12 percent, the stock’s value is
V5 1.06
1110.12211 1.124
1110.1222 1 1.191
1110.1223 1# # #,
V5$17.67.
Equation 9.1 may be modified for the growth in dividends. This is expressed in Equations 9.3 and 9.4. The only new variable is the rate of growth in the dividend (g). If it is assumed that this growth rate is fixed and will continue indefinitely into the future, the dividend-growth valuation model is
V5 D111g21
111k21 1D111g22
111k22 1 D111g23
111k23 1# # # 1 D111g2`
111k2` , 9.3
which simplifies to
V5D0111g2
k2g . 9.4
The stock’s intrinsic value depends on (1) the current dividend, (2) the growth in earnings and dividends, and (3) the required rate of return. Notice the current dividend is D0, with the subscript 0 representing the present. The application of this dividend- growth model may be illustrated by a simple example. If the required rate of return is 12 percent and the stock is currently paying a $1 per share dividend growing at 6 percent annually, the stock’s value is
V5 $11110.062
0.1220.06 5$17.67.
Any price greater than $17.67 will result in a total return of less than 12 percent.
Conversely, a price of less than $17.67 will produce an expected return in excess of 12 percent. For example, if the price is $20, the expected return is
E1r2 5$11110.062
$20 10.06
511.3%.
(Notice the expected dividend is $1.06, which is the $1 current dividend plus the antici- pated $0.06 [6 percent] increment in the dividend.) Because this return is less than the 12 percent required by the investor, this investor would not buy the stock and would sell it if he or she owned it.
If the price is $15, the expected return is E1r25 $11110.062
$15 10.06
513.1%.
dividend-growth valuation model A valuation model that uses dividends and their growth properly discounted back to the present.
This return is greater than the 12 percent required by the investor. Since the security of- fers a superior return, it is undervalued. This investor then would try to buy the security.
Only at a price of $17.67 does the stock offer a return of 12 percent. At that price it equals the return available on alternative investments of the same risk. The investment will yield 12 percent because the dividend yield during the year is 6 percent and the earnings and dividends are growing annually at the rate of 6 percent. These relation- ships are illustrated in Figure 9.1, which shows the growth in dividends and prices of the stock that will produce a constant yield of 12 percent. After 12 years, the dividend will have grown to $2.02 and the price of the stock will be $35.55. The total return on this investment remains 12 percent. During that year, the dividend will grow to $2.14, giving a 6 percent dividend yield, and the price will continue to appreciate annually at the 6 percent growth rate in earnings and dividends.
If the growth rate had been different (and the other variables remained constant), the valuation would have differed. The following illustration presents the value of the stock for various growth rates:
Growth Rate Value of the Stock
0% $ 8.83
3% $ 11.78
9% $ 35.33
11% $ 106.00
12% undefined (denominator = 0)
As the growth rate increases, so does the valuation, until the value becomes undefined (an exceedingly large number) when the growth rate equals the required return. This positive relationship indicates that when a stock offers more potential for capital gains,
fIGuRE 9.1
Earnings, dividends, and Price of Stock over Time Yielding 12 Percent Annually
$3530 2520 15
$2.00 1.751.50 1.251.00
0 2 4 6 8 10 12 Time (years)
35.55
2.02 Per-share Dividend
Per-share Price of the Stock
Source: © Cengage Learning
its valuation increases (if the dividend and the required return are not affected by the growth).
The dividend-growth valuation model assumes that the required return exceeds the rate of growth (i.e., k > g). While this may appear to be a restrictive assumption, it is logical. The purpose of the dividend-growth model is to determine what the stock is worth and then to compare this value to the actual price in order to determine whether the stock should be purchased. If a stock offers 14 percent when the investor requires 12 percent, the valuation is immaterial. It does not matter what the stock costs. Whether the price is $1 or $100,000 is irrelevant because you anticipate earning 14 percent on the amount invested when only 12 percent is required. Valuation can be material only if the growth rate (i.e., the potential capital gain) is less than the required return.
Although the previous model assumes that the firm’s earnings will grow indef- initely and that the dividend policy will be maintained, such need not be the case.
The dividend-growth model may be modified to encompass a period of increasing or declining growth or one of stable dividends. Many possible variations in growth pat- terns can be built into the model. Although these variations change the equation and make it appear far more complex, the fundamentals of valuation remain unaltered.
Valuation is still the process of discounting future cash flows back to the present at the appropriate discount rate.
To illustrate such a variation, consider the following pattern of expected earnings and dividends.
Percentage Change in Year Earnings Yearly Dividends Dividends from Previous Year
1 $1.00 $0.40 . . .
2 1.60 0.64 60.0%
3 1.94 0.77 20.3
4 2.20 0.87 13.0
5 2.29 0.905 4.0
6 2.38 0.941 4.0
7 2.48 0.979 4.0
After the initial period of rapid growth, the firm matures and is expected to grow annu- ally at the rate of 4 percent. Each year the firm pays dividends, which contribute to its current value. However, the simple model summarized in Equation 9.4 cannot be used, because the earnings and dividends are not growing at a constant rate. Equation 9.3 can be used, and when these values, along with a required rate of return of 12 percent, are inserted into the equation, the stock’s value is
V5 $0.40
1110.1221 1 $0.64
1110.1222 1 $0.77
1110.12231 $0.87 1110.1224 1 $0.905
1110.12251 $0.941
1110.1226 1 $0.979
1110.1227 1# # #
5$9.16.
This answer is derived by dividing the flow of dividends into two periods: a period of super growth (years 1 through 4) and a period of normal growth (from year 5 on).
The present value of the dividends in the first four years is V1245 $0.40
1110.12211 $0.64
1110.1222 1 $0.77
1110.1223 1 $0.87 1110.1224 5$0.361$0.511$0.551$0.55
5$1.97.
The dividend-growth model is applied to the dividends from year 5 on, so the value of the dividends during normal growth is
V52 `5 $0.871110.042
0.1220.04 5$11.31.
This $11.31 is the value at the end of year 4, so it must be discounted back to the pres- ent to determine the current value of this stream of dividend payments. That is,
$11.31
1110.12245$11.3110.6362 5$7.19.
The value of the stock, then, is the sum of the two parts.1 V5V1241V52 `
5$1.9717.195$9.16.
As this example illustrates, modifications can be made in this valuation model to account for the different periods of growth and dividends. Adjustments can also be made for differences in risk. You should realize that the model does not by itself adjust for different degrees of risk. If a securities analyst applies the model to several firms to determine which stocks are underpriced, there is the implication that investing in all the
1This valuation procedure may be summarized by the following general equation:
V 5 Vs 1 Vn.
Vs is the present value of the dividends during the period of super growth; that is, Vs5 SD0111gs2t
111k2t
Vn is the present value of the dividends during the period of normal growth; that is, Vn5 cDn111g2
k2g d a 1
111k2nb The value of the stock is the sum of the individual present values; that is,
Vs5 SD0111gs2t
111k2t 1cDn111g2
k2g d a 1
111k2nb.
firms involves equal risk. If the analyst uses the same required rate of return for each firm, then no risk adjustment has been made. The element of risk is assumed to be the same for each company.
RISk-AdjUSTEd REqUIREd RETURN ANd STOCk VALUATION
One means to adjust for risk is to incorporate into the valuation model the security market line presented earlier in Chapter 5. In that chapter, beta coefficients, which are an index of the market risk associated with the security, were used as part of the Capital Asset Pricing Model to explain returns. In this context, beta coefficients and the Capital Asset Pricing Model are used to specify the risk-adjusted required return on an investment.
The required return has two components: the risk-free rate (rf) that the investor can earn on a risk-free security such as a U.S. Treasury bill, and a risk premium. The risk premium is also composed of two components: (1) the additional return that invest- ing in securities offers above the risk-free rate, and (2) the volatility of the particular security relative to the market as a whole (i.e., the beta). The additional return is the extent to which the return on the market (rm) exceeds the risk-free rate (rm − rf). Thus, the required return (k) is
k = rf 1 (rm − rf) b. 9.5
Equation 9.5 is the same equation as the security market line in Chapter 5, which was used to explain a stock’s return. In that context, the Capital Asset Pricing Model states that the realized return depends on the risk-free rate, the risk premium associated with investing in stock, and the market risk associated with the particular stock. In this context, the same variables are used to determine the return the investor requires to make the investment. This return encompasses the expected yield on a risk-free asset, the expected risk premium associated with investing in stock, and the expected market risk associated with the specific stock. The differences between the two uses concerns time and historical versus anticipated values. In one case the expected values are being used to determine if a specific stock should be purchased now. In the other application, historical values are employed to explain the realized return on an investment that was previously made.
The following examples illustrate how to use the equation for the required return.
The risk-free rate is 3.5 percent and the investor expects that the market will rise by 10 percent. (Historical returns suggest that over a period of years stocks have yielded a return of 6 to 7 percent in excess of the return on U.S. Treasury bills. Thus, if the bills are currently yielding 3.5 percent, an expected return on the market of 10 percent is reasonable. Treasury bills are covered in more detail in Chapter 15 on government securities.) Stock A is relatively risky and has a beta coefficient of 1.8 while stock B is less volatile and has a beta of 0.8. What return is necessary to justify purchasing either stock? Certainly it would not be correct to require a return of 10 percent for either, since that is the expected return on the market. Since stock A is more volatile than the market, the required return should exceed 10 percent. However, the required return for B should be less than 10 percent; it is less volatile (less risky) than the market as a whole.