Equity Markets and Stock Valuation

Key Concepts and Skills Chapter 7 Equity Markets and Stock Valuation Chapter Outline • Common Stock Valuation • Some Features of Common and Preferred Stocks • The Stock Markets • Understand how stock prices depend on future dividends and dividend growth • Be able to compute stock prices using the dividend growth model • Understand how corporate directors are elected • Understand how stock markets work • Understand how stock prices are quoted Cash Flows to Stockholders • If you buy a share of stock, you can receive cash in two ways – The company pays dividends – You sell your shares either to another investor in the market or back to the company • As with bonds, the price of the stock is the present value of these expected cash flows One-Period Example • Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? – Compute the PV of the expected cash flows – Price = (14 + 2) / (1.2) = $13.33 – Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33 Two-Period Example • Now, what if you decide to hold the stock for two years? In addition to the $2 dividend in one year, you expect a dividend of $2.10 and a stock price of $14.70 both at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33 1-1 Three-Period Example • Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 and a stock price of $15.435 both at the end of year 3. Now how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33 Estimating Dividends: Special Cases • Constant dividend – The firm will pay a constant dividend forever – This is like preferred stock – The price is computed using the perpetuity formula • Constant dividend growth – The firm will increase the dividend by a constant percent every period • Supernormal growth Developing The Model • You could continue to push back when you would sell the stock • You would find that the price of the stock is really just the present value of all expected future dividends • So, how can we estimate all future dividend payments? Zero Growth • If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity • P0 = D / R • Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = .50 / .025 = $20 – Dividend growth is not consistent initially, but settles down to constant growth eventually Dividend Growth Model • Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + … P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + … • With a little algebra, this reduces to: P0 = D 0 (1 + g) D = 1 R-g R-g DGM – Example 1 • Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? • P0 = .50(1+.02) / (.15 - .02) = $3.92 1-2 Stock Price Sensitivity to Dividend Growth, g DGM – Example 2 P0 = 2 / (.2 - .05) = $13.33 Why isn’t the $2 in the numerator multiplied by (1.05) in this example? 250 D1 = $2; R = 20% 200 Stock Price • Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? 150 100 50 0 0 0.05 0.1 0.15 0.2 Growth Rate Stock Price Sensitivity to Required Return, R Example 7.3 Gordon Growth Company - I • Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. • What is the current price? 250 D1 = $2; g = 5% Stock Price 200 150 100 50 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Required Rate of Return Example 7.3 – Gordon Growth Company II • What is the price expected to be in year 4? P4 = D4(1 + g) / (R – g) = D5 / (R – g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50 • What is the implied return given the change in price during the four-year period? 50.50 = 40(1+return)4; return = 6% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6% • The price grows at the same rate as the dividends P0 = 4 / (.16 - .06) = $40 Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g Nonconstant Growth Problem Statement • Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? • Remember that we have to find the PV of all expected future dividends. 1-3 Nonconstant Growth – Example Solution • Compute the dividends until growth levels off D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 • Find the expected future price P2 = D3 / (R – g) = $1.449 / (.2 - .05) = $9.66 • Find the present value of the expected future cash flows Quick Quiz: Part 1 • What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%? • What if the company starts increasing dividends by 3% per year beginning with the next dividend? The required return stays at 15%. P0 = $1.20 / (1.2) + ($1.38 + 9.66) / (1.2)2 = $8.67 Finding the Required Return Example Using the DGM to Find R • Start with the DGM: D 0 (1 + g) D1 = R - g R -g rearrange and solve for R P0 = D 0 (1 + g) D1 R = + g = + g P0 P0 • Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? R = [$1(1.05)/$10.50] + .05 = 15% • What is the dividend yield? $1(1.05) / $10.50 = 10% • What is the capital gains yield? g =5% Features of Common Stock Table 7.1 • • • • Voting Rights Proxy voting Classes of stock Other Rights – Share proportionally in declared dividends – Share proportionally in remaining assets during liquidation – Preemptive right – first shot at new stock issue to maintain proportional ownership if desired 1-4 Dividend Characteristics • Dividends are not a liability of the firm until a dividend has been declared by the Board • Consequently, a firm cannot go bankrupt for not declaring dividends • Dividends and Taxes – Dividend payments are not considered a business expense; therefore, they are not taxdeductible – Dividends received by individuals have historically been taxed as ordinary income – Dividends received by corporations have a minimum 70% exclusion from taxable income Features of Preferred Stock • Dividends – Stated dividend that must be paid before dividends can be paid to common stockholders – Dividends are not a liability of the firm and preferred dividends can be deferred indefinitely – Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid • Preferred stock does not generally carry voting rights 1-5