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Source: http://www.doksinet 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 Source: http://www.doksinet 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 (ie, 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 Source: http://www.doksinet 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) 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 Source: http://www.doksinet 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 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance SOLUTIONS TO PROBLEMS: 1. a. Po = D1/(ke - g) g = 0.07 Do = $170 ke = 12 Dl = Do(1 + g) = 1.70(1 + 007) = $1819 Po = 1.819/(012 - 007) = $3638 b. g = 0.09 Do = $170 ke = 012 D1 = 1.70(1 + 009) =

$1853 Po = 1.853/(012 - 009) = $6177 c. g = 0.065 Do = $170 ke = 012 D1 = $1.70(1 + 0065) = $18105 Po = $1.8105/(012 - 0065) = $3292 2. a. Po = D1/(ke - g) g = .06 Do = $5 ke = 12 Dl = Do(1 + g) = 5(1 + .06) = $530 Po = 5.30/(12 - 06) = $8833 b. g = .06 D1 = $530 ke = 14 Po = 5.30/(14 - 06) = $6625 c. g = 06 Dl = $530 ke = 16 Po = 5.30/(16 - 06) = $53 7-5 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance d. g = .06 D1 = $530 ke = 06 Po = 5.30/(06 - 06) = Undefined ke = g, which violates assumption of constant-growth model. e. g = .06 D1 = $530 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 = 125/25 + 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 Source: http://www.doksinet 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) = $7504 P6 = 7.504/(12 - 00) = $62533 Present Value of P6: PV(P6) = P6/(1 + ke)6 = 62.533/(1 + 12)6 = 62533 x PVIF12,6 = 62.533 X 507 = $31704 Value of Common Stock (P0): P0 = PV (First 6-Years Dividends) + PV(P6) = 25.651 + 31704 = $5736 (tables) 5. FVn = PVo(1 + g)n PVo = $.70 FV5 = $1.30 n=5 7-7 Source: http://www.doksinet 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 - 1842 x (14% - 13%) = 132% 1.925 - 1842 Therefore g = .132 ( or 132% -- 1318% by calculator) Po = D1/(ke - g) Do = $1.30 ke = .20 D1 = Do(1 + g) = 1.30(1 + 132) = $14716 Po = 1.4716/(20 - 132) = $2164 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) = 300(PVIF15,1) = 3.00(870) = $2610 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 Source: http://www.doksinet 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) = $4118 P4 = D5/(ke - g2) = 4.118/(15 - 06) = $45756 Present Value of P4 PV(P4) = P4/(1 + ke)4 = P4 x PVIF.15,4 = 45.756 x 572 = $26172 Value of Common Stock: Po = PV(D1) + PV(Next 3-Years Dividends) + PV(P4) = $2.610 + $7039 + $26172 = $3582 (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 Source: http://www.doksinet 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) = $3896 P4 = 3.896/(15 - 06) = $43289 Present Value of P4 PV(P4) = 43.289 x 572 = $24761 Value

of Common Stock: Po = $2.610 + $6789 + $24761 = $3416 (tables) 7. P0 = D/ke = $2.00/016 = $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 Source: http://www.doksinet 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) = $2391 P4 = 2.391/(14 - 05) = $26567 Present Value of P4: PV(P4) = P4/(1 + ke)4 = $26.567/(1 + 14)4 = $26.567(PVIF14,4) = $26567 x 0592 = $15728 Value of Common Stock (Po): Po = PV(First 4-Years Dividends) + PV(P4) = $5.614 + $15728 = $2134 (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 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 Source: http://www.doksinet 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) = $2976 P6 = D7/(ke - g3) = 2.976/(18 - 05) = $22892 7-12 $3.466 Source: http://www.doksinet 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 0370 = $8470 Value of Common Stock Po = PV(First 3-Years Dividends) + PV(Next 3-Years Dividends) + PV(P6) = $4.275 + $3466 + $8470 = $1621 (tables) 10. a. FVn = PVo(1+ g)n PVo = $2.00; FV6 = $400; n = 6 4.00 = 200(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 = $2240 2 2.00(1 + 12)2 = $2509 3 2.00(1 + 12)3 = $28l0 4 2.00(1 + 12)4 = $3147 7-13 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance 5 2.00(1 + 12)5 = $3525 6 2.00(1 + 12)6 = $3948 *Note: The (1 + 0.12)t factors can be obtained from Table I, ie, (1 + 0.12)t = FVIF12,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/(018 - 012) = $3733 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 Source: http://www.doksinet 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 + 006) = $4185 P6 = $4.185/(018 - 006) = $34875 Present Value of P6: PV(P6) = P6/(1 + ke)6 = $34.875/(1 +

018)6 = $34875 x PVIF(018,6) = $34.875 X 0370 = $12904 Value of Common Stock (Po) Po = PV(First 6-Years Dividends) + PV(P6) = $10.034 + $12904 = $2294 (tables) 11. D0 = $1.50 D1 = $1.50(115) = $1725 D2 = $1.72(115) = $1984 D3 = $1.98(115) = $2281 D4 = $2.28(110) = $2509 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) + $1984(797) + $2281(712) + $2509(636) + 1.5P0(636) P0 = $137.85 (tables) 12. The dividend at the end of two years = $1 (FVIF020,2) = $144 7-15 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance D3 = $1.44(106) = $1526 D4 = $1.53(106) = $1618 D5 = $1.62(106) = $1715 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/(015 - 006) = $1906 13. a. P0 = $340(PVIF15,1) + $374(PVIF15,2) + $411(PVIF15,3) + [$4.36/(15 - 06](PVIF15,3) = $40.36 b. Price at the beginning of year 3 = [$4.11 + $436/(15 -

06)](PVIF15,1) = $4572 c. $4036 - 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 Source: http://www.doksinet 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(115)t PVIF(024,t) for D1 - D3 1 $3.00 (115)1 = $3.45 0.806 2.781 2 $3.00 (115)2 = $3.968 0.650 2.579 3 3.00(115)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) = $5563 (106) = $5897 7-17 Dt x PVIF(0.24,t) 2.353 $10.104 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance P4 = $5.897/(024 - 006) = $32760 Present Value of P4: PV(P4) = P4/(1 + ke)4 = $32.760 x PVIF(024,4) = $32.760 x 0423 = $13857 Po = PV (First 4-Years Dividends) + PV (P4) = $10.104 + $13857 = $2396 (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(109)1 = $218 0.806 $1.757 2 2.00(109)2 = $2376 0.650 1.544 3 2.00(109)3 = $2590 0.524

1.357 4 2.590(107)1= $2771 0.423 1.172 5 2.590(107)2 = $2965 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) = $3084 P5 = $3.084 / (024 - 004) = $1542 7-18 Dt x PVIF(0.24,t) $6.841 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance Present Value of P5: PV(P5) = P5 / (1 + ke)5 = $15.42 x PVIF(024,5) = $15.42 x 0341 = $5258 Value of Common Stock (Po): Po = PV (First 5-Years Dividends) + PV (P5) = $6.8412 + $5258 = $1210 (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) = $150 (105) = $1575 P4 = $1.575/(018 - 005) = $12115 Present Value of P4: 7-19 Dt x PVIF0.18,t Source:

http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance PV(P4) = P4/(1 + ke)4 = $12.115 x PVIF(018,4) = $12.115 x 0516 = $6251 Po = PV (First 4-Years Dividends) + PV(P4) = $1.411 + $6251 = $766 (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 (125) = $2.50 0.862 $2.155 2 2.50 (115) = $2.875 0.743 $2.136 3 2.50 (115)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) = $3306 (106) = $3504 P3 = $3.504/(016 - 006) = $3504 Present Value of P3: PV(P3) = P3/(1 + ke)3 = $35.04 x PVIF(016,3) = $35.04 x 0641 = $2246 Po = PV (First 3-Years Dividends) + PV(P3) = $6.410 + $2246 = $2887 (tables) b. Recall that, in present value terms, the beginning of year 2 is the same as the end 7-20 Source: http://www.doksinet 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(PVIF016,2) + P3(PVIF016,2) = $2.875(0862) + $3306(0743) + $3504(0743) = $30.97 (tables) 20. D1 = $1.00 D2 = $2.00 D3 = D2 (1 + g) = $2.00 (110) = $220 P3 = 1.5 P0 P0 = PV(D1) + PV(D2) + PV (D3) + PV (P3) = $1.00 (0833) + $200 (0694) + $220 (0579) + (1.5 P0)(0579) P0 = $3.495 + 0869 P0 P0 = $26.68 (tables) 21. P0 = $0.75(PVIF2,1) + $0863(PVIF2,2) + $0992(PVIF2,3) + ($1.141 + $30)(PVIF2,4) P0 = $0.75(833) + $0863(694) + $0992(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 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance 7 7.119 3.560 P 6 =

$3.56/(020 - 008) = $29667 P 0 = $0 + $0.45(PVIF 02,2 ) +$0675(PVIF 02,3 ) + $0844(PVIF 02,4 ) + $2637(PVIF 02,5 ) + ($3.296 + $29667) (PVIF 02,6 ) = $1321 (calculator accuracy) 23. P0 = $1(PVIF2,1) + $120(PVIF2,2) + $144(PVIF2,3) + $1.728((PVIF2,4) + ($2074 + $40)(PVIF2,5) P0 = $1(.833) + $12(694) + $144(579) + $1728(482) + ($2.074 + $40)(402) = $20.25 (tables) 24. D0 = $3 D1 = $3(1.15) = $345 D2 = $3.45(115) = $3968 D3 = $3.97(115) = $4563 D4 = $4.56(110) = $5019 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) + $3968(797) + $4563(712) + $5019(636) + 1.4P0(636) P0 = $115.73 (tables) 25. D0 = $0 D1 = $0 D2 = $2.00 7-22 Source: http://www.doksinet Chapter 7 Common Stock: Characteristics, Valuation and Issuance D3 = $2.00(115) = $230 D4 = $2.30(115) = $2645 D5 = $2.645(115) = $3042 D6 = $3.042(110) = $3346 P6 = estimated EPS x estimated P/E multiple = $7 x 15 = $105 P0 = $2(PVIF 0.15,2 ) + $230(PVIF 015,3 )

+$2645(PVIF 015,4 ) + $3.042(PVIF 015,5 ) + ($3346 + $105) (PVIF 015,6 ) = $52.89 (calculator accuracy); $5286 (tables) 26. a The dividend yield for AT&T is 36%; for Boeing it is 16%; and for Johnson & Johnson 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. $3943 (assuming these data come from the Wall Street Journal, which has a one day lag until publication; or $39.17 = ($3943 - $026), the problem is interpreted to mean 7-23 Source: http://www.doksinet 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 = 07 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 = 012(PVIF 02,1 ) + 144(PVIF 02,2 ) + 173(PVIF 02,3 ) + 1.70(P 0 ) (PVIF 02,3 ) P 0 = .12(833) + 144(694) + 173(579) + 17(579)(P 0 ) P 0 = $19.11 (tables) 7-24