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Foundations of Finance, Seventh Edition  219

CHAPTER 8

Valuation and Characteristics of Stock CHAPTER ORIENTATION This chapter continues the introduction begun in Chapter 7 of the concepts underlying asset valuation. 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.

CHAPTER OUTLINE I.

Preferred Stock A.

Features of preferred stock 1.

Owners of preferred stock receive dividends instead of interest.

2.

Most preferred stocks are perpetuities (non-maturing).

3.

Multiple classes, each having different characteristics, can be issued.

4.

In the case of bankruptcy, preferred stock has priority over common stock with regard to claims on assets.

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.

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 to periodically set aside an amount of money for the retirement of its preferred stock.

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220  Keown/Martin/Petty  Instructor’s Manual with Solutions B.

Valuation of preferred stock (Vps): 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: Vps = =

II.

Common Stock A.

B.

Features of Common Stock 1.

As owners of the corporation, common shareholders have the right to 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.

Valuing common stock 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: Return on equity x

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 growth in corporate earnings.

4.

The earnings growth of a firm should be reflected in a higher price for the firm's stock.

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Foundations of Finance, Seventh Edition  221 5.

In finding the value of a common stock (V cs), we should discount all future expected dividends (Dl, D2, D3, D) to the present, at the required rate of return for the stockholder (rcs). That is: Vcs =

6.

D1 D2 D + +...+ 1 2 (1 + rcs )  (1 + rcs ) (1 + rcs )

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 Vcs

III.

=

D1 = rcs - g

D 0 (1 + g) rcs - g

Shareholder's Expected Rate of Return 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: expected rate of return = or D r ps = Pps

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.

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222  Keown/Martin/Petty  Instructor’s Manual with Solutions 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, r cs is r cs

=

+

=

D1 Pcs

+ g

Since dividend ÷ price is the "dividend yield," the Expected rate of return = +

ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1.

Preferred stock is commonly 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. Preferred stock is similar to 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 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 as bonds do, the cumulative feature is necessary to protect the rights of preferred stockholders.

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Foundations of Finance, Seventh Edition  223 Other protective features generally serve to allow for voting rights in the event of nonpayment of dividends, or they restrict the payment of common stock dividends 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 their 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 that interest rates decline, and cheaper funding becomes available, 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 both the profitability of the firm and 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.

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. Dividend income for common stockholders differs from preferred stockholders, in that no specified dividend amount is to be received. However, common stockholders are permitted to participate in the growth of the company. Price appreciation is a result of this growth (their second source of return).

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224  Keown/Martin/Petty  Instructor’s Manual with Solutions

SOLUTIONS TO END-OF-CHAPTER PROBLEMS 8-1. A

B

Annual dividend

$4.50

$4.25

Market Price

$35.00

$36.00

$4.50/$35=12.86%

$4.25/$36 =11.81%

Expected return

You would choose stock A, which has an expected rate 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. 8-2.

Growth rate = return on equity x retention rate Thus: growth rate

Retention rate = return on equity = 8-3.

a.

.07 = .58 or 58% .12

Growth rate = return on equity x retention rate = .115 x 0.55 = 0.0633 or 6.335

b.

Expected rate of return =

c.

= + growth rate

$3.25(1+ .0633) + 0.0633 = 01496 or 14.96% $40

Since the 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.

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Foundations of Finance, Seventh Edition  225

8-4.

Value (Vcs) = $32.50

=

$1 + growth rate .12  growth rate

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% 8-5. Value(Vps) =

dividend rate x par value required rate of return

= = = $116.67 8-6.

Expected Rate of Return k ps

8-7.

= = = or .0463, or 4.63%

a.

Expected return = = = .085 = 8.5%

b.

Given your 8 percent required rate of return, the stock is worth $42.50 to you Value = = = $42.50 Since the expected rate of return (8.5%) is greater than your required rate of return (8%) or since the current market price, ($40) is less than $42.50, the stock is undervalued and you should buy.

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226  Keown/Martin/Petty  Instructor’s Manual with Solutions

8-8.

Value (Vcs)

=

+

$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% rate of return. 8-9.

a.

Expected rate ( k cs ) = of return

Dividend in Year 1 + Market Price

k cs = + .10 = .1889 k cs = 18.9%

b.

Vcs = = $28.57 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.

8-10. Value (Vcs)

=

Vcs

=

Vcs

=

$24.50

8-11. Growth rate

=

return on equity x retention rate

=

(18%) (40%) = 7.2%

8-12. Expected Rate of Return k cs ) =

_ = k cs _ = k cs 8-13. Value (Vcs)

+ Growth Rate + 0.095 = 0.193 19.3%d

=

+

Vcs

=

+

Vcs

=

$39.96

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Foundations of Finance, Seventh Edition  227 8-14.

If the expected rate of return is represented by k cs : =

Dividend in year 1 (1 + r cs )

k cs

=

- 1

k cs

=

- 1 = 0.1823

k cs

=

18.23%

Current Price

8-15. a.

k ps

+

Price in year 1 (1 + r cs )

= = = 10.91%

b.

Value (Vps) = = = $36

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.

8-16. a.

b.

Expected Rate of Return =

Investor's Value

+

=

+ 0.08 = 0.1407

=

14.07%

= = =

c.

8-17.

$57.02

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).

D Vps  k ps

=

6 = $50 per share .12

8-18. growth rate = return on equity x earnings retention rate = .16% x .6 = 9.6% growth rate 8-19.

Kristen

Titus

Annual Dividend

$2.00

$3.25

Market Price

$23.00

$31.00

Expected Return

$2/$23 = 8.7%

$3.25/$31 = 10.5%

You should choose Titus stock. It has a greater expected return than your required rate of return—10.48% versus 9%. On the other hand, Kristen stock’s expected rate of return does not meet your required rate of return. 8-20. Expected rate of return

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228  Keown/Martin/Petty  Instructor’s Manual with Solutions Expected return Value

=

Dividend = Selling Price

Dividend Required Rate of Return

=

$1.55 = $22.00

$1.55 9%

=

0.0704 or 7% =

$17.22

This stock is worth $17.22 to you (less than the market price of $221), so you should not buy the stock. 8-21. Expected return Expected return

=

Dividend Selling Price

$5.25 $40.00

=

=

0.1312

or

13.12% 8-22. Expected rate of return Expected return

Last Year Dividend (1 + Growth Rate) Price

=

+

Growth Rate Expected return

=

3(1.07) $30

+

0.07

=

0.177 or 17.7%

8-23. Expected rate of return Expected return

Dividend Selling Price

=

=

$2.33 = $36.72

0.0635 or 6.4%

You should not purchase this stock because the expected rate of return of 6.35% is less than your required rate of return of 8%. 8-24. Expected rate of return Last Year Dividend (1 + Growth Rate) + Price

= Expected return

=

1.45(1.12) + 0.12 = $42.65

0.1581 or 15.81%

SOLUTION TO MINI CASE a.

Growth Rate

Value of each investment based on your required rate of return: Capital Cities ABAC bond: 12 6 ©2011 Pearson Education, Inc. Publishing as Prentice Hall

Foundations of Finance, Seventh Edition  229 87.50 1000 

ANSWER

-1230.56 10

Vb

=



t 1

$87.50 (1 + .06) t

+

$1,000 (1 + .06)12

= $87.50(7.3601) + $1,000(.55839) = $644.01 + $558.39 = $1,230.56 Southwest Bancorp Preferred Stock: Vps



$2.5 t t 1 (1 + .07)

= 

However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to Vps

= =

$2.50 .07

= $35.71 Emerson Electric Common Stock: Step 1: Estimate Growth Rate Company's earnings have increased from $2.40 to $4.48 in five years. What annual compound growth rate would cause an investment to increase in five years? Growth Rate (g)

= (3.063/1.49) (1/5) – 1 = 15.48%

Step 2: Solve for Value Vcs

=

  t 1

$1.32(1 + .1548) t (1 + .15) t

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230  Keown/Martin/Petty  Instructor’s Manual with Solutions If the percent growth rate (g) is assumed constant, the equation may be reduced to Vcs

= = =

$1.320(1 + 0.1548) .15  .0.1548

=

1.5243 0.0048

= $317.56 b.

Your Value Bond

$1,230.56

Selling Price $1,314.00

Preferred Stock

35.71

25.5

Common Stock

317.56

36.75

Choose only the preferred stock because it is the only security selling for a price lower than the value of investment based on your required rate of return. c.

Common Stock: Growth Rate (g) = 13.3% - 3% = 10.3% Vcs

= =

$1.32(1 + 0.1248) .15  0.1248

=

1.4847 0.0252

= $58.92 Your Value

Selling Price

58.92

36.75

Common Stock

You would prefer not to buy the Emerson Electric stock because its selling price is lower than the investment based on your required rate of return. d.

Bond: 10

$1,314 =

 t 1

$87.50 (1 + k b ) t

+

$1,000 (1 + k b )10

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Foundations of Finance, Seventh Edition  231 12 1,314 87.50 1000 

ANSWER

Required Rate of Return

5.17

= 5.17%

Preferred Stock: Vps

=

39

= $2.50 / Required Rate of Return

Required Rate of Return

=

2.50 25.5

= 9.8% Common Stock: Vcs

=

80

=

$1.32(1 + 0.1548) k  0.1548

k

=

1.5243 + 0.1548 36.75

= 19.63%

ALTERNATIVE PROBLEMS WITH SOLUTIONS ALTERNATIVE PROBLEMS 8-1A. (Preferred Stock Valuation) What is the value of a preferred stock where the dividend rate is 16 percent on a $100 par value? The appropriate discount rate for a stock of this risk level is 12 percent. 8-2A. (Preferred Stockholder Expected Return) Shewmaker’s preferred stock is selling for $55.16 and pays $2.35 in dividends. What is your expected rate of return if you purchase the security at the market price? 8-3A. (Preferred Stockholder Expected Return) You own 250 shares of McCormick Resources’ preferred stock, which currently sells for $38.50 per share and pays annual dividends of $3.25 per share. a.

What is your expected return?

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232  Keown/Martin/Petty  Instructor’s Manual with Solutions b.

If you require an 8 percent return, given the current price, should you sell or buy more stock?

8-4A. (Common Stock Valuation) You intend to purchase Bama, Inc., common stock at $52.75 per share, hold it one year, and sell after a dividend of $6.50 is paid. How much will the stock price have to appreciate if your required rate of return is 16 percent? 8-5A. (Common Stockholder Expected Return) Blackburn & Smith’s common stock currently sells for $23 per share. The company’s executives anticipate a constant growth rate of 10.5 percent and an end-of-year dividend of $2.50. a.

What is the expected rate of return if you buy the stock for $23?

b.

If you require a 17 percent return, should you purchase the stock?

8-6A. (Common Stock Valuation) Gilliland Motor, Inc., paid a $3.75 dividend last year. At a constant growth rate of 6 percent, what is the value of the common stock if the investors require a 20 percent rate of return? 8-7A. (Measuring Growth) Given that a firm’s return on equity is 24 percent and management plans to retain 60 percent of earnings for investment purposes, what will be the firm’s growth rate? 8-8A. (Common Stockholder Expected Return) The common stock of Bouncy-Bob Moore Co. is selling for $33.84. The stock recently paid dividends of $3 per share and has a projected constant growth rate of 8.5 percent. If you purchase the stock at the market price, what is your expected rate of return? 8-9A. (Common Stock Valuation) Honeybee common stock is expected to pay $1.85 in dividends next year, and the market price is projected to be $40 by year end. If the investor’s required rate of return is 12 percent, what is the current value of the stock? 8-10A. (Common Stock Expected Rate of Return) The market price for M. Simpson & Co.’s common stock is $44. The price at the end of one year is expected to be $47, and dividends for next year should be $2. What is the expected rate of return? 8-11A. (Preferred Stock Valuation) Gree’s preferred stock is selling for $35 in the market and pays a $4 annual dividend. a.

What is the expected rate of return of the stock?

b.

If an investor’s required rate of return is 10 percent, what is the value of the stock to the investor?

c.

Should the investor acquire the stock?

8-12A. (Common Stock Valuation) The common stock of KPD paid $1 in dividends last year. Dividends are expected to grow at an 8 percent annual rate for an indefinite number of years. a.

If KPD’s current market price is $25, what is the stock’s expected rate of return?

b.

If your required rate of return is 11 percent, what is the value of the stock to you? ©2011 Pearson Education, Inc. Publishing as Prentice Hall

Foundations of Finance, Seventh Edition  233 c.

Should you make the investment?

8-13A. (Comprehensive Problem in Valuing Securities) You are considering three investments. The first is a bond that is selling in the market at $1,200. The bond has a $1,000 par value, pays interest at 14 percent, and is scheduled to mature in 12 years. For bonds of this risk class, you believe that a 12 percent rate of return should be required. The second investment that you are analyzing is a preferred stock ($100 par value) that sells for $80 and pays an annual dividend of $12. Your required rate of return for this stock is 14 percent. The last investment is a common stock ($35 par value) that recently paid a $3 dividend. The firm’s earnings per share have increased from $4 to $8 in 10 years, which also reflects the expected growth in dividends per share for the indefinite future. The stock is selling for $25, and you think a reasonable required rate of return for the stock is 20 percent. a.

Calculate the value of each security based on your required rate of return.

b.

Which investment(s) should you accept? Why?

c.

1.

If your required rates of return changed to 14 percent for the bond, 16 percent for the preferred stock, and 18 percent for the common stock, how would your answers change to parts (a) and (b)?

2.

Assuming again that your required rate of return for the common stock is 20 percent, but the anticipated constant growth rate changes to 12 percent, would your answers to parts (a) and (b) be different?

SOLUTIONS TO ALTERNATIVE PROBLEMS 8-1A. Value(Vps)

= = = $133.33

8-2A. Expected Rate of Return

_ = = = 4.26% k ps 8-3A. a. b.

Expected return = = = .0844 = 8.44% Given your 8 percent required rate of return, the stock is worth $40.62 to you Value = = = $40.625 Since the expected rate of return (8.44%) is greater than your required rate of return (8%) or since the current market price ($38.50) is less than $40.62, the stock is undervalued and you should buy.

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234  Keown/Martin/Petty  Instructor’s Manual with Solutions 8-4A. Value ( Vcs)

= +

$52.75 = + Rearranging and solving for P1: P1 = $52.75 (1.16) - $6.50 P1 = $54.69 The stock would have to increase $1.94 ($54.69 - $52.75) or 3.6 percent ($1.94/$52.75) to earn a 16% rate of return. 8-5A. a.

Expected rate of return = + Expected rate of return

b.

cs

= + .105

= .2137 = 21.37%

Vcs = = $38.46 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.

8-6A. Value (Vcs)

=

Vcs

=

Vcs

= $28.39

8-7A. Growth rate

= return on equity x retention rate = (24%) (60%) = 14.4%

8-8A. Expected Rate of Return = + Growth Rate Expected rate of return

8-9A. Value (Vcs) Vcs

=

+ 0.085 = 0.181 = 18.1%

= + = +

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Foundations of Finance, Seventh Edition  235 Vcs

= $37.37

8-10A. If the expected rate of return is represented by

Current Price =

Price in Year 1 Dividend in Year 1 + (1 + expected return) (1 + expected return)

Expected rate of return

Expected rate of return

Expected rate of return

8-11A. a.

k ps

_ : k cs

= - 1

= - 1 = 0.1136

= 11.36%

= = = 11.43%

b.

Value (Vps ) = = = $40

c.

The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.43 percent). Also, the value of the stock to the investor ($40) exceeds the existing market price ($35). You should buy the stock.

8-12A. a.

Expected Rate of Return = + = + 0.08 = 0.1232 = 12.32%

b.

Investor's Value

= = = $36.00

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236  Keown/Martin/Petty  Instructor’s Manual with Solutions c.

8-13A. a.

Yes, the expected rate of return is greater than your required rate of return (12.32 percent versus 11 percent). Also, your value of the stock ($36.00) is larger than the current market price ($25.00). Value (Vb) based upon your required rate of return: Bond: Vb

12



=

t 1

$140 $1,000 + t (1 + .12)12 (1 + .12)

= $140(6.194) + $1,000(.257) = $867.16 + $257 = $1,124.16 Preferred Stock: Vps =





$12

t  1 (1 + .14)

t

However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to Vps = = = $85.71 Common Stock: Step 1: Estimate Growth Rate Company's earnings have doubled ($4 to $8) in ten years. What annual compound growth rate would cause an investment to double in ten years? Looking in Appendix B (Compound sum of $1) an interest factor of 2.000 for ten years is closest to seven percent (1.967). Thus, at about seven percent, money would double in ten years. (The same conclusion could have been reached by using Appendix D but by using a .500 present value interest factor.) Growth Rate (g) = 7% Step 2: Solve for Value ©2011 Pearson Education, Inc. Publishing as Prentice Hall

Foundations of Finance, Seventh Edition  237

Vcs

=

 $3(1 + .07)t



t t  1 (1 + .20)

If the seven percent growth rate (g) is assumed constant, the equation may be reduced to Vcs

= = = = = $24.69

b. Bond Preferred Stock Common Stock

Your Value $1,124.16 85.71 24.69

Selling Price $1,200.00 80.00 25.00

Buy only the Preferred stock; it is the only investment in which the market price is less than the value to you. c.

(1)

Bond: Vb

=

12



t 1

$140 + (1 + .14) t

= $140(5.660) + $1,000(.2076) = $792.40 + $207.60 = $1,000.00 Still do not buy; it is not worth $1,200.00. Preferred Stock: Vps

= = $75.00

Do not buy. Your value is less than what you would have to pay for the stock.

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238  Keown/Martin/Petty  Instructor’s Manual with Solutions

Common Stock: Vcs

= = $29.18

Buy. Your value is greater than what you would have to pay for the stock. (2)

Assuming a growth rate of 12 percent: Vcs

= = = $42

Buy. Because of the expected increase in future dividends, the stock is now worth more to you ($42) than you would have to pay for it ($25)— assuming that the selling price did not increase also.

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