1. Incorrect If the expected rate of return on a stock exceeds the required rate,

Your answer: The stock is experiencing nonconstant growth.

The correct answer: The stock is a good buy.

Incorrect. An investor would be willing to pay the current market price for a security if

the expected rate of return implied by a given market price equals the required rate of return.

Therefore, if the expected rate exceeds the required rate, the stock is a good buy.

--------------------------------------------------------------------------------

2. Correct The preemptive right is important to shareholders because it

Your answer: Entitles the common shareholders to maintain a proportionate share of

ownership in the firm.

Correct. A preemptive right entitles shareholders to maintain a proportionate share of

ownership in the firm and does not dilute their ownership base.

--------------------------------------------------------------------------------

3. Incorrect The required rate of return on the common stock of New Net Corporation is

14 percent. The stock's dividend is $1.50 and is expected to grow at a constant rate of 9 percent

during the year. The projected price of the stock at the end of the year is $45. What is the value

of the stock today?

Your answer: $45.00.

The correct answer: $40.90.

Incorrect. Vcs = [$1.50(1.09)]/1.14 + 45/1.14 = 1.43 + 39.47 = $40.90.

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4. Incorrect A share of preferred stock pays an annual dividend of $6 per share. If

investors require a 12 percent rate of return, what is the value of this preferred stock?

Your answer: $46.75

The correct answer: $50.00

Incorrect. Vps = D/kps = $6/0.12 = $50.

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5. Incorrect The Smith Company is undertaking a large project and needs additional

funds. The company plans to issue preferred stock with an annual dividend of $6 per share and a

par value of $30. If the required rate of return is 15 percent, what should be the stock's market

value?

Your answer: $70

The correct answer: $40

Incorrect. Vps = D/kps = $6/0.15 = $40.

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6. Incorrect The Royal Honor Corporation is growing at a constant rate of 6 percent per

year. It has both common stock and preferred stock outstanding. The cost of preferred stock

(kps) is 8 percent. The par value of the preferred stock is $120, and the stock has a stated

dividend of 10 percent of par. What is the market value of the preferred stock?

Your answer: $120

The correct answer: $150

Incorrect. The dividend is calculated as: 10% × $120 = $12. We know that: Vps = D/kps

so 12/.08 = $150.

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7. Correct A share of preferred stock pays a quarterly dividend of $2.50. If the price of

this preferred stock is currently $50, what is the required rate of return?

Your answer: 20%

Correct. Annual dividend = $2.50(4) = $10. kps = D/Vps = $10/$50 = 0.20 = 20%.

--------------------------------------------------------------------------------

8. Correct You want to buy a share of stock today and to hold it for 2 years. You believe

that you will not receive a dividend at the end of Year 1, but you will receive a dividend of $6.50

at the end of Year 2. You plan on selling the stock for $150 at the end of Year 2. If your expected

rate of return is 16 percent, how much should you be willing to pay for this stock today?

Your answer: $116.31

Correct. Financial calculator solution: N = 2; I = 16; FV = 150.00 + 6.50 = 156.50. CPT

PV = -$116.31. Vcs = PV dividend in 2 years + present value of market price in 2 years =

6.50/(1.16)2 + 50/(1.16)2 = $116.31.

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9. Correct You are trying to determine the appropriate price to pay for a share of

common stock. If you purchase this stock, you plan to hold it for 1 year. At the end of the year

you expect to receive a dividend of $5.50 and then sell the stock for $154. The required rate of

return for this stock is 16 percent. What should be the current price of this stock?

Your answer: $137.50

Correct. Vcs = $5.50/1.16 + $154/1.16 = 4.74 + 132.76 = $137.50.

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10. Incorrect The last dividend on a corporation's common stock was $4.00, and the

expected growth rate is 10 percent. If you require a rate of return of 20 percent, what is the

highest price you should be willing to pay for this stock?

Your answer: $33.75

The correct answer: $44.00

Incorrect. Vcs = D1/kcs- g = $4.00(1.1)/(0.20 - 0.10)

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11. Incorrect A share of common stock has just paid a dividend of $2.00. If the expected

constant, long run growth rate for this stock is 15 percent, and if investors require a 19 percent

rate of return, what is the price of the stock?

Your answer: $71.86

The correct answer: $57.50

Incorrect. Vcs = D1/kcs - g. Vcs = $2.00(1.15)/0.19 - 0.15 = $57.50.

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12. Incorrect A share of common stock has a current price of $42.50 and is expected to

grow at a constant rate of 10 percent. If you require a 12 percent rate of return, what is the

current dividend being paid on this stock?

Your answer: $1.75

The correct answer: $0.77

Incorrect. Vcs = D1/kcs - g. 42.50 = D1/.12 - .10, so D1 = 42.50(.12 - .10) = $0.85. D1 =

Do(1+g) so Do = D1/(1+g) = .85/1.1 = $0.77.

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13. Incorrect Coffee Caboodle, Inc.'s most recent dividend was $2.40 per share and this

dividend is expected to grow at a rate of 6 percent per year. The required rate of return on this

stock is 10.2%. What is the price of the stock today?

Your answer: $72.14

The correct answer: $60.57

Incorrect. D1 = $2.40 × 1.06 = $2.544. The price of the stock today is $2.544/(0.102 -

0.06) = $60.57.

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14. Incorrect The most current dividend paid by the Colorado Company was $1.00. The

company's growth rate is expected to be a constant 5 percent and the required rate of return on

this stock is 12 percent. What is the current price of Colorado Company's common stock?

Your answer: $33.33

The correct answer: $15.00

Incorrect. Vcs = D1/kcs - g. Vcs = 1.00 (1.05)/.12 - .05 = $15.00

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15. Incorrect Grant Corporation's stock is selling for $40 in the market. The company's

required rate of return on the stock is 13.8%. The most recent dividend paid was $2 and

dividends are expected to grow at a constant rate. What is the growth rate for this stock?

Your answer: 13.80%

The correct answer: 8.38%

Incorrect. Using the constant growth model, Vcs = D1/kcs - g, we can solve for the

growth rate as $40 = [$2(1 + g)]/(13.8% - g) or g = 8.38%.

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16. Incorrect Preferred stock valuation usually treats the preferred stock as a:

Your answer: long-term bond

The correct answer: perpetuity

Incorrect. Preferred stock generally receives a constant dividend from the investment in

each period. A level cash-flow stream continuing indefinitely is a perpetuity.

--------------------------------------------------------------------------------

17. Incorrect The Land Dairy Co. has net income of $450,000 this year. The book value

of the company's common stock is $3 million dollars. The company's dividend payout ratio is

60% and is expected to remain this way. What is Land Dairy's growth rate?

Your answer: 3%

The correct answer: 6%

Incorrect. G = ROE × R, where ROE = Net income/common book value. ROE =

$450,000/$3,000,000 = 15%. R = profit-retention rate. If the dividend payout rate is 60%, the

profit retention rate must be 40%. Therefore, g = 15% × 40% = 6%.

--------------------------------------------------------------------------------

18. Correct Cumulative preferred stock:

Your answer: requires dividends in arrears to be carried over into the next period

Correct. This is the cumulative feature that requires all past unpaid preferred stock

dividends be paid before any common stock dividends are declared.

CHAPTER 8

Stock Valuation

Homework Solutions

ANSWERS TO

END-OF-CHAPTER QUESTIONS

8-1. Preferred stock is often 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, such as no fixed maturity date, 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

stockholder, this is not the most advantageous combination. On one hand, the dividends are

limited as with bond interest, 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 common

shareholder wealth maximization, which involves getting money to the common shareholders

(dividends), preferred arrearages provide a barrier to achieving this goal.

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 frequent protective features serve to allow for voting rights in the event of

nonpayment of dividends or to 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. Fixed rate preferred stock has dividends that do not vary from the fixed amount or

from period to period.

Adjustable rate preferred stock is preferred stock that has quarterly dividends that

fluctuate with interest rates under a formula that ties the dividend payment at either a premium or

discount to the highest of the three-month Treasury bill rate, the 10-year Treasury bond constant

maturity rate, or the 20-year Treasury bond constant maturity rate. The rates have maximum and

minimum levels called the dividend rate band.

The purpose of allowing the dividend rate to fluctuate is to minimize the

fluctuation in the value of the preferred stock. It is also very appealing in times of high and

fluctuating interest rates.

8-5. With PIK (payment-in-kind) preferred stock, investors receive no dividends

initially; they merely get more preferred stock, which in turn pays dividends in even more

preferred stock. Usually after 5 or 6 years, if all goes well for the issuing company, cash

dividends should replace the preferred stock dividends, generally ranging from 12 percent to 18

percent, to entice investors to purchase PIK preferred.

8-6. 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. It gives the preferred stockholder a higher cash return than the common

stock but allows for sharing in some of the future appreciation of the common stock if they

convert the stock.

Preferred stock may be callable by the issuer so that in the event 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 requires a slightly higher rate

of return. Call of a convertible preferred stock enables a company to turn the preferred stock into

common equity; i.e., calling it without having to spend the cash.

8-7. 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.

8-8. 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 the present value of future cash flows with the actual selling price of the security in

the market.

8-9. The required rate of return is the discount rate that equates the present value of

future cash flows with the intrinsic value of the security. As with the internal rate of return for a

capital budgeting problem, we have to find the rate of return that sets the future cash flows equal

to the cost of the security. This rate may have to be developed by trial and error.

8-10. The two types of return are 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, price appreciation, is realized.

 

SOLUTIONS TO

END-OF-CHAPTER PROBLEMS

Solutions to Problem Set A

8-1A. Value (Vps) = $50.00

8-2A. Growth rate = 9.6%

8-3A. Value (Vps) = $116.67

8-4A. Expected Rate of Return

k- ps = .0463, or 4.63%

8-5A. (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 the value ($42.50), the stock is undervalued

and you should buy.

8-6A. 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.

8-7A. (a) k- cs = .1889, or 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.

8-8A. Vcs = $24.50

8-9A. Growth rate = 7.2%

8-10A. Expected Rate of Return ( ) = 0.193, or 19.3%

8-11A. Value (Vcs) = $39.95

8-12A. If the expected rate of return is represented by :

= 0.1823, or 18.23%

8-13A.

= 0.1091, or 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.

8-14A.(a) Expected Rate of Return = 0.1407, or 14.07%

(b) Investor's Value = $57.02

(c) Yes, the expected rate of return (14.07%) is greater than your required rate of

return (10.5 percent). Also, your value of the stock ($57.02) is greater than the current market

price ($23.50).

339

CHAPTER 8

STOCK VALUATION

Answers to Concepts Review and Critical Thinking Questions

1. The value of any investment depends on its cash flows; i.e., what investors will

actually receive. The

cash flows from a share of stock are the dividends.

2. Investors believe the company will eventually start paying dividends (or be sold to

another company).

3. In general, companies that need the cash will often forgo dividends since dividends are

a cash

expense. Young, growing companies with profitable investment opportunities are one

example;

another example is a company in financial distress. This question is examined in depth in

a later

chapter.

4. The general method for valuing a share of stock is to find the present value of all

expected future

dividends. The dividend growth model presented in the text is only valid (i) if dividends

are expected

to occur forever, that is, the stock provides dividends in perpetuity, and (ii) if a constant

growth rate

of dividends occurs forever. A violation of the first assumption might be a company that

is expected

to cease operations and dissolve itself some finite number of years from now. The stock

of such a

company would be valued by the methods of this chapter by applying the general method

of

valuation. A violation of the second assumption might be a start-up firm that isn’t

currently paying

any dividends, but is expected to eventually start making dividend payments some

number of years

from now. This stock would also be valued by the general dividend valuation method of

this chapter.

5. The common stock probably has a higher price because the dividend can grow,

whereas it is fixed on

the preferred. However, the preferred is less risky because of the dividend and liquidation

preference,

so it is possible the preferred could be worth more, depending on the circumstances.

6. The two components are the dividend yield and the capital gains yield. For most

companies, the

capital gains yield is larger. This is easy to see for companies that pay no dividends. For

companies

that do pay dividends, the dividend yields are rarely over five percent and are often much

less.

7. Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the

dividend

growth rate and the capital gains yield are the same.

8. In a corporate election, you can buy votes (by buying shares), so money can be used to

influence or

even determine the outcome. Many would argue the same is true in political elections,

but, in

principle at least, no one has more than one vote.

9. It wouldn’t seem to be. Investors who don’t like the voting features of a particular class

of stock are

under no obligation to buy it.

10. Investors buy such stock because they want it, recognizing that the shares have no

voting power.

Presumably, investors pay a little less for such shares than they would otherwise.

Solutions to Questions and Problems

Basic

1. P0 = D0 (1 + g) / (R – g) = $1.75 (1.06) / (.12 – .06) = $30.92

P3 = D3 (1 + g) / (R – g) = D0 (1 + g)4 / (R – g) = $1.75 (1.06)4 / (.12 – .06) = $36.82

340

P15 = D15 (1 + g) / (R – g) = D0 (1 + g)16 / (R – g) = $1.75 (1.06)16 / (.12 – .06) =

$74.09

2. R = D1 / P0 + g = ($2.50 / $48.00) + .05 = 10.21%

3. Dividend yield = D1 / P0 = 5.21%; capital gains yield = 5%

4. P0 = D1 / (R – g) = $4.00 / (.13 – .04) = $44.44

5. R = dividend yield + capital gains yield = .042 + .07 = 11.2%

6. Dividend yield = 1/2(.14) = .07 = capital gains yield

D1 = .07($60) = $4.20; D0(1 + g) = D1, D0 = $4.20 / (1.07) = $3.93

7. P0 = $9.00(PVIFA11%,8) = $46.32

8. R = D/P0 = $8.50/$124 = 6.85%

Intermediate

9. P6 = D6 (1 + g) / (R – g) = D0 (1 + g)7 / (R – g) = $3.00 (1.075)7 / (.13 – .075) =

$90.49

P3 = [$3.00 (1.075)4 / (1.12)] + [$3.00 (1.075)5 / (1.12)2] + [$3.00 (1.075)6 / (1.12)3] +

[$90.49 / (1.12)3]

= $74.72

P0 = $3.00(1.075)/(1.18) + $3.00(1.075)2/(1.18)2 + $3.00(1.075)3/(1.18)3 +

$74.72/(1.18)3

= $52.97

10. P9 = D10 / (R – g) = $7.00 / (.14 – .06) = $87.50; P0 = $87.50 / 1.149 = $26.91

11. P0 = $8 / (1.11) + $10 / (1.11)2 + $12 / (1.11)3 + $14 / (1.11)4 = $33.32

12. P4 = D4 (1 + g) / (R – g) = $2.00 (1.05) / (.16 – .05) = $19.09

P0 = $6.50 / (1.16) + $5.00 / (1.16)2 + $3.00 / (1.16)3 + $21.09 / (1.16)4 = $22.89

13. P3 = D3 (1 + g) / (R – g) = D0 (1 + g1)3 (1 + g2) / (R – g) = $2.25 (1.32)3 (1.07) /

(.15 – .07) = $69.21

P0 = [$2.25(1.32) / (1.15)] + [$2.25(1.32)2 / (1.15)2] + [$2.25(1.32)3 / (1.15)3] + [$69.21

/ (1.15)3]

= $54.46

14. D3 = D0 (1.25)3; D4 = D0 (1.25)3 (1.18)

P4 = D4 (1 + g) / (R – g) = D0 (1 + g1)3 (1 + g2) (1 + g3) / (R – g)

= D0 (1.25)3 (1.18) (1.08) / (.15 – .08) = 35.56D0

P0 = $60.00 = D0{(1.25/1.15) + (1.25/1.15)2 + (1.25/1.15)3 + [(1.25)3(1.18) + 35.56] /

1.154}

D0 = $60.00 / $25.20 = $2.38; D1 = $2.38(1.25) = $2.98

15. P0 = D0 (1 + g) / (R – g) = $9.00 (0.92) / (.14 + .08) = $37.64

16. P0 = $45 = D0 (1 + g) / (R – g) ; D0 = $45(.12 – .08) / (1.08) = $1.67

17. P5 = $8.00 / .06 = $133.33; P0 = $133.33 / (1.06)5 = $99.63

18. Dividend yield = .013 = $0.48 / P0; P0 = $0.48/.013 = $36.92

Stock up $0.95, so yesterday’s closing price = $36.92 – $0.95 = $35.97

P/E = 51; EPS = $36.92 / 51 = $0.72 = NI / shares; NI = $0.72(2,000,000) = $1.44M

341

Challenge

19. W: P0 = D0(1 + g) / (R – g) = $4.50(1.10)/(.20 – .10) = $49.50

Dividend yield = D1/P0 = 4.50(1.10)/49.50 = 10%; capital gains yield = .20 – .10 = 10%

X: P0 = D0(1 + g) / (R – g) = $4.50/(.20 – 0) = $22.50

Dividend yield = D1/P0 = 4.50/22.50 = 20%; capital gains yield = .20 – .20 = 0%

Y: P0 = D0(1 + g) / (R – g) = $4.50(0.95)/(.20 + .05) = $17.10

Dividend yield = D1/P0 = 4.50(0.95)/17.10 = 25%; capital gains yield = .20 – .25 = – 5%

Z: P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2) / (R – g) = $4.50(1.2)2(1.12)/(.20

– .12) = $90.72

P0

= $4.50 (1.2) / (1.2) + $4.50 (1.2)2 / (1.2)2 + $90.72 / (1.2)2 = $72.00

Dividend yield = D1/P0 = 4.50(1.2)/72.00 = 7.5%; capital gains yield = .20 – .075 =

12.5%

In all cases, the required return is 20%, but the return is distributed differently between

current

income and capital gains. High growth stocks have an appreciable capital gains

component but a

relatively small current income yield; conversely, mature, negative-growth stocks provide

a high

current income but also price depreciation over time.

20. a. P0 = D0(1 + g) / (R – g) = $2.50(1.08)/(.14 – .08) = $45.00

b. Next four dividends: $2.50(1.08)/4 = $0.675

Effective quarterly rate: 1.14.25 – 1 = .0333

Effective D1 = $0.675(FVIFA3.33%,4) = $2.84

P0 = $2.84/.06 = $47.30

21. P0 = $4.00(1.20)/(1.13) + $4.00(1.20)(1.15)/(1.13)2 +

$4.00(1.20)(1.15)(1.10)/(1.13)3

+ [$4.00(1.20)(1.15)(1.10)(1.05)/(.13 – .05)]/(1.13)3 = $68.01

22. P = $4.00(1.20)/(1 + R) + $4.00(1.20)(1.15)/(1 + R)2 + $4.00(1.20)(1.15)(1.10)/(1 +

R)3

+ [$4.00(1.20)(1.15)(1.10)(1.05)/(R – .05)]/(1 + R)3 = $104.05 ;

Using trial and error, or a calculator with a root solving function, gives R = 10.25%

23. g1 = 16%, g2+ = 5%, D0 = $2, and r = 16%

a. P0 = {2[1.16/1.16]+2[1.16/1.16]2+…+2[1.16/1.16]7=2(7)}+2.00(1.16)7(1.05)/(.16

– .05)

[1/1.16]7=(2)(7)+2.00(1.16)7(1.05)/(.16-.05)[1/1.16]7 = 33.09

b. P0 = [2.00(1.05)/(.16-.05)] = 19.09

c. Let T = number of years of 16% growth that the market is expecting. At a current price

of $50 per

share, this implies that:

50 = 2(1.16/1.16) + 2(1.16/1.16)2 + ... + 2(1.16/1.16)T + [2(1.16)T(1.05)/(.16 – .05)]

[1/1.16]T

Simplifying: 50 = 2T + [2(1.05)/(.16 – .05)] or 50 = 2T + 19.09. This implies that T =

15.455

years

If you believe that the stock will grow at a 16% rate for more than 15.455 years then it is

a good

buy. Otherwise it would not make sense to purchase it.

24. a. Total value of the shares = $50,000/(0.15 – 0.03) = $416,667

Price per share = $416,667/200,000 = $2.08

b. The value today of the growth opportunities is

-$100,000 + $32,000/(0.15-0.03) = $166,667

NPVGO = $166,667

c. The price will rise by the NPVGO.

($416,667 + $166,667)/200,000 = $2.92

The problem implicitly assumes that all net cash flows can be paid out of dividends.

25. a. P/E of Pacific Energy Company:

EPS = ($800,000/500,000) = $1.60

NPVGO = {$100,000/500,000}/0.17 = $1.18

P/E = (1/0.17) + (1.18/1.6) = 6.62

b. P/E of Ottawa Valley Bluechips, Inc.:

NPVGO = {$200,000/500,000}/(0.17-0.10) = $5.71

P/E = (1/0.17) + (5.71/1.6) = 9.45

APPENDIX 8A

A.1 a. Ignoring the possibility of a tie, Cumulative votes needed: (1/6) 1,000,000 =

166,667

b. Ignoring the possibility of a tie, Straight votes needed: (1/2) 1,000,000 = 500,000