Solution manual financial management 10e by keown chapter 08

                                                                                                                                                                                                               CHAPTER 8 Stock Valuation                                                                                                                                                                                                                CHAPTER ORIENTATION This chapter continues the introduction of concepts underlying asset valuation began in Chapter We are specifically concerned with valuing preferred stock and common stock We also look at the concept of a stockholder’s expected rate of return on an investment CHAPTER OUTLINE I Preferred Stock A Features of preferred stock Owners of preferred stock receive dividends instead of interest Most preferred stocks are perpetuities (non-maturing) Multiple classes, each having different characteristics, can be issued Preferred stock has priority over common stock with regard to claims on assets in the case of bankruptcy Most preferred stock carries a cumulative feature that requires all past unpaid preferred stock dividends to be paid before any common stock dividends are declared Preferred stock may contain other protective provisions, such as granting voting rights in the event of non-payment of dividends Preferred stock may contain provisions to convert to a predetermined number of shares of common stock Some preferred stock contains provisions for an adjustable rate of return If there is a participation feature, it allows preferred stockholders to participate in earnings beyond the payment of the stated dividend 10 Payment-in-kind (PIK) preferred stock, grants the investor additional preferred stock instead of dividends for a given period of time Eventually cash dividends are paid 205 11 B Retirement features for preferred stock are frequently included a Callable preferred refers to a feature which allows preferred stock to be called, or retired, like a bond b A sinking fund provision requires the firm periodically set aside an amount of money for the retirement of its preferred stock Valuation of preferred stock (V ps): The value of a preferred stock equals the present value of all future dividends If the stock is nonmaturing, where dividends are expected in equal amount each year in perpetuity, the value may be calculated as follows: Vps = = II Common Stock A B Features of Common Stock As owners of the corporation, common shareholders have the right to the residual income and assets after bondholders and preferred stockholders have been paid Common stockholders are generally the only security holders with the right to elect the board of directors Preemptive rights (if granted) entitle the common shareholder to maintain a proportionate share of ownership in the firm Common stockholder’s liability as an owner of the corporation is limited to the amount invested in the stock Common stock’s value is equal to the present value of all future cash flows expected to be received by the stockholder Valuing common stock Company growth occurs by: a the infusion of new capital, or b the retention of earnings, which is called internal growth The internal growth rate of a firm equals: Return on equity  Although the bondholder and preferred stockholder are promised a specific amount each year, the dividend for common stock is based on the profitability of the firm and management's decision either to pay dividends or retain profits for reinvestment The common dividend typically increases with the growth in corporate earnings 206 The earnings growth of a firm should be reflected in a higher price for the firm's stock In finding the value of a common stock (V cs), we should discount all future expected dividends (Dl, D2, D3, , D) to the present at the required rate of return for the stockholder (k cs) That is: Vcs = D1 D2 D + + + (1  k cs ) (1  k cs ) (1  k cs )  If we assume that the amount of dividend is increasing by a constant growth rate each year, Dt D0 (l + g)t = where g = the growth rate D0 = the most recent dividend payment If the growth rate, g, is the same each year, t, and is less than the required rate of return, kcs, the valuation equation for common stock can be reduced to Vcs III = = Shareholder's Expected Rate of Return A The shareholder's expected rate of return is of great interest to financial managers because it tells about the investor’s expectations B Preferred stockholder's expected rate of return: If we know the market price of a preferred stock and the amount of the dividends to be received, the expected rate of return from the investment can be determined as follows: expected rate of return = or D k ps = P C Common stockholder's expected rate of return: The expected rate of return for common stock can be calculated from the valuation equations previously discussed 207 Assuming that dividends are increasing at a constant annual growth rate, g, we can show that the expected rate of return for common stock, kcs is k cs = + = + g Since dividend ÷ price is the "dividend yield," the Expected rate of return = + IV Appendix: The Relationship between Value and Earnings A Earnings and Value Relationship: The nongrowth firm Nongrowth firms retain no profits for reinvestment purposes a Investments are made to maintain status quo b Earnings and dividend growth stream is constant from year to year Value on nongrowth common stock, V ng: Vng  B EPS1 D  k cs k cs a Value of share changes in direct relationship with changes in earnings per share b Changes in the investor’s required rate of return will change share value Earnings and Value Relationship: The growth firm Growth firm reinvests profits back into the business Value of stock equals the present value of the dividend stream plus the present value of the future growth resulting from reinvesting future earnings Vcs  EPS1  NVDG k cs a NVDG is the net value of any dividend growth resulting from reinvestment of future earnings b Present value (PV 1) from reinvesting part of the firms earnings in year equals: PV1  a r EPS1 ROE  (r  EPS1 ) k cs Using the constant-growth model to value NVDG, 208 NVDG  PV1 k cs  g b The value of a share of stock is therefore: Vcs  EPS1 PV1  k cs k cs  g Value of stock is influenced by a Size of the firm’s EPS, b Percentage of profits retained, c Spread between return generated on new investments and the investor’s required rate of return 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 209 8-4 Fixed rate preferred stock has dividends that 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 10year 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 or 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 210 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) 8-2A Growth rate 8-3A Value (Vps) 8-4A = $6 12 = $50.00 = return on equity x retention rate = (16%)  (60%) = 9.6% = 14  $100 12 = $14 12 = $116.67 Expected Rate of Return kps 8-5A (a) (b) you = Expected return = Dividend = $1.95 = 0463, or 4.63% $42.16 Price $3.40 Dividend = = 085 = 8.5% $40 Price Given your percent required rate of return, the stock is worth $42.50 to Value = Dividend $3.40 = = $42.50 Required Rate of Return 08 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 211 8-6A Value (Vcs) = Dividend in Year Price in Year + (1  Required Rate) (1  Required Rate) $50 = $6 P1 + (1  15) (1  15) 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 percent ($1.50/$50) to earn a 15% rate of return 8-7A (a) (b) Expected rate of return (k cs ) Vcs = Dividend in Year growth + rate Market Price kcs = $2.00 + 10 $22.50 kcs = 1889, or 18.9% = $2.00 = $28.57 17  10 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 Value (Vcs) = Vcs = Vcs = 8-9A Growth rate Last Year Dividend (1  Growth Rate) (Required Rate  Growth Rate) $24.50 = return on equity x retention rate = (18%)  (40%) = 7.2% 8-10A Expected Rate of Return ( k cs ) = Last Year Dividend (1  Growth Rate) + Growth Rate Price k cs = + 0.095 k cs = 0.193, or 19.3% 212 8-11A Value (V cs) = Dividend in Year Price in Year + (1  Required Rate) (1  Required Rate) Vcs = $1.85 $42.50 + (1.11) (1.11) Vcs = $39.95 8-12A If the expected rate of return is represented by k cs : Current Price = Dividend in Year Price in Year + (1  k cs ) (1  k cs ) k cs = Dividend in Year  Price in Year - Current Price k cs = $2.84  $48.00 - $43.00 k cs = 0.1823, or 18.23% k ps = $3.60 Dividend = $33.00 Price k ps = 0.1091, or 10.91% (b) Value (Vps) = (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 8-13A (a) 8-14A.(a) (b) Dividend = $3.60 = $36 Required Rate of Return 0.10 Expected Rate of Return Investor's Value = Dividend in Year Growth + Rate Market Price = $1.32(1.08) + 0.08 $23.50 = 0.1407, or 14.07% = Dividend in Year Required Rate of Return - Growth Rate = $1.32(1.08) 0.105  0.08 = $57.02 213 (c) 8-15A (a) (b) 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) Dividend yield: Dividend  stock price = Using the nominal average returns of 12.2% for large-company stocks and the 3.8% nominal average return for U.S Treasury Bills as shown in Table 61, the computation would be as follows: = risk  free  market risk  free  + beta    rate  rate  return = 3.8% + 1.10  (12.2% - 3.8%) = 13.04% Expected rate of return = Dividend in Year Growth + Rate Market Price 13.04% = $1.12 + g $49 Expected rate of return (c) $1.12 = 0.0229, or 2.29% $49 1304 = 0229 + g g = 1075, or 10.75% 8-16A Johnson & Johnson EPS (diluted) Dividend 2003 $2.40 $0.925 2002 $2.16 $0.795 Stock Price (6/24/04): $55.75 Growth rate: $2.40 = $1.39 (1 + i) i = 1463, or 14.63% D1 k cs =  P  g $0.925 (1.1463)  1463 k cs =  $55.75 k cs = .0190, or 1.90% 214 2001 $1.84 $0.70 2000 $1.61 $0.62 1999 $1.39 $0.55 8-17A k ps = $4.50 Dividend = $25 Price k ps = 0.18, or 18% (b) Value (Vps) = (c) The investor's required rate of return (14 percent) is less than the expected rate of return for the investment (18 percent) Also, the value of the stock to the investor ($32.14) exceeds the existing market price ($25), so buy the stock (a) Investor's Value (a) Dividend = $4.50 = $32.14 Required Rate of Return 0.14 8-18A (b) (c) 8-19A (a) Expected Rate of Return Dividend in Year Required Rate of Return - Growth Rate = $2.30(1.05) 0.15  0.05 = $24.15 = Dividend in Year Growth + Rate Market Price = $2.30(1.05) + 0.05 $33 = 0.1232, or 12.32% No, the expected rate of return (12.32%) is less than your required rate of return (15 percent) Also, your value of the stock ($24.15) is less than the current market price ($33) Growth rate = = (b) = return on equity x retention rate (17%)  (30%) = 5.1% (i) If retention rate is 40%: Growth rate = = return on equity x retention rate (17%)  (40%) = 6.8% (ii) If retention rate is 25%: Growth rate = = return on equity x retention rate (17%)  (25%) = 4.25% 215 8-20A (a) (b) Expected rate of return (k cs ) = Dividend in Year growth + rate Market Price kcs = $1.75(1  0.04) + 0.04 $29.50 kcs = 1017, or 10.17% Vcs $1.75(1  0.04) = $18.20 14  0.04 = No, not purchase the stock The expected return is less than your required rate of return Also, the stock is selling for $29.50, while it is only worth $18.20 to you SOLUTION TO INTEGRATIVE PROBLEM Value (Vb) based upon your required rate of return: Bond: Vb = $140 12  t 1 (1  12) t + $1,000 (1  12)12 12 12 140 1000 CPT  ANSWER  $12 ­1123.89 Preferred Stock: Vps =  t 1 (1  14) t However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to Vps = Dividend Required Rate of Return = $12 14 = $85.71 Common Stock: Step 1: Determine Growth Rate 216 10 $4.00 =    t 1 $0.00 (1  k b ) t  $8.00 (1  k b )10 10  CPT ANSWER  7.177% Growth Rate (g) = 7.177% Step 2: Vcs Solve for Value =   t 1 $3(1  07177) t (1  20) t If the growth rate (g) is assumed constant, the equation may be reduced to Vcs = Dividend at Year End Required Rate of Return  Growth Rate = D1 k cs  g = $3(1  07177 ) 20  07177 = $25.08 Bond Preferred Stock Common Stock Your Value $1,123.89 85.71 25.08 Selling Price $1,200.00 80.00 25.00 The bond should not be purchased because its market value is selling above its value to you You can choose between the preferred stock and the common stock, because both have market values less than their values to you 217 Bond: Value (Vb) 12 =    t 1 $140 (1  14) t  $1,000 (1  14)12 ANSWER ­1000.00 12 14 140 1000  CPT You would not buy the bond; it is not worth $1,200.00 Preferred Stock: Vps = $12 16 = $75.00 Do not buy Your value is less than what you would have to pay for the stock($80) Common Stock: Vcs = $3(1  07177 ) 18  07177 = $29.71 Buy Your value is greater than what you would have to pay for the stock($25) Assuming a growth rate of 12 percent: Vcs  3(1  12)  $42.00 20  12 Buy the stock Because of the expected increase in future dividends, the stock is now worth more to you ($42) than you would have to pay for it ($25) –assuming that the selling price did not increase also 218 Solutions to Problem Set B 8-1B Value (Vps) 8-2B Growth rate 8-3B Value (Vps) 8-4B = $7 10 = $70.00 = return on equity x retention rate = (24%) × (70%) = 16.8% = 16  $100 12 = $16 12 = $133.33 Expected Rate of Return 8-5B (a) (b) kps = Dividend = $2.35 = 0426, or 4.26% $55.16 Price Expected return = $3.25 Dividend = = 0844 , or 8.44% $38.50 Price Given your percent required rate of return, the stock is worth $40.63 to you Value = Dividend $3.25 = = $40.63 Required Rate of Return 08 Since the expected rate of return (8.44%) is greater than your required rate of return (8%), or since the current market price ($38.50) is less than the value ($40.63), the stock is undervalued and you should buy 8-6B Value (Vcs) = Dividend in Year (1  Required Rate) $52.75 = $6.50 P1 + (1  16) (1  16) + Price in Year (1  Required Rate) Rearranging and solving for P1: P1 = $52.75 (1.16) - $6.50 P1 = $54.69 The stock would have to increase $1.94 ($54.69 - $52.75), or 3.68 percent, ($1.94/$52.75) to earn a 16% rate of return 219 8-7B (a) (b) 8-8B 8-9B Expected rate of return (k cs ) = k cs = $2.50 + 105 $23.00 k cs = 0.2137, or 21.37% Dividend in Year Market Price Growth Rate $2.50 = $38.46 17  105 The expected rate of return exceeds your required rate of return, which means that the value of the security to you is greater than the current market price Thus, you should buy the stock Vcs = Value (Vcs) = Last Year Dividend (1  Growth Rate) (Required Rate  Growth Rate) Vcs = $3.75(1  06) 20  06 Vcs = $28.39 Growth rate = return on equity x retention rate (24%)  (60%) = 14.4% = 8-10B + Expected Rate of Return ( k cs ) = Last Year Dividend (1  Growth Rate) + Price Growth Rate = k cs 8-11B 8-12B Value (Vcs) $3.00(1.085) $33.84 + 0.085 = 0.1812, or 18.12% Dividend in Year (1  Required Rate) = Vcs = $1.85 (1.12) Vcs = $37.37 + + Price in Year (1  Required Rate) $40.00 (1.12) If the expected rate of return is represented by k cs : Current Price = Dividend in Year (1  k cs ) + Price in Year (1  k cs ) k cs = Dividend in Year  Price in Year - Current Price k cs = $2.00  $47.00 - $44.00 220 = k cs 8-13B (a) k ps = 0.1136, or 11.36% $4.00 Dividend = = 11.43% $35.00 Price Dividend Required Rate of Return = $4.00 = $40 0.10 (b) Value (Vps ) = (c) The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.43 percent) Also, the value of the stock to the investor ($40) exceeds the existing market price ($35) The investor should buy the stock 8-14B (a) (b) (c) 8-15B (a) (b) Expected Rate of Return Investor's Value Dividend in Year Market Pirce + = $1.00(1.08) $25.00 = 0.1232, or 12.32% = Dividend in Year Required Rate of Return  Growth Rate = $1.00(1.08) 0.11  0.08 + 0.08 = $36.00 Yes, the expected rate of return is greater than your required rate of return (12.32 percent versus 11 percent) Also, your value of the stock ($36.00) is higher than the current market price ($25.00) Dividend yield: Dividend  stock price = $1.20 = 2.22% $54 Using the nominal average returns of 12.2% for large-company stocks and the 3.8% nominal average return for U.S Treasury Bills as shown in Table 61, the computation would be as follows: Expected rate of return (c) =  market risk  free    rate   return = risk  free + beta  rate = 3.8% + 0.90  (12.2% - 3.8%) = 11.36% Expected rate of return = Dividend in Year Market Price 11.36% = $1.20 + g $54 1136 = 0222 + g g = 0914, or 9.14% 221 + Growth Rate 8-16B Note to Instructor: Before the 10th edition of Financial Management was completed, we had not verified the earnings per share data for First Union Corporation After the text went to production, we realized that First Union was merged into Wachovia Bank in 2001 We then planned to use the Wachovia earnings per share data, only to discover the significant volatility of the firm’s earnings over the past five years, which appears as follows: Earnings per share (diluted) 2003 $3.18 2002 $2.60 2001 $1.45 2000 $0.07 1999 $3.33 Since Wachovia’s earnings per share has actually decreased over the last five years, the growth rate in earnings per share is =1.146 percent (using years to compute the growth rate) Clearly, the historical earnings per share not provide a reasonable estimate of future earnings per share, which regrettably makes the problem difficult to use without having a meaningful growth estimate Thus, the problem can only be used to show that relying on historical data does not always provide reasonable results $2.25 $19.50 k ps = Dividend Price k ps = 0.1154, or 11.54% (b) Value (Vps) = (c) The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.54 percent) Also, the value of the stock to the investor, ($22.50) exceeds the existing market price ($19.50), so buy the stock (a) Investor's Value 8-17B (a) = Dividend = $2.25 = $22.50 Required Rate of Return 0.10 8-18B (b) (c) Expected Rate of Return = Dividend in Year Required Rate of Return - Growth Rate = $1.95(1.05) 0.12  0.05 = $29.25 = Dividend in Year Growth + Rate Market Price = $1.95(1.05) + 0.05 $26 = 0.1288, or 12.88% Yes, the expected rate of return (12.88%) is greater than your required rate of return (12 percent) Also, your value of the stock ($29.25) is greater than the current market price ($26) 222 8-19B (a) (b) Growth rate = return on equity x retention rate = (13%)  (20%) = 2.6% (i) If retention rate is 35%: Growth rate = return on equity x retention rate = (13%)  (35%) = 4.55% (ii) If retention rate is 13%: Growth rate 8-20B (a) (b) = return on equity x retention rate = (13%)  (13%) = 1.69% Expected rate of return (k cs ) = Dividend in Year growth + rate Market Price kcs = $3.15(1  0.07) + 0.07 $33.75 kcs = 1699, or 16.99% Vcs = $3.15(1  0.07) = $84.26 11  0.07 Yes, purchase the stock The expected return is significantly more than your required rate of return Also, the stock is selling for $33.75, while it is worth $84.26 to you Solutions to Appendix 8A 8A-1 Using the NVDG model, Vcs = EPS1 k cs where kcs = the investor's required rate of return EPS1 = the firm's earning per share in year g = the growth rate, which is the firm's earnings retention rate times its return on equity PV1 =  r x EPS1 x ROE    - (r x EPS1) k cs   r = the firm's earnings retention rate ROE = the firm's return on equity investment + 223 PV1 k cs  g For our problem, PV1 = = $4.0625 - $3.25 = $0.8125 Vcs = and  (0.65) x ($5) x (0.20)  - (0.65 x $5)   0.16   $5 $0.8125  16 16  (0.65)(0.20) = $31.25 + $27.08 = $58.33 Using the more traditional dividend-growth model, we get: Vcs = D1 k cs  g Since D1 = EPS1(1 - the retention rate), and g = the retention rate x return on equity ($5)(1  65) = $1.75 = $58.33 16  (.65)(.20) 03 8A-2 Given the EPS1 is expected to be $7 and the investor's required rate of return is 18 percent, the value of the stock, assuming no growth opportunities would be: EPS1 $7 Vcs = = $38.89  k cs 18 Vcs = where kcs = the investor's required rate of return EPS1 = the firm's earning per share in year To compute the present value of the growth opportunities, NVDG, for each scenario, we use the following equation: NVDG = where PV1 = g = r ROE = = PV1 k cs  g  r x EPS1 x ROE    - (r x EPS1) k cs   the growth rate, which is the firm's earnings retention rate times its return on equity the firm's earnings retention rate the firm's return on equity investment 224 Given the different possible retention rates and ROEs, we may solve for the respective PV1s The results are as follows: Possible ROEs 16% 18% 24% Different Retention Rates 0% 30% 0.00 -0.23 0.00 0.00 0.00 0.70 60% -0.47 0.00 1.40 We next calculate the NVDG for each scenario by dividing the above PV1 values by kcs - g, which gives the following results: Possible Different Retention Rates ROEs 0% 30% 60% 16% 0.00 -1.77 -5.56 18% 0.00 0.00 0.00 24% 0.00 6.48 38.89 Adding the $38.89 price, assuming no growth, to the above NVDGs, we get: Possible ROEs 16% 18% 24% Different Retention Rates 0% 30% 38.89 37.12 38.89 38.89 38.89 45.37 60% 33.33 38.89 77.78 Thus, our results show that value is created only when management reinvests at above the investor's required rate of return That is, growth may actually decrease the firm's value if the profitability of the new investments are not adequate enough to satisfy the investor's required returns 225 ... Growth + Rate Market Price = $1.32(1 .08) + 0 .08 $23.50 = 0.1407, or 14.07% = Dividend in Year Required Rate of Return - Growth Rate = $1.32(1 .08) 0.105  0 .08 = $57.02 213 (c) 8-15A (a) (b) Yes,... Dividend in Year Market Pirce + = $1.00(1 .08) $25.00 = 0.1232, or 12.32% = Dividend in Year Required Rate of Return  Growth Rate = $1.00(1 .08) 0.11  0 .08 + 0 .08 = $36.00 Yes, the expected rate of... 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) 8-2A Growth rate 8-3A Value (Vps)