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After reading this chapter, students should be able to: • Identify some of the more important rights that come with stock ownership and define the following terms: proxy, proxy fight, takeover, and preemptive right. • Briefly explain why classified stock might be used by a corporation and what founders’ shares are. • Differentiate between closely held and publicly owned corporations and list the three distinct types of stock market transactions. • Determine the value of a share of common stock when: (1) dividends are expected to grow at some constant rate, (2) dividends are expected to remain constant, and (3) dividends are expected to grow at some super-normal, or nonconstant, growth rate. • Calculate the expected rate of return on a constant growth stock. • Apply the total company (corporate value) model to value a firm in situations when the firm does not pay dividends or is privately held. • Explain why a stock’s intrinsic value might differ between the total company model and the dividend growth model. • Explain the following terms: equilibrium, marginal investor, and Efficient Markets Hypothesis (EMH); distinguish among the three levels of market efficiency; briefly explain the implications of the EMH on financial decisions; and discuss the results of empirical studies on market efficiency and the implication of behavioral finance on those results. • Read and understand the stock market page given in the daily newspaper. • Explain the reasons for investing in international stocks and identify the “bets” an investor is making when he does invest overseas. • Define preferred stock, determine the value of a share of preferred stock, or given its value, calculate its expected return.
After reading this chapter, students should be able to: • Identify some of the more important rights that come with stock ownership and define the following terms: proxy, proxy fight, takeover, and preemptive right. • Briefly explain why classified stock might be used by a corporation and what founders’ shares are. • Differentiate between closely held and publicly owned corporations and list the three distinct types of stock market transactions. • Determine the value of a share of common stock when: (1) dividends are expected to grow at some constant rate, (2) dividends are expected to remain constant, and (3) dividends are expected to grow at some super- normal, or nonconstant, growth rate. • Calculate the expected rate of return on a constant growth stock. • Apply the total company (corporate value) model to value a firm in situations when the firm does not pay dividends or is privately held. • Explain why a stock’s intrinsic value might differ between the total company model and the dividend growth model. • Explain the following terms: equilibrium, marginal investor, and Efficient Markets Hypothesis (EMH); distinguish among the three levels of market efficiency; briefly explain the implications of the EMH on financial decisions; and discuss the results of empirical studies on market efficiency and the implication of behavioral finance on those results. • Read and understand the stock market page given in the daily newspaper. • Explain the reasons for investing in international stocks and identify the “bets” an investor is making when he does invest overseas. • Define preferred stock, determine the value of a share of preferred stock, or given its value, calculate its expected return. Learning Objectives: 8 - 1 Chapter 8 Stocks and Their Valuation LEARNING OBJECTIVES This chapter provides important and useful information on common and preferred stocks. Moreover, the valuation of stocks reinforces the concepts covered in both Chapters 6 and 7, so Chapter 8 extends and reinforces those chapters. We begin our lecture with a discussion of the characteristics of common stocks, after which we discuss how stocks are valued in the market and how stock prices are reported in the press. We conclude the lecture with a discussion of preferred stocks. The details of what we cover, and the way we cover it, can be seen by scanning Blueprints Chapter 8. For other suggestions about the lecture, please see the “Lecture Suggestions” in Chapter 2, where we describe how we conduct our classes. DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods) Lecture Suggestions: 8 - 2 LECTURE SUGGESTIONS 8-1 True. The value of a share of stock is the PV of its expected future dividends. If the two investors expect the same future dividend stream, and they agree on the stock’s riskiness, then they should reach similar conclusions as to the stock’s value. 8-2 A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the following ways: 1. All three derive their values from a series of cash inflows coupon payments from the perpetual bond, and dividends from both types of stock. 2. All three are assumed to have indefinite lives with no maturity value (M) for the perpetual bond and no capital gains yield for the stocks. 8-3 Yes. If a company decides to increase its payout ratio, then the dividend yield component will rise, but the expected long-term capital gains yield will decline. 8-4 No. The correct equation has D 1 in the numerator and a minus sign in the denominator. 8-5 a. The average investor in a listed firm is not really interested in maintaining his proportionate share of ownership and control. If he wanted to increase his ownership, he could simply buy more stock on the open market. Consequently, most investors are not concerned with whether new shares are sold directly (at about market prices) or through rights offerings. However, if a rights offering is being used to effect a stock split, or if it is being used to reduce the underwriting cost of an issue (by substantial underpricing), the preemptive right may well be beneficial to the firm and to its stockholders. b. The preemptive right is clearly important to the stockholders of closely held firms whose owners are interested in maintaining their relative control positions. Answers and Solutions: 8 - 3 ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1 D 0 = $1.50; g 1-3 = 5%; g n = 10%; D 1 through D 5 = ? D 1 = D 0 (1 + g 1 ) = $1.50(1.05) = $1.5750. D 2 = D 0 (1 + g 1 )(1 + g 2 ) = $1.50(1.05) 2 = $1.6538. D 3 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 ) = $1.50(1.05) 3 = $1.7364. D 4 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) = $1.50(1.05) 3 (1.10) = $1.9101. D 5 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) 2 = $1.50(1.05) 3 (1.10) 2 = $2.1011. 8-2 D 1 = $0.50; g = 7%; k s = 15%; 0 P ˆ = ? .25.6$ 07.015.0 50.0$ gk D P ˆ s 1 0 = − = − = 8-3 P 0 = $20; D 0 = $1.00; g = 10%; 1 P ˆ = ?; k s = ? 1 P ˆ = P 0 (1 + g) = $20(1.10) = $22. k s = 0 1 P D + g = $20 )$1.00(1.10 + 0.10 = $20 $1.10 + 0.10 = 15.50%. k s = 15.50%. 8-4 D p = $5.00; V p = $60; k p = ? k p = p p V D = $60.00 $5.00 = 8.33%. 8-5 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2. b. 0 1 2 3 | | | | 1.25 1.50 1.80 1.89 37.80 = 05.010.0 89.1 − The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows: Answers and Solutions: 8 - 4 SOLUTIONS TO END-OF-CHAPTER PROBLEMS k s = 10% g s = 20% g s = 20% g n = 5% .80.37$ 05.010.0 )05.1(80.1$ = − c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF 0 = 0, CF 1 = 1.50, CF 2 = 1.80 + 37.80 = 39.60, I = 10, and then solve for NPV = $34.09. 8.6 The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm. Firm Value = FCF 1 /(WACC – g) Firm Value = $150,000,000/(0.10 - 0.05) Firm Value = $3,000,000,000. To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares outstanding. Equity Value per share = Equity Value/Shares outstanding Equity Value per share = $3,000,000,000/50,000,000 Equity Value per share = $60. Each share of common stock is worth $60, according to the corporate valuation model. 8-7 a. 0 1 2 3 4 | | | | | 3,000,000 6,000,000 10,000,000 15,000,000 Using a financial calculator, enter the following inputs: CF 0 = 0; CF 1 = 3000000; CF 2 = 6000000; CF 3 = 10000000; CF 4 = 15000000; I = 12; and then solve for NPV = $24,112,308. b. The firm’s terminal value is calculated as follows: .000,000,321$ 07.012.0 )07.1(000,000,15$ = − Answers and Solutions: 8 - 5 WACC = 12% c. The firm’s total value is calculated as follows: 0 1 2 3 4 5 | | | | | | 3,000,000 6,000,000 10,000,000 15,000,000 16,050,000 PV = ? 321,000,000 = 07.012.0 000,050,16 − Using your financial calculator, enter the following inputs: CF 0 = 0; CF 1 = 3000000; CF 2 = 6000000; CF 3 = 10000000; CF 4 = 15000000 + 321000000 = 336000000; I = 12; and then solve for NPV = $228,113,612. d. To find Barrett’s stock price, you need to first find the value of its equity. The value of Barrett’s equity is equal to the value of the total firm less the market value of its debt and preferred stock. Total firm value $228,113,612 Market value, debt + preferred 60,000,000 (given in problem) Market value of equity $168,113,612 Barrett’s price per share is calculated as: .81.16$ 000,000,10 612,113,168$ = 8-8 FCF = EBIT(1 – T) + Depreciation – esexpenditur Capital - ∆ capital working operating Net = $500,000,000 + $100,000,000 - $200,000,000 - $0 = $400,000,000. Firm value = gWACC FCF − = 06.010.0 000,000,400$ − = 04.0 000,000,400$ = $10,000,000,000. This is the total firm value. Now find the market value of its equity. MV Total = MV Equity + MV Debt $10,000,000,000 = MV Equity + $3,000,000,000 MV Equity = $7,000,000,000. This is the market value of all the equity. Divide by the number of shares to find the price per share. $7,000,000,000/200,000,000 = $35.00. Answers and Solutions: 8 - 6 g n = 7% WACC = 12% 8-9 a. Terminal value = 07.013.0 )07.1(40$ − = 06.0 80.42$ = $713.33 million. b. 0 1 2 3 4 | | | | | -20 30 40 42.80 ($ 17.70) 23.49 522.10 753.33 $527.89 Using a financial calculator, enter the following inputs: CF 0 = 0; CF 1 = -20; CF 2 = 30; CF 3 = 753.33; I = 13; and then solve for NPV = $527.89 million. c. Total value t=0 = $527.89 million. Value of common equity = $527.89 - $100 = $427.89 million. Price per share = 00.10 89.427$ = $42.79. 8-10 The problem asks you to determine the value of 3 P ˆ , given the following facts: D 1 = $2, b = 0.9, k RF = 5.6%, RP M = 6%, and P 0 = $25. Proceed as follows: Step 1: Calculate the required rate of return: k s = k RF + (k M - k RF )b = 5.6% + (6%)0.9 = 11%. Step 2: Use the constant growth rate formula to calculate g: %.303.0g g 25$ 2$ 11.0 g P D k ˆ 0 1 s == += += Step 3: Calculate 3 P ˆ : 3 P ˆ = P 0 (1 + g) 3 = $25(1.03) 3 = $27.3182 ≈ $27.32. Alternatively, you could calculate D 4 and then use the constant growth rate formula to solve for 3 P ˆ : D 4 = D 1 (1 + g) 3 = $2.00(1.03) 3 = $2.1855. 3 P ˆ = $2.1855/(0.11 – 0.03) = $27.3182 ≈ $27.32. 8-11 V p = D p /k p ; therefore, k p = D p /V p . Answers and Solutions: 8 - 7 33.713V 3 op = g n = 7% WACC = 13% × 1/1.13 × 1/(1.13) 2 × 1/(1.13) 3 a. k p = $8/$60 = 13.3%. b. k p = $8/$80 = 10.0%. c. k p = $8/$100 = 8.0%. d. k p = $8/$140 = 5.7%. 8-12 .75.23$ 20.0 75.4$ 05.015.0 )95.0(5$ )05.0(15.0 )]05.0(1[5$ gk )g1(D gk D P ˆ s 0 s 1 0 == + = −− −+ = − + = − = 8-13 a. k i = k RF + (k M - k RF )b i . k C = 9% + (13% - 9%)0.4 = 10.6%. k D = 9% + (13% - 9%)(-0.5) = 7%. Note that k D is below the risk-free rate. But since this stock is like an insurance policy because it “pays off” when something bad happens (the market falls), the low return is not unreasonable. b. In this situation, the expected rate of return is as follows: C k ˆ = D 1 /P 0 + g = $1.50/$25 + 4% = 10%. However, the required rate of return is 10.6 percent. Investors will seek to sell the stock, dropping its price to the following: .73.22$ 04.0106.0 50.1$ P ˆ C = − = At this point, %6.10%4 73.22$ 50.1$ k ˆ C =+= , and the stock will be in equilibrium. 8-14 Calculate the dividend cash flows and place them on a time line. Also, calculate the stock price at the end of the supernormal growth period, and include it, along with the dividend to be paid at t = 5, as CF 5 . Then, enter the cash flows as shown on the time line into the cash flow register, enter the required rate of return as I = 15, and then find the value of the stock using the NPV calculation. Be sure to enter CF 0 = 0, or else your answer will be incorrect. D 0 = 0; D 1 = 0; D 2 = 0; D 3 = 1.00; D 4 = 1.00(1.5) = 1.5; D 5 = 1.00(1.5) 2 = 2.25; D 6 = 1.00(1.5) 2 (1.08) = $2.43. 0 P ˆ = ? 0 1 2 3 4 5 6 | | | | | | | 1.00 1.50 2.25 2.43 0.658 +34.71 = 0.858 18.378 36.96 Answers and Solutions: 8 - 8 k s = 15% g s = 50% g n = 8% 08.015.0 43.2 − × 1/(1.15) 3 × 1/(1.15) 4 × 1/(1.15) 5 $19.894 = 0 P ˆ 5 P ˆ = D 6 /( k s - g) = $2.43/(0.15 - 0.08) = $34.71. This is the stock price at the end of Year 5. CF 0 = 0; CF 1-2 = 0; CF 3 = 1.0; CF 4 = 1.5; CF 5 = 36.96; I = 15%. With these cash flows in the CFLO register, press NPV to get the value of the stock today: NPV = $19.89. 8-15 a. The preferred stock pays $8 annually in dividends. Therefore, its nominal rate of return would be: Nominal rate of return = $8/$80 = 10%. Or alternatively, you could determine the security’s periodic return and multiply by 4. Periodic rate of return = $2/$80 = 2.5%. Nominal rate of return = 2.5% × 4 = 10%. b. EAR = (1 + NOM/4) 4 - 1 EAR = (1 + 0.10/4) 4 - 1 EAR = 0.103813 = 10.3813%. 8-16 The value of any asset is the present value of all future cash flows expected to be generated from the asset. Hence, if we can find the present value of the dividends during the period preceding long-run constant growth and subtract that total from the current stock price, the remaining value would be the present value of the cash flows to be received during the period of long-run constant growth. D 1 = $2.00 × (1.25) 1 = $2.50 PV(D 1 ) = $2.50/(1.12) 1 = $2.2321 D 2 = $2.00 × (1.25) 2 = $3.125 PV(D 2 ) = $3.125/(1.12) 2 = $2.4913 D 3 = $2.00 × (1.25) 3 = $3.90625 PV(D 3 ) = $3.90625/(1.12) 3 = $2.7804 Σ PV(D 1 to D 3 ) = $7.5038 Therefore, the PV of the remaining dividends is: $58.8800 – $7.5038 = $51.3762. Compounding this value forward to Year 3, we find that the value of all dividends received during constant growth is $72.18. [$51.3762(1.12) 3 = $72.18.] Applying the constant growth formula, we can solve for the constant growth rate: 3 P ˆ = D 3 (1 + g)/(k s – g) $72.1807 = $3.90625(1 + g)/(0.12 – g) $8.6616 - $72.18g = $3.90625 + $3.90625g $4.7554 = $76.08625g 0.0625 = g Answers and Solutions: 8 - 9 6.25% = g. Answers and Solutions: 8 - 10 [...]... put into effect Answers and Solutions: 8 - 16 Answers and Solutions: 8 - 17 SPREADSHEET PROBLEM 8-26 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com INTEGRATED CASE Mutual of Chicago Insurance Company Stock Valuation 8-27 ROBERT BALIK AND CAROL KIEFER ARE SENIOR... AND MULTIPLY BY (1.30) TO GET D 1 = $2.60; MULTIPLY THAT RESULT BY 1.3 TO GET D2 = $3.38, AND SO FORTH THEN RECOGNIZE THAT AFTER YEAR 3, BON TEMPS BECOMES A CONSTANT GROWTH STOCK, AND AT ˆ ˆ P3 IS THAT POINT P3 CAN BE FOUND USING THE CONSTANT GROWTH MODEL THE PRESENT VALUE AS OF t = 3 OF THE DIVIDENDS IN YEAR 4 AND BEYOND AND IS ALSO CALLED THE TERMINAL VALUE ˆ WITH THE CASH FLOWS FOR D1, D2, D3, AND. .. YIELD = 6.0% AND DIVIDEND YIELD = 7.0% I FINALLY, ASSUME THAT BON TEMPS’ EARNINGS AND DIVIDENDS ARE EXPECTED TO DECLINE BY A CONSTANT 6 PERCENT PER YEAR, THAT IS, g = -6% WHY WOULD ANYONE BE WILLING TO BUY SUCH A STOCK, AND AT WHAT PRICE SHOULD IT SELL? EACH YEAR? WHAT WOULD BE THE DIVIDEND YIELD AND CAPITAL GAINS YIELD IN ANSWER: [SHOW S8-21 AND S8-22 HERE.] THE COMPANY IS EARNING SOMETHING AND PAYING... RESPONSIBLE FOR EQUITY INVESTMENTS HAVING BONDS) AND A MAJOR NEW CLIENT, THE CALIFORNIA LEAGUE OF CITIES, HAS REQUESTED THAT MUTUAL OF CHICAGO PRESENT AN INVESTMENT SEMINAR TO THE MAYORS OF THE REPRESENTED CITIES, AND BALIK AND KIEFER, WHO WILL MAKE THE ACTUAL PRESENTATION, HAVE ASKED YOU TO HELP THEM TO ILLUSTRATE THE COMMON STOCK VALUATION PROCESS, BALIK AND KIEFER HAVE ASKED YOU TO ANALYZE THE BON TEMPS... distribution between dividend yield and capital gains yield will differ: The dividend yield will start off lower and the capital gains yield will start off higher for the 5-year supernormal growth condition, relative to the 2-year supernormal growth state The dividend yield will increase and the capital gains yield will decline over the 5-year period until dividend yield = 4% and capital gains yield = 6%... = $2(1.05) = $2.10; 3 | D3 ˆ P3 4 | D4 D 2 = $2(1.05)2 = $2.21; D3 = $2(1.05)3 = $2.32 b Financial Calculator Solution: Input 0, 2.10, 2.21, and 2.32 into the cash flow register, input I = 12, PV = ? PV = $5.29 c Financial Calculator Solution: Input 0, 0, 0, and 34.73 into the cash flow register, I = 12, PV = ? PV = $24.72 d $24.72 + $5.29 = $30.01 = Maximum price you should pay for the stock e D (1... s Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash flow register, input I = 12, PV = ? PV = $39.43 c 2003 D1/P0 = $2.01/$39.43 = 5.10% Capital gains yield = 6.90* Expected total return = 12.00% 2008 D6/P5 = $3.70/$52.80 = 7.00% Capital gains yield = 5.00 Expected total return = 12.00% Answers and Solutions: 8 - 13 *We know that ks is 12 percent, and the dividend... AGENCY THAT SUPPLIES WORD PROCESSOR OPERATORS AND COMPUTER PROGRAMMERS TO BUSINESSES WITH TEMPORARILY HEAVY WORKLOADS YOU ARE TO ANSWER THE FOLLOWING QUESTIONS A DESCRIBE BRIEFLY THE LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS ANSWER: [SHOW S8-1 THROUGH S8-5 HERE.] THE COMMON STOCKHOLDERS ARE THE OWNERS OF A CORPORATION, AND AS SUCH THEY HAVE CERTAIN RIGHTS AND PRIVILEGES AS DESCRIBED BELOW 1 OWNERSHIP... gains yield will equal 5 percent, and the total return will be 12 percent d People in high income tax brackets will be more inclined to purchase “growth” stocks to take the capital gains and thus delay the payment of taxes until a later date The firm’s stock is “mature” at the end of 2007 e Since the firm’s supernormal and normal growth rates are lower, the dividends and, hence, the present value of... VALUE BACK TO YEAR 0, AND THE SUM OF THESE FOUR PVs IS THE VALUE OF THE STOCK TODAY, P0 = $54.107 THE DIVIDEND YIELD IN YEAR 1 IS 4.80 PERCENT, AND THE CAPITAL GAINS YIELD IS 8.2 PERCENT: DIVIDEND YIELD = $2.600 = 0.0480 = 4.8% $54.107 CAPITAL GAINS YIELD = 13.00% - 4.8% = 8.2% DURING THE NONCONSTANT GROWTH PERIOD, THE DIVIDEND YIELDS AND CAPITAL GAINS YIELDS ARE NOT CONSTANT, AND THE CAPITAL GAINS . 1.00(1.5) 2 (1. 08) = $2.43. 0 P ˆ = ? 0 1 2 3 4 5 6 | | | | | | | 1.00 1.50 2.25 2.43 0.6 58 +34.71 = 0 .85 8 18. 3 78 36.96 Answers and Solutions: 8 - 8 k s = 15% g s = 50% g n = 8% 08. 015.0 43.2 − ×. $8/ $80 = 10.0%. c. k p = $8/ $100 = 8. 0%. d. k p = $8/ $140 = 5.7%. 8- 12 .75.23$ 20.0 75.4$ 05.015.0 )95.0(5$ )05.0(15.0 )]05.0(1[5$ gk )g1(D gk D P ˆ s 0 s 1 0 == + = −− −+ = − + = − = 8- 13. $2 28, 113,612 Market value, debt + preferred 60,000,000 (given in problem) Market value of equity $1 68, 113,612 Barrett’s price per share is calculated as: .81 .16$ 000,000,10 612,113,1 68$ = 8- 8