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This chapter continues the introduction of concepts underlying asset valuation begun in Chapter 7. We are specifically concerned with valuing preferred stock and common stock. We also look at the concept of a stockholder’s expected rate of return on an investment.
A. The Characteristics of Preferred Stock
1. Owners of preferred stock receive dividends instead of interest.
2. Most preferred stocks are perpetuities (nonmaturing).
3. Multiple classes, each having different characteristics, can be issued.
4. Preferred stock has priority over common stock with regard to claims on assets in the case of bankruptcy.
5. Most preferred stock carries a cumulative feature that requires all past unpaid preferred stock dividends to be paid before any common stock dividends are declared.
6. Preferred stock may contain other protective provisions.
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7. Preferred stock contains provisions to convert to a predetermined number of shares of common stock.
8. Retirement features for preferred stock are frequently included.
a. Callable preferred refers to a feature which allows preferred stock to be called or retired, like a bond.
b. A sinking fund provision requires the firm periodically to set aside an amount of money for the retirement of its preferred stock.
The value of a preferred stock equals the present value of all future dividends. If the stock is nonmaturing, where dividends are expected in equal amount each year in perpetuity, the value may be calculated as follows:
Valueps = annual dividend required rate of return =
A. The Characteristics of Common Stock
1. As owners of the corporation, common shareholders have the right to the residual income and assets after bondholders and preferred stockholders have been paid.
2. Common stock shareholders are generally the only security holders with the right to elect the board of directors.
3. Preemptive rights entitle the common shareholder to maintain a proportionate share of ownership in the firm.
4. Common stock shareholders’ liability as owners of the corporation is limited to the amount of their investment.
5. Common stock’s value is equal to the present value of all future cash flows expected to be received by the stockholder.
A. Using the Dividend Valuation Model
1. Company growth occurs either by:
a. The infusion of new capital.
b. The retention of earnings, which we call internal growth. The internal growth rate of a firm equals:
2. Although the bondholder and preferred stockholder are promised a specific amount each year, the dividend for common stock is based on the profitability of the firm and the management’s decision either to pay dividends or retain profits for reinvestment.
3. The common dividend typically increases along with the growth in corporate earnings.
4. The earnings growth of a firm should be reflected in a higher price for the firm’s stock.
5. In finding the value of a common stock (Vcs), we should discount all future expected dividends (D1, D2, D3 , D) to the present at the required rate of return for the stockholder (rcs). That is:
6. If we assume that the amount of dividend is increasing by a constant growth rate each year; that is, the dividend in year t, Dt, equals:
Dt = D0 (l + g)t
where g = the growth rate
D0 = the most recent dividend payment
If the growth rate, g, is the same each year and is less than the required rate of return, rcs, the valuation equation for common stock can be reduced to
A. The shareholder’s expected rate of return is of great interest to financial mangers because it tells about the investor’s expectations.
B. Preferred stockholder’s expected rate of return
If we know the market price of a preferred stock and the amount of the dividends to be received, the expected rate of return from the investment can be determined as follows:
Preferred stock expected rate of return = annual dividend market price of the stock
C. Common stockholder’s expected rate of return
1. The expected rate of return for common stock can be calculated from the valuation equations discussed earlier.
2. Assuming that dividends are increasing at a constant annual growth rate (g), we can show that the expected rate of return for common stock, csr is
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Common
8-1. Preferred stock is many times referred to as a hybrid security. This is because preferred stock has many characteristics of both common stock and bonds. It has characteristics of common stock: no fixed maturity date, the nonpayment of dividends does not force bankruptcy, and the nondeductibility of dividends for tax purposes. But it is like bonds because the dividends are fixed in amount like interest payments. From the point of view of the preferred stock shareholder, this is not the most delightful combination. On one hand, the dividends are limited as with bonds, but the security of forced payment by the threat of bankruptcy is not there. Thus, from the point of view of the investor, the worst features of common stock and bonds are combined.
8-2. To a certain extent, preferred stock dividends can be thought of as a liability. The major difference between preferred dividends in arrears and normal liabilities is that nonpayment of them cannot force the firm into bankruptcy. However, since the goal of the firm is shareholder wealth maximization, which involves getting money to the shareholders (dividends), preferred arrearages do provide an effective block for the goal of the firm.
8-3. A cumulative feature requires all past unpaid preferred stock dividends be paid before any common stock dividends are declared. A stockholder would like preferred stock to have a cumulative dividend feature because without it there would be no reason why preferred stock dividends would not be omitted or passed when common stock dividends were passed. Since preferred stock does not have the dividend enforcement power of interest from bonds, the cumulative feature is necessary to protect the rights of preferred stockholders.
Other protective features serve generally to allow for voting rights in the event of nonpayment of dividends, or they restrict the payment of common stock dividend if sinking-fund payments are not met or if the firm is in financial difficulty. In effect, the protective features included with preferred stock are similar to the restrictive provisions included with long-term debt.
8-4. Convertibility allows a preferred stockholder to convert or exchange preferred stock for shares of common stock at a predetermined exchange rate. This option gives preferred stockholders more freedom in investment decisions by allowing them to convert into common stock at their discretion.
Preferred stock may be callable by the issuer so that in the event interest rates decline and cheaper funding becomes available, then the stock may be called and new securities may be issued at a lower cost. To agree to the call feature, the investor will require a slightly higher rate of return.
8-5. Both values are based on future cash flows to be received by stockholders. Preferred stock typically has a predetermined constant dividend. For common stock, the dividend is based on the profitability of the firm and on management’s decision to pay dividends or to retain the profits for reinvestment purposes. Thus, the growth of future dividends is a prime distinguishing feature of common stock.
8-6. The expected rate of return is the rate of return that may be expected from purchasing a security at the prevailing market price. Thus, the expected rate of return is the rate that equates future cash flows with the actual selling price of the security in the market.
8-7. The expected rate of return is the discount rate that equates the present value of future expected cash flows with the value of the security.
8-8. The two types of return include dividend income and capital gains. The dividend income for common stockholders differs from preferred stockholders in that no specified dividend amount is to be received. However, the common stockholders are permitted to participate in the growth of the company. As a result of this growth, their second source of return, that of price appreciation, results.
c. The investor’s required rate of return (10 percent) is less than the expected rate of return for the investment (10.91 percent). Also, the value of the stock to the investor ($36) exceeds the existing market price ($33). So buy the stock.
c. Since he stock has an expected rate of return of 14.96 percent, which is greater than your 13 percent required rate of return, you should invest.
Solving for the growth rate, g:
$32.50(0.12 –g) = $1 + g,
$3.90 – $32.50g = $1 + g
$2.90 = $33.50g
g = 0.0866 or 8.66%
8-12. Value (Vcs) = Dividend in Year 1 (1 + Required Rate) +
in Year 1 (1 + Required Rate)
$50 =
Rearranging and solving for P1:
P1 = $50 (1.15) – $6
P1 = $51.50
The stock would have to increase $1.50 ($51.50 – $50) or 3 percent ($1.50/$50) to earn a 15 percent rate of return.
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= 14.07%
b. Investor’s Value = last year dividend (1 growth rate) required rate of returngrowth rate
= $1.32(1.08) 0.1050.08 = $57.02
c. Yes, the expected rate of return is greater than your required rate of return (14 percent versus 10.5 percent). Also, your value of the stock ($57.02) is larger than the current market price ($23.50).
8-17. growth rate = return on equity × earnings retention rate
= 0.16% × 0.6 = 9.6% growth rate
8-18. Expected rate of return = dividend in year1 market price + growth rate
10% = $34.14 $0.70 + growth rate
Rearranging and solving for the growth rate, g:
g = 10% –14 $34 $0.70 = 8%
8-19. Expected rate of return = dividend in year1 market price + growth rate where dividend in year 1 = dividend last year × (1 + growth rate)
= $1.10 × (1.04) = $1.14
So the expected rate of return would be: 91 $64 14 $1 + 4.0% = 5.8% 8-20
a. Expected return = dividend market price = $3.25
b. Given your 8 percent required rate of return, the stock is worth $40.62 to you
=
required
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Since the expected rate of return (8.44 percent) is greater than your required rate of return (8 percent) or since the current market price, ($38.50) is less than $40.63, the stock is undervalued and you should buy.
You would choose stock A, which has an expected rare of return greater than your required rate of return 12.86 percent versus 12 percent. On the other hand, stock B’s expected rate of return does not meet your required rate of return. 8-22.
b. Given your 8 percent required rate of return, the stock is worth $42.50 to you
Since the expected rate of return (8.5 percent) is greater than your required rate of return (8 percent) or since the current market price, ($40) is less than $42.50, the stock is undervalued and you should buy.
You should choose Titus stock. It has a greater expected return than your required rate of return 10.48 percent versus 9 percent. On the other hand, Kristen stock’s expected rate of return does not meet your required rate of return.
This stock is worth $17.22 to you (less than the market price of $221), so you should not buy the stock.
You should not purchase this stock because the expected rate of return of 6.35 percent is less than your required rate of return of 8 percent.
The expected rate of return exceeds your required rate of return, which means that the value of the security to you is greater than the current market price. Thus, you should buy the stock.
Yes, purchase the stock. The expected return is greater than your required rate of return. Also, the stock is selling for only $22.50, while it is worth $28.57 to you.
8-30. return of rate Expected = pricemarket rate)growth (1
8-31. If the expected rate of return is represented by cs r :
8-33. Expected rate of return = pricemarket rate)growth (1dividend last year + Growth Rate
a. Value of each investment based on your required rate of return:
However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to
Emerson Electric Common Stock:
Step 1: Estimate growth rate
Company’s earnings have increased from $2.23 to $3.30in five years. What annual compound growth rate would cause an investment to increase in five years?
Using a TIBAII Plus we can solve for the growth rate by determining I/Y:
Thus, earnings have been growing at an 8.15 percent rate.
Step 2: Solve for Value
If the percent growth rate (g) is assumed constant, the equation may be reduced to
end required rate
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You would consider buying the bonds and preferred stock. They are selling for a price lower than the value of investment based on your required rate of return. The common stock, on the other hand, is selling for more than your investment value
c. Emerson Electric common stock:
growth
g) = 8.15% + 1% = 9.15%
You would now choose to buy the Emerson Electric stock because it now is selling at a price that is lower than the investment value based on your required rate of return.
d. The rate of return you would be indifferent with is also the security’s expected rate of return.
e. Bank of America bond expected rate of return:
Expected rate of return = 6.11%
Southwest Bank Corp. preferred stock expected rate of return: Market price, Pps = return expectedrateof dividend
$26.25 = $2.63 expected rate of return
Solving for expected rate of return = $26.25 63 $2 = 10%
Emerson Electric common stock expected rate of return: Market price, pcs = rategrowthreturn- ofraterequired end at year dividend
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