Chapter 6 - Word



CHAPTER 7

COMMON STOCK: CHARACTERISTICS, VALUATION AND ISSUANCE

ANSWERS TO QUESTIONS:

1. a. Nonvoting stock - common stock that is issued when the firm wishes to raise additional equity capital but does not want to give up voting power.

b. Stock split - the issuance of a number of new shares in exchange for each old share held by a stockholder in order to lower the stock price to a more desirable trading level.

c. Reverse stock split - the issuance of one new share in exchange for a number of old shares held by a stockholder in order to raise the stock price to a more desirable trading level.

d. Stock dividend - a dividend to stockholders in the form of additional shares of stock instead of cash.

e. Book value - total common stockholders' equity divided by the number of shares outstanding.

f. Treasury stock - shares of common stock that have been repurchased by the company.

2. No, the retained earnings figure on the balance sheet is simply the cumulative amount of earnings that have been retained over time. At the time when income is retained, these dollars may be used to purchase additional long-term assets. As a result, the retained earnings amount is not available for current dividends. Current dividends are paid out of cash (or earnings) and not out of retained earnings.

3. Reasons for stock repurchases:

• tax considerations – Under current tax laws, capital gains income is taxed at lower rates than dividend income for individual taxpayers. Also, there is a tax advantage to share repurchases because taxes on capital gains income can be deferred into the future when the stock is sold. (See Chapter 14 for additional discussion of this point.)

• financial restructuring - the firm can gain the benefits of increased financial leverage through the issuance of debt and using the proceeds to repurchase its common stock.

• future corporate needs - repurchased stock can be used in future acquisitions of other companies, executive stock options, exercise of warrants, and conversion of convertible securities.

• disposition of excess cash - funds that the company does not feel can be profitably invested in the foreseeable future can be used to repurchase stock.

• reduction of takeover risk - by increasing the price of the firm's stock and concentrating ownership in the hands of a smaller number of investors, share repurchases can be used to reduce the returns to investors who might be considering acquisition of the firm.

4. For common stock, par value typically is a low figure of little significance. Book value is common stockholders’ equity divided by the number of common shares issued and outstanding. The market value of a common stock depends in general on the outlook for the firm and the economy (i.e. future earnings and dividends and their risk) and normally bears little relationship to book value and no relationship to par value.

5. Stockholder rights often include the following:

• Dividend rights - right to share equally on a per share basis in any dividend distributions.

• Asset rights - in the event of liquidation, the right to assets that remain after the obligations to creditors have been satisfied.

• Voting rights - the right to vote on stockholder matters, such as the election of the board of directors.

• Preemptive rights - the right to share proportionately in any new stock sold.

6. The valuation of common stock is more complicated than the valuation of bonds and preferred stocks due to the following factors:

a. Common stock returns can take two different forms--cash dividend payments and/or increases in the stock price.

b. Common stock dividend payments normally are expected to grow and not remain constant. Hence the relatively simple annuity and perpetuity formulas used in the valuation of bonds and preferred stocks are generally not applicable to common stocks.

c. The future returns from common stocks (i.e., cash dividends and/or price appreciation) are more uncertain than the returns from bonds and preferred stocks.

7. A firm that reinvests all its earnings and pays no cash dividends can still have a value greater than zero when evaluated using the general dividend valuation model because at some future point in time it will be able to start paying cash dividends to its stockholders. In addition to ordinary cash dividends, the stockholders' returns could take the form of liquidating dividends if the firm sells its assets and goes out of business. Alternatively, the returns could consist of the proceeds from the sale of its outstanding common stock if the firm is acquired by another company.

8. The financial decisions of the firm affect both expected future dividend payments of the firm (D1, D2,...) as well as the (marginal) investor's required rate of return (ke). Shareholder wealth (stock price) is a function of these variables and hence is a function of the financial decisions of the firm.

9. a An upward shift in interest rates and investors’ required rates of return would cause ke to increase and the price of the firm's stock (Po) to decrease.

b. A reduction in the future growth potential of the firm's earnings and dividends due to increased foreign competition would lower the firm's future dividends (D1, D2,...) and hence decrease the stock price (Po).

c. An increase in the riskiness of the firm's common stock due to larger South American investments by the firm would increase the (marginal) investor's required rate of return (ke) and hence decrease the stock price (Po), unless the growth potential of these investments outweighed the increase risk.

10. a Dividend yield (D1/Po)

b. Price appreciation yield (g); growth rate of earnings, dividends, and stock price.

11. In the perpetual bond, preferred stock, and (constant dividend) common stock valuation models, the returns to the investor (i.e., interest, preferred dividends, and common dividends respectively) are assumed to remain the same each period forever and hence can be treated as a perpetuity. The only differences in the three models are the symbols used to represent the returns of the investor (I, Dp, and D respectively) and the investor's required rates of return (kd, kp, and ke respectively).

12. Book value per share, which equals total common stockholders’ equity divided by the number of shares outstanding, can change as the result of

• Additions to (or subtractions from) retained earnings provided by current period earnings (losses)

• Issuance (sale) of new shares of common stock

• Purchase of existing shares of common stock (Treasury stock) by the company

• Payment of dividends, which reduces retained earnings.

13. With majority voting, each stockholder has one vote for each share held. Shareholders are allowed to cast one vote for each director candidate of their choice. As a result, if two slates of people are running for the board, the one that receives more than 50% of the vote wins. With cumulative voting, each shareholder has as many votes as there are directors to be elected, thereby increasing an individual candidate's chance of being elected. As a result, cumulative voting makes it easier for stockholders with minority views to elect sympathetic board members.

14. An investment banker is a financial institution which acts as a financial advisor to client businesses. Investment bankers play a key role in assisting corporations in obtaining new financing. Investment bankers often function as underwriters. In an underwriting, a group of investment bankers agrees to purchase a new security issue at a set price and then offers it for sale to investors.

15. In a direct placement (also termed a private placement) the sale of an entire security offering is made to one or more institutional investors rather than the general public. In a public cash offering, the securities are offered for sale to the general public. In a rights offering, a firm issues a security (called a right ) to its existing stockholders, who then may either sell the right or exercise it to buy additional shares of the firm's stock.

16. A best efforts offering is more risky than an underwritten offering for a firm trying to raise capital. However, the opposite is true for investment bankers. As a result, well established, profitable firms normally can raise capital with an underwritten offering while smaller, start-up firms frequently have to rely on a best efforts offering to raise capital.

17. Direct issuance costs include the underwriting spread and other direct costs, including legal and accounting fees, taxes, the cost of SEC registration, and printing costs. Other issuance costs include the cost of management time in preparing the offering, the cost of underpricing a new (initial) equity offering below the correct market value, the cost of stock price declines for stock offerings by firms whose shares are already outstanding, and by the cost of other incentives provided to the investment banker.

18. With a shelf registration, a firm initially files a master registration statement with the SEC. Then the firm is free to sell small increments of the offering over a 2-year period merely by filing a brief statement with the SEC. With other public security offerings, the firm has to file a lengthy registration statement with the SEC each time it wishes to sell securities.

SOLUTIONS TO PROBLEMS:

1. a. Po = D1/(ke - g)

g = 0.07 Do = $1.70 ke = .12

Dl = Do(1 + g) = 1.70(1 + 0.07) = $1.819

Po = 1.819/(0.12 - 0.07) = $36.38

b. g = 0.09 Do = $1.70 ke = 0.12

D1 = 1.70(1 + 0.09) = $1.853

Po = 1.853/(0.12 - 0.09) = $61.77

c. g = 0.065 Do = $1.70 ke = 0.12

D1 = $1.70(1 + 0.065) = $1.8105

Po = $1.8105/(0.12 - 0.065) = $32.92

2. a. Po = D1/(ke - g)

g = .06 Do = $5 ke = .12

Dl = Do(1 + g) = 5(1 + .06) = $5.30

Po = 5.30/(.12 - .06) = $88.33

b. g = .06 D1 = $5.30 ke = .14

Po = 5.30/(.14 - .06) = $66.25

c. g = .06 Dl = $5.30 ke = .16

Po = 5.30/(.16 - .06) = $53.

d. g = .06 D1 = $5.30 ke = .06

Po = 5.30/(.06 - .06) = Undefined

ke = g, which violates assumption of constant-growth model.

e. g = .06 Dl = $5.30 ke = .04

Po = 5.30/(.04 - .06) = $-265.

ke < g, which violates assumption of constant-growth model.

3. Po = $25 D1 = $1.25 ke = .12

ke = D1/Po + g

.12 = 1.25/25 + g

g = .07 (or 7%)

4. Present Value of First 6-Years' Dividends:

6

( [Do(1 + g1)t/(1 + ke)t]; Do = $5.00; g1 = .07; ke = .12

t=1

Present Value

Year Dividend Interest Factor Present Value

t Dt = 5.00(1 + .07)t PVIF.12,t Dt x PVIF.12,t

1 5.00(1 + .07)1 = .893 $ 4.778

$5.35

2 5.00(1 + .07)2 = .797 4.563

5.725

3 5.00(1 + .07)3 = .712 4.361

6.125

4 5.00(1 + .07)4 = .636 4.168

6.554

5 5.00(1 + .07)5 = .567 3.976

7.013

6 5.00(1 + .07)6 = .507 3.805

7.504

PV (First 6-Years' Dividends) $25.651

Value of Stock at End of Year 6:

P6 = D7/(ke - g2) g2 = .00

D7 = D6(1 + g2) = 7.504(1 + .00) = $7.504

P6 = 7.504/(.12 - .00) = $62.533

Present Value of P6:

PV(P6) = P6/(1 + ke)6 = 62.533/(1 + .12)6 = 62.533 x PVIF.12,6

= 62.533 X .507 = $31.704

Value of Common Stock (Po):

Po = PV (First 6-Years' Dividends) + PV(P6)

= 25.651 + 31.704 = $57.36

5. FVn = PVo(1 + g)n

PVo = $.70 FV5 = $1.30 n = 5

1.30 = .70(1 + g)5

(1 + g)5 = 1.857

The term (1 + g)5 represents the future value interest factor

(FVIFg,5) found in Table I at the back of the book. Reading

across the Period = 5 row, one finds (1 + g)5 between the i = 13%

and i = 14% columns. Interpolating between these values yields

i = 13% + 1.857 - 1.842 x (14% - 13%) = 13.2%

1.925 - 1.842

Therefore g = .132 ( or 13.2%)

Po = D1/(ke - g) Do = $1.30 ke = .20

D1 = Do(1 + g) = 1.30(1 + .132) = $1.4716

Po = 1.4716/(.20 - .132) = $21.64

6. a. 4

Po = D1/(1 + ke) + ( [D1(1 + g1)t-1/(1 + ke)t]

t=2

+ [D5/(ke - g2)]/[(1 + ke)4]

ke = .15 Do = $2.50 D1 = $3.00 g1 = .09 g2 = .06

Present Value of First Year Dividend

PV(D1) = 3.00/(1 + .15) = 3.00(PVIF.15,1)

= 3.00(.870) = $2.610

Present Value of Next 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt = 3.00(1 + .09) t-1 PVIF.15,t Dt x PVIF.15,t

2 3.00(1 + .09)1 = .756 $2.472

$3.270

3 3.00(1 + .09)2 = .658 2.345

$3.564

4 3.00(1 + .09)3 = .572 2.222

$3.885

PV(Next 3-Years' Dividends) $7.039

Value of Stock at End of Year 4

D5 = D4(1 + g2) = 3.885(1 + .06) = $4.118

P4 = D5/(ke - g2) = 4.118/(.15 - .06) = $45.756

Present Value of P4

PV(P4) = P4/(1 + ke)4 = P4 x PVIF.15,4

= 45.756 x .572 = $26.172

Value of Common Stock:

Po = PV(D1) + PV(Next 3-Years' Dividends) + PV(P4)

= $2.610 + $7.039 + $26.172 = $35.82

b. ke = .15 Do = $2.50 D1 = $3.00 g1 = .07 g2 = .06

Present Value of First Year Dividend

PV(D1) = $2.610 (same as part (a))

Present Value of Next 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt=3.00(1 + .07)t-1 PVIF.15,t Dt x PVIF.15,t

2 3.00(1 + .07)1 = .756 $2.427

$3.210

3 3.00(1 + .07)2 = .658 2.260

$3.435

4 3.00(1 + .07)3 = .572 2.102

$3.675

PV(Next 3-Years' Dividends) $6.789

Value of Stock at End of Year 4

D5 = 3.675(1 + .06) = $3.896

P4 = 3.896/(.15 - .06) = $43.289

Present Value of P4

PV(P4) = 43.289 x .572 = $24.761

Value of Common Stock:

Po = $2.610 + $6.789 + $24.761 = $34.16

7. P0 = D/ke

= $2.00/0.16

= $12.50

8. Present Value of First 4-Year's Dividends:

4

( [Do(1 + g1)t/(1 + ke)t]; Do = $1.50; g1 = .11; ke = .14

t=1

Present Value

Year Dividend Interest Factor Present Value

t Dt = 1.50(1 + .11)t PVIF.14,t Dt x PVIF.14,t

1 1.50(1 + .11)1 = .877 1.460

$1.6650

2 1.50(1 + .11)2 = .769 1.421

$1.8482

3 1.50(1 + .11)3 = .675 1.385

$2.0514

4 1.50(1 + .11)4 = .592 1.348

$2.2771

PV (First 4-Years' Dividends) $5.614

Value of Stock at End of Year 4:

P4 = D5/(ke - g2) g2 = .05

D5 = D4(1 + g2) = 2.2771(1 + .05) = $2.391

P4 = 2.391/(.14 - .05) = $26.567

Present Value of P4:

PV(P4) = P4/(1 + ke)4 = $26.567/(1 + .14)4

= $26.567(PVIF.14,4) = $26.567 x 0.592 = $15.728

Value of Common Stock (Po):

Po = PV(First 4-Years' Dividends) + PV(P4)

= $5.614 + $15.728 = $21.34

3 6

9. Po = ( [Do(1 + g1)t/(1 + ke)t] + ( [D3(1 + g2)t-3/(1 + ke)t]

t=1 t=4

+ [D7/(ke - g3)]/[(1 + ke)6]

ke = 0.18; Do = $1.50; g1 = 0.15; g2 = 0.075; g3 = 0.05

Present Value of First 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt = 1.50(1 + .15)t PVIF.18,t Dt x PVIF.18,t

1 1.50(1 + .15)1 = .847 $1.461

$1.725

2 1.50(1 + .15)2 = .718 1.425

$1.984

3 1.50(1 + .15)3 = .609 1.389

$2.281

PV (First 3-Years' Dividends) $4.275

Present Value of Next 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt = 2.281(1 + .075)t-3 PVIF.18,t Dt x PVIF.18,t

4 2.281(1 + .075)1 = .516 $1.265

$2.452

5 2.281(1 + .075)2 = .437 1.152

$2.636

6 2.281(1 + .075)3 = .370 1.049

$2.834

PV (Next 3-Years' Dividends) $3.466

Value of Stock at End of Year 6

D7 = D6(1 + g3) = 2.834(1 + .05) = $2.976

P6 = D7/(ke - g3) = 2.976/(.18 - .05) = $22.892

Present Value of P6

PV(P6) = P6/(1 + ke)6 = P6 x PVIF(0.18,6)

= 22.892 x 0.370 = $8.470

Value of Common Stock

Po = PV(First 3-Years' Dividends) +

PV(Next 3-Years' Dividends) + PV(P6)

= $4.275 + $3.466 + $8.470 = $16.21

10. a. FVn = PVo(1+ g)n

PVo = $2.00; FV6 = $4.00; n = 6

4.00 = 2.00(1 + g)6

(1 + g)6 = 2.000

The term (1 + g)6 represents the future value interest factor (FVIFg,6) in Table I at the back of the book. Reading across the Period = 6 row, one finds (1 + g)6 in the i ” 12% column.

Therefore g ” 0.12 (or 12%).

b. Dt = Do(1 + g)t; Do = $2.00

Year Dividend*

t Dt = 2.00(1 + g)t

1 2.00(1 + .12)1 = $2.240

2 2.00(1 + .12)2 = $2.509

3 2.00(1 + .12)3 = $2.8l0

4 2.00(1 + .12)4 = $3.147

5 2.00(1 + .12)5 = $3.525

6 2.00(1 + .12)6 = $3.948

*Note: The (1 + 0.12)t factors can be obtained from Table I, i.e.,

(1 + 0.12)t = FVIF.12,t

Earnings per year will be exactly two times the projected dividends.

c. Po = D1/(ke - g)

ke = 0.18; g = 0.12; D1 = $2.240

Po = 2.240/(0.18 - 0.12) = $37.33

d. The firm's earnings and dividends probably cannot continue to grow indefinitely at 12% (above-normal rate). Eventually the growth rate will decline - which violates an assumption of the constant-growth model.

e. Present value of First 6-Years' Dividends:

6

( [Do(1 + g1)t/(1 + ke)t]

t=1

Year Dividend P.V. Interest Factor Present Value

t Dt PVIF.18,t Dt x PVIF.18,t

1 $2.240 .847 $1.897

2 2.509 .718 1.801

3 2.810 .609 1.711

4 3.147 .516 1.624

5 3.525 .437 1.540

6 3.948 .370 1.461

PV (First 6-Years' Dividends) $10.034

Value of Stock at End of Year 6:

P6 = D7/(ke - g2); g2 = 0.06

D7 = D6(1 + g2) = $3.948(1 + 0.06) = $4.185

P6 = $4.185/(0.18 - 0.06) = $34.875

Present Value of P6:

V(P6) = P6/(1 + ke)6 = $34.875/(1 + 0.18)6 = $34.875 x PVIF(0.18,6)

= $34.875 X 0.370 = $12.904

Value of Common Stock (Po)

Po = PV(First 6-Year's Dividends) + PV(P6)

= $10.034 + $12.904 = $22.94

11. D0 = $1.50

D1 = $1.50(1.15) = $1.72

D2 = $1.72(1.15) = $1.98

D3 = $1.98(1.15) = $2.28

D4 = $2.28(1.10) = $2.51

P4 = 1.5(P0) (Note that the end of year 4 is the same as the beginning of year 5, in present value terms.)

P0 = $1.72(.893) + $1.98(.797) + $2.28(.712) + $2.51(.636)

+ 1.5P0(.636)

P0 = $137.69

12. The dividend at the end of two years = $1 (FVIF0.20,2) = $1.44

D3 = $1.44(1.06) = $1.53

D4 = $1.53(1.06) = $1.62

D5 = $1.62(1.06) = $1.72

The price of the stock at the beginning of year 5 is the same as at the end of year 4, or

P4 = $1.72/(0.15 - 0.06) = $19.11

13. a P0 = $3.40(PVIF.15,1) + $3.74(PVIF.15,2) + $4.11(PVIF.15,3)

+ [$4.36/(.15 - .06](PVIF.15,3)

= $40.36

b. Price at the beginning of year 3

= [$4.11 + $4.36/(.15 - .06)](PVIF.15,1) = $45.72

c. $40.36 - The value of the stock does not depend on the length of the intended holding period

14. Underwriting spread = Selling price to public - Proceeds to company

= ($30 x 10,000,000) - $287,506,114

= $12,493,886

15. a Number of shares = [(No. of directors desired)(No. of shares outstanding)]/[(No. of directors being elected + 1] + 1

Number of shares = [(1)(1,500,000)]/[4 + 1] + 1 = 300,001

This number of shares will guarantee election. Consider the following close race:

300,001

300,000

300,000

300,000

299,999

300,001 will assure election.

But you could be elected with fewer votes, e.g., 250,000 votes:

350,000

350,000

350,000

250,000

200,000

b. Number of shares = [(2)(1,500,000)]/[4 + 1] + 1 = 600,001

c. If the voting procedure is majority, 750,001 shares are necessary to guarantee election of a slate. Thus, you need to run a slate of 4 directors.

16. Present Value of First 4-Years' Dividends:

Present Value

Year Dividend Interest Factor Present Value

t Dt = 3.00(1.15) PVIF(0.24,t) Dt x PVIF(0.24,t)

for D1 - D3

1 $3.00 (1.15)1 = 0.806 2.781

$3.45

2 $3.00 (1.15)2 = 0.650 2.579

$3.968

3 3.00(1.15)3 = 0.524 2.391

$4.563

4 D4 = D3 + $1.00 = 0.423 2.353

$5.563

PV(First 4-Years' Dividends) $10.104

Value of Stock at End of Year 4:

P4 = D5/(ke - 0.06)

D5 = D4 (1.06) = $5.563 (1.06) = $5.897

P4 = $5.897/(0.24 - 0.06) = $32.760

Present Value of P4:

PV(P4) = P4/(1 + ke)4 = $32.760 x PVIF(0.24,4)

= $32.760 x 0.423 = $13.857

Po = PV (First 4-Years' Dividends) + PV (P4)

= $10.104 + $13.857 = $23.96

17. Present Value of First 5-Years' Dividends:

Year Dividend Present Value Present Value

Interest Factor

t Dt = 2.00(1+g) PVIF(0.24,t) Dt x PVIF(0.24,t)

1 2.00(1.09)1 = $2.18 0.806 $1.757

2 2.00(1.09)2 = $2.376 0.650 1.544

3 2.00(1.09)3 = $2.590 0.524 1.357

4 2.590(1.07)1= $2.771 0.423 1.172

5 2.590(1.07)2 = $2.965 0.341 1.011

PV (First 5-Years' Dividend) $6.841

Value of Stock at End of Year 5:

P5 = D6 / (ke - 0.04)

D6 = D5 (1.04) = $3.084

P5 = $3.084 / (0.24 - 0.04) = $15.42

Present Value of P5:

PV(P5) = P5 / (1 + ke)5 = $15.42 x PVIF(0.24,5)

= $15.42 x 0.341 = $5.26

Value of Common Stock (Po):

Po = PV (First 5-Years' Dividends) + PV (P5)

= $6.84 + $5.26 = $12.10

18. Present Value of First 4-Years' Dividends:

Present Value

Year Dividend Interest Factor Present Value

t Dt PVIF0.18,t Dt x PVIF0.18,t

1 $0.00 0.847 $0.000

2 0.25 0.718 0.180

3 0.75 0.609 0.457

4 1.50 0.516 0.774

PV (First 4-Years ' Dividends) $1.411

Value of Stock at End of Year 4:

P4 = D5/(ke - 0.05)

D5 = D4 (1.05) = $1.50 (1.05) = $1.575

P4 = $1.575/(0.18 - 0.05) = $12.115

Present Value of P4:

PV(P4) = P4/(1 + ke)4 = $12.115 x PVIF(0.18,4)

= $12.115 x 0.516 = $6.251

Po = PV (First 4-Years' Dividends) + PV(P4)

= $1.411 + $6.251 = $7.66

19. a Present Value of First 3-Years' Dividends:

Present Value

Year Dividend Interest Factor Present Value

t Dt PVIF0.16,t Dt x PVIF0.16,t

1 2.00 (1.25) = 0.862 $2.155

$2.50

2 2.50 (1.15) = 0.743 $2.136

$2.875

3 2.50 (1.15)2 = 0.641 $2.119

3.306

PV(First 3-Years' Dividends) $ 6.410

Value of Stock at End of Year 3:

P3 = D4/(ke - 0.06)

D4 = D3 (1.06) = $3.306 (1.06) = $3.504

P3 = $3.504/(0.16 - 0.06) = $35.04

Present Value of P3:

PV(P3) = P3/(1 + ke)3 = $35.04 x PVIF(0.16,3)

= $35.04 x 0.641 = $22.46

Po = PV (First 3-Years' Dividends) + PV(P3)

= $6.410 + $22.46 = $28.87

b. Recall that, in present value terms, the beginning of year 2 is the same as the end of year 1, however the year one dividend is not received.

P1 = D2(PVIF0.16,1) + D3(PVIF0.16,2) + P3(PVIF0.16,2)

= $2.875(0.862) + $3.306(0.743) + $35.04(0.743)

= $30.97

20. D1 = $1.00 D2 = $2.00

D3 = D2 (1 + g) = $2.00 (1.10) = $2.20

P3 = 1.5 P0

P0 = PV(D1) + PV(D2) + PV (D3) + PV (P3)

= $1.00 (0.833) + $2.00 (0.694) + $2.20 (0.579)

+ (1.5 P0)(0.579)

P0 = $3.495 + 0.869 P0

P0 = $26.68

21. P0 = $0.75(PVIF.2,1) + $0.86(PVIF.2,2) + $0.99(PVIF.2,3)

+ ($1.14 + $30)(PVIF.2,4)

P0 = $0.75(.833) + $0.86(.694) + $0.99(.579) + ($1.14 + $30)(.482)

= $16.80

22. Earnings growth rate for first 3 years = 50%, 25% for the following 3 years, and 8% thereafter. Required equity return = 20%. Payout rate of 20% in years 2-4, and 50% thereafter.

Year Earnings Dividends

0 $1.00 $0.00

1 1.50 0.00

2 2.25 0.45

3 3.38 0.68

4 4.22 0.84

5 5.27 2.64

6 6.59 3.30

7 7.12 3.56

P6 = $3.56/(0.2 0 - 0.08) = $29.67

P0 = $0 + $0.45(PVIF0.2,2) +$0.68(PVIF0.2,3) + $0.84(PVIF0.2,4) + $2.64(PVIF0.2,5)

+ ($3.30 + $29.67) (PVIF0.2,6) = $13.21 (calculator accuracy)

23. P0 = $1(PVIF.2,1) + $1.20(PVIF.2,2) + $1.44(PVIF.2,3)

+ $1.73((PVIF.2,4) + ($2.07 + $40)(PVIF.2,5)

P0 = $1(.833) + $1.2(.694) + $1.44(.579) + $1.73(.482)

+ ($2.07 + $40)(.402)

= $20.25

24. D0 = $3

D1 = $3(1.15) = $3.45

D2 = $3.45(1.15) = $3.97

D3 = $3.97(1.15) = $4.56

D4 = $4.56(1.10) = $5.02

P4 = 1.4(P0) - Note the beginning of year 5 is the same as the end of year 4 in present value terms.

P0 = $3.45(.893) + $3.97(.797) + $4.56(.712) + $5.02(.636)

+ 1.4P0(.636)

P0 = $115.69

25. D0 = $0

D1 = $0

D2 = $2.00

D3 = $2.00(1.15) = $2.30

D4 = $2.30(1.15) = $2.645

D5 = $2.645(1.15) = $3.04

D6 = $3.04(1.10) = $3.35

P6 = estimated EPS x estimated P/E multiple

= $7 x 15 = $105

P0 = $2(PVIF0.15,2) + $2.30(PVIF0.15,3) +$2.645(PVIF0.15,4) + $3.04(PVIF0.15,5)

+ ($3.35 + $105) (PVIF0.15,6) = $52.89 (calculator accuracy)

26. ke by the CAPM = ke = 6.9% + 1.3(14% - 6.9%) = 16.1%

Constant growth model:

ke = [D0(1 + g) / P0] + g

0.161= [2(1 + g) / $50] + g

g = 0.116 or 11.6%

This is not a sustainable growth rate, given an overall nominal growth rate in the economy of 5-6%.

27. a. The dividend yield for Duke Energy is 2.8%; for Johnson and Johnson it is 1.2%; and for Sara Lee it is 2.7%.

b. These firms differ with respect to expected earnings and dividend growth, with Sara Lee likely having the lowest expected growth and Johnson and Johnson the highest expected growth.

c. P/E for Duke Energy = 15 times

P/E for Johnson and Johnson = 32 times

d. Johnson and Johnson’s higher expected growth rate more than offsets the relatively lower expected risk of Duke Energy.

e. Investors in the preferred stock have no chance for a growth in the dividend payout rate, while investors in Duke Energy’s common stock will benefit from any growth in earnings and dividends.

$20.92 = ($21.12 - $0.20)

28. a. Number of votes cast = 0.7 x 1,000,000 = 700,000

i. 350,000 + 1

ii. 350,000 +1

iii. 350,000 +1

b. i. Number of shares = [(1) x (700,000)] / [(9) + 1] + 1 = 70,001

ii. Number of shares = [(2) x (700,000)] / [(9) + 1] + 1 = 140,001

iii. Number of shares = [(5) x (700,000)] / [(9) + 1] + 1 = 350,001

29. No recommended solution.

30. P0 = 0.12(PVIF0.2,1) + .144(PVIF0.2,2) + .173(PVIF0.2,3) + 1.70(P0) (PVIF0.2,3)

P0 = .12(.833) + .144(.694) + .173(.579) + 1.7(.579)(P0)

P0 = $19.11

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