Preview: Common Stock, Characteristics, Valuation and Issuance

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Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 7-1 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 firms 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 7-2 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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) investors required rate of return (ke).

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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 firms stock (Po) to decrease. b. A reduction in the future growth potential of the firms earnings and dividends due to increased foreign competition would lower the firms future dividends (D1, D2,...) and hence decrease the stock price (Po). c. An increase in the riskiness of the firms common stock due to larger South American investments by the firm would increase the (marginal) investors 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 investors 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 candidates chance of being elected. As a result, cumulative 7-3 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 firms 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. 7-4 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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

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= $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. 7-5 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 D1 = $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 Σ[D0(1 + g1)t/(1 + ke)t]; D0 = $5.00; g1 = .07; ke = .12 t=1 Present Value Year Dividend t Dt = 5.00(1 + .07)t 1 Interest Factor PVIF.12,t 5.00(1 + .07)1 = $5.35 .893 7-6 Present Value Dt x PVIF.12,t $ 4.778 Chapter 7 Common Stock: Characteristics,

Valuation and Issuance 2 5.00(1 + .07)2 = 5.725 .797 4.563 3 5.00(1 + .07)3 = 6.125 .712 4.361 4 5.00(1 + .07)4 = 6.554 .636 4.168 5 5.00(1 + .07)5 = 7.013 .567 3.976 6 5.00(1 + .07)6 = 7.504 .507 3.805 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 (P0): P0 = PV (First 6-Years Dividends) + PV(P6) = 25.651 + 31.704 = $57.36 (tables) 5. FVn = PVo(1 + g)n PVo = $.70 FV5 = $1.30 n=5 7-7 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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% -- 13.18% by calculator) 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) + Σ [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 t Dt = 3.00(1 + .09) t-1 P.V. Interest Factor PVIF.15,t 7-8 Present Value Dt x PVIF.15,t Chapter 7 Common Stock: Characteristics, Valuation and Issuance 2 3.00(1 + .09)1 = $3.270 .756 $2.472 3 3.00(1 + .09)2 = $3.564 .658 2.345 .572 2.222 3.00(1 + .09)3 = $3.885 4 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 (tables) 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 t Dt=3.00(1 + .07)t-1 2 P.V. Interest Factor PVIF.15,t 3.00(1 + .07)1 = $3.210 .756 7-9 Present Value Dt x PVIF.15,t $2.427 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 3 3.00(1 + .07)2 = $3.435 .658 2.260 4 3.00(1 + .07)3 = $3.675 .572 2.102 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 (tables) 7. P0 = D/ke = $2.00/0.16 = $12.50 8. Present Value of First 4-Years

Dividends: 4 Σ [Do(1 + g1)t/(1 + ke)t]; Do = $1.50; g1 = .11; ke = .14 t=1 Year Dividend t Dt = 1.50(1 + .11)t 1 Present Value Interest Factor PVIF.14,t 1.50(1 + .11)1 = $1.6650 .877 7-10 Present Value Dt x PVIF.14,t 1.460 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 2 1.50(1 + .11)2 = $1.8482 .769 1.421 3 1.50(1 + .11)3 = $2.0514 .675 1.385 4 1.50(1 + .11)4 = $2.2771 .592 1.348 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 (tables) 9. 3 6 Po = Σ [Do(1 + g1)t/(1 + ke)t] + Σ [D3(1 + g2)t-3/(1 + ke)t] t=1 t=4 6 + [D7/(ke - g3)]/[(1 + ke) ] ke = 0.18; Do = $1.50; g1 = 0.15; g2 = 0.075; g3 = 0.05

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Present Value of First 3-Years Dividends Year t Dividend Dt = 1.50(1 + .15)t P.V. Interest Factor PVIF.18,t 7-11 Present Value Dt x PVIF.18,t Chapter 7 Common Stock: Characteristics, Valuation and Issuance 1 1.50(1 + .15)1 = $1.725 .847 $1.461 2 1.50(1 + .15)2 = $1.984 .718 1.425 3 1.50(1 + .15)3 = $2.281 .609 1.389 PV (First 3-Years Dividends) $4.275 Present Value of Next 3-Years Dividends Year Dividend t Dt = 2.281(1 + .075)t-3 P.V. Interest Factor Present Value PVIF.18,t Dt x PVIF.18,t 4 2.281(1 + .075)1 = $2.452 .516 $1.265 5 2.281(1 + .075)2 = $2.636 .437 1.152 6 2.281(1 + .075)3 = $2.834 .370 1.049 PV (Next 3-Years Dividends) 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 7-12 $3.466 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 (tables) 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 t Dividend* 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 7-13 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 firms

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 Σ [Do(1 + g1)t/(1 + ke)t] t=1 Year Dividend P.V. Interest Factor t Dt PVIF.18,t Present Value 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 7-14 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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: PV(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-Years Dividends) + PV(P6) = $10.034 + $12.904 = $22.94 (tables) 11. D0 = $1.50 D1 =

$1.50(1.15) = $1.725 D2 = $1.72(1.15) = $1.984 D3 = $1.98(1.15) = $2.281 D4 = $2.28(1.10) = $2.509 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 = $1.725(.893) + $1.984(.797) + $2.281(.712) + $2.509(.636) + 1.5P0(.636) P0 = $137.85 (tables) 12. The dividend at the end of two years = $1 (FVIF0.20,2) = $1.44 7-15 Chapter 7 Common Stock: Characteristics, Valuation and Issuance D3 = $1.44(1.06) = $1.526 D4 = $1.53(1.06) = $1.618 D5 = $1.62(1.06) = $1.715 The price of the stock at the beginning of year 5 is the same as at the end of year 4, or P4 = $1.715/(0.15 - 0.06) = $19.06 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 7-16 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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: Year Dividend Present Value Interest Factor Present Value t Dt = 3.00(1.15)t PVIF(0.24,t) for D1 - D3 1 $3.00 (1.15)1 = $3.45 0.806 2.781 2 $3.00

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(1.15)2 = $3.968 0.650 2.579 3 3.00(1.15)3 = $4.563 0.524 2.391 4 D4 = D3 + $1.00 = 0.423 $5.563 PV(First 4-Years Dividends) Value of Stock at End of Year 4: P4 = D5/(ke - 0.06) D5 = D4 (1.06) = $5.563 (1.06) = $5.897 7-17 Dt x PVIF(0.24,t) 2.353 $10.104 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 (tables) 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) 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) 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 7-18 Dt x PVIF(0.24,t) $6.841 Chapter 7 Common Stock: Characteristics, Valuation and Issuance Present Value of P5: PV(P5) = P5 / (1 + ke)5 = $15.42 x PVIF(0.24,5) = $15.42 x 0.341 = $5.258 Value of Common Stock (Po): Po = PV (First 5-Years Dividends) + PV (P5) = $6.8412 + $5.258 = $12.10 (tables) 18. Present Value of First 4-Years Dividends: Year Dividend Present Value Interest Factor PVIF0.18,t Present Value t Dt 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: 7-19 Dt x PVIF0.18,t Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 (tables) 19.

a. Present Value of First 3-Years Dividends: Year t Present Value Interest Factor Dividend Dt PVIF0.16,t Present Value Dt x PVIF0.16,t 1 2.00 (1.25) = $2.50 0.862 $2.155 2 2.50 (1.15) = $2.875 0.743 $2.136 3 2.50 (1.15)2 = 3.306 0.641 $2.119 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 (tables) b. Recall that, in present value terms, the beginning of year 2 is the same as the end 7-20 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 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 (tables) 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 (tables) 21. P0 = $0.75(PVIF.2,1) + $0.863(PVIF.2,2) + $0.992(PVIF.2,3) + ($1.141 + $30)(PVIF.2,4) P0 = $0.75(.833) + $0.863(.694) + $0.992(.579) + ($1.141 + $30)(.482) = $16.81 (tables) 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 0 1 2 3 4 5 6 Earnings $1.00 1.50 2.25 3.375 4.219 5.273 6.592 7-21 Dividends $0.00 0.00 0.45 0.675 0.844 2.637 3.296 Chapter 7 Common Stock: Characteristics, Valuation and Issuance 7 7.119 3.560 P 6 = $3.56/(0.20 - 0.08) = $29.667 P 0 = $0 + $0.45(PVIF 0.2,2 ) +$0.675(PVIF 0.2,3 ) + $0.844(PVIF 0.2,4 ) + $2.637(PVIF 0.2,5 ) + ($3.296 + $29.667) (PVIF 0.2,6 ) = $13.21 (calculator accuracy) 23. P0 = $1(PVIF.2,1) + $1.20(PVIF.2,2) + $1.44(PVIF.2,3) +

$1.728((PVIF.2,4) + ($2.074 + $40)(PVIF.2,5) P0 = $1(.833) + $1.2(.694) + $1.44(.579) + $1.728(.482) + ($2.074 + $40)(.402) = $20.25 (tables) 24. D0 = $3 D1 = $3(1.15) = $3.45 D2 = $3.45(1.15) = $3.968 D3 = $3.97(1.15) = $4.563 D4 = $4.56(1.10) = $5.019 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) + $3.968(.797) + $4.563(.712) + $5.019(.636) + 1.4P0(.636) P0 = $115.73 (tables) 25. D0 = $0 D1 = $0 D2 = $2.00 7-22 Chapter 7 Common Stock: Characteristics, Valuation and Issuance D3 = $2.00(1.15) = $2.30 D4 = $2.30(1.15) = $2.645 D5 = $2.645(1.15) = $3.042 D6 = $3.042(1.10) = $3.346 P6 = estimated EPS x estimated P/E multiple = $7 x 15 = $105 P0 = $2(PVIF 0.15,2 ) + $2.30(PVIF 0.15,3 ) +$2.645(PVIF 0.15,4 ) + $3.042(PVIF 0.15,5 ) + ($3.346 + $105) (PVIF 0.15,6 ) = $52.89 (calculator accuracy); $52.86 (tables) 26. a. The dividend yield for AT&T is 3.6%; for Boeing it is 1.6%; and for Johnson & Johnson

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it is 2.5%. b. These firms differ with respect to expected earnings and dividend growth, with AT&T likely having the lowest expected growth and Boeing the highest expected growth. c. P/E for Boeing = 31 times P/E for Johnson and Johnson = 16 times d. Boeing’s higher expected growth rate more than offsets the relatively lower expected risk of AT&T. e. $39.43 (assuming these data come from the Wall Street Journal, which has a one day lag until publication; or $39.17 = ($39.43 - $0.26), the problem is interpreted to mean 7-23 Chapter 7 Common Stock: Characteristics, Valuation and Issuance the day before the closing price reported in the Wall Street Journal 27. 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 28. No

recommended solution. 29. P 0 = 0.12(PVIF 0.2,1 ) + .144(PVIF 0.2,2 ) + .173(PVIF 0.2,3 ) + 1.70(P 0 ) (PVIF 0.2,3 ) P 0 = .12(.833) + .144(.694) + .173(.579) + 1.7(.579)(P 0 ) P 0 = $19.11 (tables) 7-24