2 Learning objectives 1. Distinguish between the intrinsic value and price of a share of common stock. 2. Calculate the intrinsic value of a firm using dividend discount models Constant dividend growth model Multistage dividend growth model 3. Use the constant growth model to relate growth opportunities to stock value. 4. Calculate the P/E ratio for a constant growth firm. 5. Discuss the free cash flow valuation methods.
3 Concept Map FI400 Portfolio Theory Asset Pricing Equity Fixed Income Market Efficiency Derivatives Foreign Exchange
4 Why equity valuation? Identify mispriced equity securities. How? By calculating intrinsic or true value of a stock using valuation models. These valuation models make use of information concerning current & future profitability. This approach of identifying mispriced stocks is called fundamental analysis.
5 Intrinsic value vs. market price (1) Intrinsic value, V 0 Present value of all expected future cash flows to the stock investor. The cash flows are discounted at the appropriate required rate of return, k. Expected future cash flows consist of: 1. cash dividends 2. sale price: proceeds from the ultimate sale of the stock
6 Intrinsic value vs. market price (2) Intrinsic value is your (the analysts) estimate of what a stock is really worth. Intrinsic value (V 0 ) can differ from the current market price (P 0 ). If V 0 > P 0 : stock is underpriced => buy If V 0 sell or dont buy.
7 Market equilibrium In market equilibrium, Everyone has the same intrinsic value. So, intrinsic value equals market price, i.e., V 0 = P 0. Everyone also demands the same required rate of return from the stock. So everyone has the same k. In addition, expected HPR = k. This common required rate of return is called the market capitalization rate. Market capitalization rate: required rate of return which the market (i.e., everyone) uses to discount future cash flows.
8 Equity valuation models Dividend discount models Constant dividend growth model Multistage (non-constant) dividend growth model Price-earnings ratio (P/E) Free cash flow models
9 Dividend discount models (DDMs) Dividend discount models say that the intrinsic value of a stock is equal to the present value of all expected future dividends. What about cash flow from the ultimate sale of the stock? Is that included? Yes, because stock price at time of sale is again determined by expected dividends at the time of sale.
10 Dividend discount model: General formula This formula cannot be implemented because it requires dividend forecasts every year into the indefinite future. To implement the DDM, we make assumptions about how dividends evolve over time.
11 Two versions of DDM We look at 2 assumptions: Dividends grow at constant rate Constant dividend growth model Dividends grow at different rates over different periods. At some future date, dividend growth settles down to a constant rate. Multistage (non-constant) dividend growth model
12 Constant dividend growth model (1) 1. Assume that dividends grow at a constant rate, g, per period forever. 2. Given this assumption, the intrinsic value equals D 0 = Dividend that the firm just paid Required rate of return or discount rate Dividend growth rate Dont panic. D 1 = D 0 (1 + g)
13 Constant dividend growth model (2) Warning: The model works only if k > g. Useful properties. All other things unchanged, If D 1 increases (decreases), V 0 increases (decreases). If g increases (decreases), V 0 increases (decreases). If k increases (decreases), V 0 decreases (increases).
14 Constant dividend growth model (3) Suppose the market is in equilibrium. This means that stock price is equal to intrinsic value, i.e., P 0 = V 0. Then, stock price is expected to grow at the same rate as dividends. That is, the expected rate of price appreciation in any year will equal the constant growth rate, g. P 1 = P 0 ( 1 + g ) = V 1 = V 0 ( 1 + g )
15 Expected HPR and k (1) Continue to assume that P 0 = V 0. Then, expected HPR, E(r) is, Dividend yield Capital gains yield
16 Expected HPR and k (2) If stock is selling at intrinsic value, P 0 = V 0 Then required rate of return, k, must equal the expected HPR. Therefore, When everyone agrees on the same k (in equilibrium), we can use the above formula to compute market capitalization rate.
17 Constant dividend stream If g = 0, then dividends do not grow and stay the same forever. We have a constant dividend stream – a perpetuity. The constant dividend stream assumption is a special case of the constant growth model with g = 0. Implication: with constant dividend stream, we continue to use the preceding equations but set g to 0.
18 Applying the constant growth DDM (1) A common stock pays an annual dividend per share of $2.10. The risk-free rate is 7% and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $2.10 forever, what is the value of the stock? (to two decimal places) Verify that V 0 = $19.09
19 Applying the constant growth DDM (2) The risk-free rate of return is 10%, the required rate of return on the market is 15%, and High-Flyer stock has a beta coefficient of 1.5. If the dividend per share expected during the coming year, D 1, is $2.50 and g = 5%, at what price should a share sell? Hint: use the CAPM to get the market capitalization rate.
20 Applying the constant growth DDM (3) Big Oil Inc. just paid a dividend of $10 (i.e., D 0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. The market capitalization rate is 15%. What is the price of Big Oils common stock? (to 2 decimal places) Verify that price = $94.55
21 Applying the constant growth DDM (4) The price of a stock in the market is $62. You know that the firm has just paid a dividend of $5 per share (i.e., D 0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the market capitalization rate for this stock (to 2 decimal places)?
22 Applying the constant growth DDM (5) A firm is expected to pay a dividend of $5.00 on its stock next year. The current price of this stock is $40 and investors require a return of 20%. The firms dividends grow at a constant rate. What is the constant dividend growth rate (g)? use k = (D 1 /P 0 ) + g Verify that g = 7.5%
23 Applying the constant growth DDM (6) In order to use the constant dividend growth model to value a stock it must be true that: a. The required rate of return is less than the expected dividend growth rate. b. The expected dividend growth rate is greater than zero. c. The next dividend (D1) is expected to be greater than $1.00. d. The expected dividend growth rate is less than the required rate of return. Which statement is correct?
24 Stock prices & investment/growth opportunities How do we figure out dividend growth rate, g ? Growth rate depends on: 1. Investment opportunities embodied in return on equity, ROE 2. Reinvestment of earnings, represented by earnings retention ratio, b. Earnings retention ratio is also called the plowback ratio. Growth rate, g = ROE x b
25 Earnings retention ratio and dividend payout ratio Earnings retention rate = reinvested earnings/ total earnings. A related measure is the dividend payout ratio. Dividend payout ratio = dividends paid/ total earnings = 1 – retention rate
26 Problem Geoscience Corp. has a beta of 1.2 and its most recent EPS is $10 per share. The company just paid 40% of its earnings in dividends. Geoscience Corp will earn an ROE of 20% per year on all reinvested earnings forever. The risk-free rate is 8% and the expected return on the market portfolio is 15%. a) What is the intrinsic value (V 0 ) of a share of Geosciences stock (to two decimal places)? b) If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one- year HPR on Geoscience Corp.s stock?
27 Earnings retention ratio affects growth Suppose ROE > 0Growth policy No-growth policy Earnings retention ratio, bb > 0b = 0 Growth rate, gg > 0g = 0 Bottomline: If a company reinvests some portion of earnings back into the business (b > 0), future earnings and dividends will grow (i.e., g > 0). Otherwise, earnings and dividends will not grow.
28 Is growth always beneficial? Does having positive growth always increase stock price? No. It depends on the attractiveness of the firms investment opportunities, ROE. Compared to a no-growth policy, If ROE > k, then retaining earnings (i.e., b > 0) will increase stock price. If ROE < k, then retaining earnings will decrease stock price.
29 Consider two companies Growth Prospects, Inc (GP) Dead Beat, Inc (DB) No-growth earnings per share$5 Market capitalization rate, k12.5% No-growth price per share5/0.125 = 40 ROE15%10%
30 Suppose both companies reinvest 60% of next years earnings… Growth Prospects, Inc (GP) Dead Beat, Inc (DB) Earnings retention ratio, b0.6 Next years dividend per share, D 1 = (1 – b) x 5 $2 Dividend growth rate, g = ROE x b 9%6% Constant dividend growth model share price 2/(0.125 – 0.09) = /(0.125 – 0.06) = 30.77
31 Compare GP and DB Growth Prospects, Inc (GP) Dead Beat, Inc (DB) ROE15%10% Market capitalization rate, k12.5% No-growth price per share (1)40 Constant div. growth Price (2) Present value of growth opportunities, PVGO = (2) – (1) PVGO = Price per share – no-growth price per share
32 Problems involving growth (1) MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming years earnings are expected to be $2 per share. The market capitalization rate is 12%. A. At what price will the stock sell today? B. At what price do you expect MF shares to sell for in 3 years?
33 Problems involving growth (2) Even Better Products has come out with a new and improved product. As a result, the firm projects an ROE of 20%, and it will maintain a retention ratio of Its earnings in one year will be $2 per share. Investors expect a 12% rate of return on the stock. a) Calculate the stock price. b) What is the present value of growth opportunities (PVGO)? c) What would be the stock price and PVGO if the firm reinvests only 20% of its earnings?
34 Multi-stage dividend growth 1 With this assumption, dividends grow at different rates for different periods of time. Eventually, dividends will grow at a constant rate forever. Time line is very useful for valuing this type of stocks. To value such stocks, also need the constant growth formula. Best way to learn is through an example.
35 Multi-stage dividend growth 2 ABC Co. is expected to pay dividends at the end of the next three years of $2, $3, $3.50, respectively. After three years, the dividend is expected to grow at 5% constant annual rate forever. If the market capitalization rate for this stock is 15%, what is the current stock price? T = 0 $2.00$3.00$3.50 Dividends grow at 5% forever T =1T = 2T = 3T = 4
36 What to do? 1. Place yourself at t = 3 and use the constant growth formula to find PV of dividend stream after year 3. Call this P Find the PV of P Find PV of dividends at t=1, t=2 and t=3. 4. Current stock price = sum of 2, 3 and 4.
37 Apply the method to find ABCs stock price P 3 = (3.5 x (1.05))/(0.15 – 0.05) = Current stock price, P 0
38 Another type of multi-stage growth problem Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D 0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)? Use timeline to see the problem better. Verify that stock price = $25.29
39 Price-earnings (P/E) ratios P/E ratio is the ratio of current price per share (P 0 ) to next years expected earnings per share (EPS). How do we use P/E ratio to value a stock? 1. Forecast next years EPS, E Forecast P/E ratio, P 0 /E Multiple P/E by EPS to get current estimate of price. (P 0 /E 1 ) x E 1 = P 0
40 P/E ratio and constant growth model If a company has a constant dividend growth rate and the market is in equilibrium (i.e., V 0 =P 0 ), then we have an explicit formula for the P/E ratio! Recall that b = retention ratio, k = market capitalization rate.
41 P/E questions (1) ABC Co. has an ROE of 25%, a CAPM beta of 1.2 and a retention ratio of 40%. The risk-free rate is 6% and the market risk premium is 5%. What is ABCs P/E ratio?
42 P/E questions (2) Analog Electronic Corporation has an ROE = 9% and a beta of It plans to maintain indefinitely its traditional plowback ratio of 2/3. The most recent earnings per share is $3 per share. The expected market return is 14% and the risk-free rate is 6%. a) What is Analogs stock price? b) Calculate the P/E (P 0 /E 1 ) ratio. c) Calculate the PVGO.
43 Free Cash Flow Valuation Approach Dividend discount models dont work for companies which do not pay dividends. For non-dividend paying companies, we can use free cash flow valuation approach. There are two versions: Free cash flow to the firm (FCFF) Free cash flow to equity holders (FCFE)
44 Free Cash Flow to the Firm (FCFF) (1) FCFF: cash flow that accrues from the firms operations, net of investments in capital and net working capital. FCFF represent cash flows available to both debt and equity holders. FCFF = EBIT(1 – t c ) + Depreciation – capital expenditures – increase in NWC EBIT = earnings before interest and taxes t c = corporate tax rate NWC (net working capital) = current asset – current liability
Free Cash Flow to the Firm (FCFF) (2) Capital expenditure includes: 1. acquiring fixed, and in some cases, intangible assets 2. repairing an existing asset so as to improve its useful life 3. upgrading an existing asset if its results in a superior fixture 4. preparing an asset to be used in business 5. restoring property or adapting it to a new or different use 6. starting or acquiring a new business 45
46 Free Cash Flow to the Firm (FCFF) (3) Find the PV of the firm by discounting the year- by-year FCFF plus some estimate of terminal value, P T. Firm Value= where Market value of equity = Firm value – market value of debt.
47 Free Cash Flow to Equity Holders (FCFE) FCFE: Free cash flow available to equity holders. FCFE = FCFF – interest expense(1 – t c ) + increases in net debt Find the market value of equity by discounting the year- by-year FCFE plus some estimate of terminal value, P T. is the cost of equity.
48 Summary 1. Distinguish between the intrinsic value and price. 2. Calculate intrinsic value using dividend discount models Constant dividend growth model Multistage dividend growth model 3. Discuss the use of the P/E ratio to value common stock. 4. Calculate the P/E ratio for a constant growth firm. 5. Discuss the free cash flow valuation methods.
Practice 5 Chapter 13: 5,6,7,10,11,13,15, 17,19, 49