The Valuation of Common Stock Where do Stock Prices Come From?

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70391 - Finance The Valuation of Common Stock Where do Stock Prices Come From?

2 Finance The Valuation of Common Stock Where do Stock Prices Come From? Finance Fall 2016 Tepper School of Business Carnegie Mellon University c 2016 Chris Telmer. Some content from slides by Bryan Routledge. Used with permission :14

Stock Valuation Total Debt Share Price Number of Shares Market Value of Equity Market Value of the Firm Intrinsic Value of Operations (Discounted FCF) Non-Operating Assets (Cash) Efficient Markets

3 Stock Valuation Total Debt Share Price Number of Shares Market Value of Equity Market Value of the Firm Intrinsic Value of Operations (Discounted FCF) Non-Operating Assets (Cash) Efficient Markets Market forces will tend to drive market value toward intrinsic value Discounted by Cost of Capital (%) Investors required rate-of-return Future Free Cash Flow (FCF) Profitability and Efficiency Profit margins Operating efficiency Capital (asset) efficiency ROIC Growth Opportunities New customers New products R&D, innovation Sustainability Barriers to entry Specialized skills, processes Patent protection Brand loyalty Market Interest Rates Risk Capital Markets Capital Structure (firm s choice of debt and equity) Stock Valuation 2

4 Game Plan Where do stock prices come from? :1: Multiples of comparables :2: Dividend discount model :3: Dividend discount model with growth and earnings reinvestment :4: PV the firm, subtract the debt: Price per Share (PPS) = PV(FCF) Debt Number of Shares Stock Valuation 3

5 Multiples of Comparables Stock Valuation 4

6 Multiples of Comparables :: Compare some accounting ratio of the company of interest to some appropriate ( comparable ) benchmark (e.g., industry average, similar companies) :: Most common: price-earnings-ratio, P/E ratio :: Also: market-book ratio, price-dividend ratio, EV/EBITDA, etc. Stock Valuation 5

Growth Hunt Lifts Tech Stocks Source: WSJ, July 20 2015 Already sky high,

7 Growth Hunt Lifts Tech Stocks Source: WSJ, July Already sky high, valuations risk further as NASDAQ Composite surges to record Stock Valuation 6

8 Toothless Fangs and Bats Source: Toothless, Financial Times, LEX, June 15, 2016 China has a lot of eyeballs, but its internet companies are valued more cheaply than their US counterparts. Concerns about regulation and trustworthiness of service may be factors, as well as a lack of investor familiarity. The country s top internet companies are all listed outside mainland China Internet stocks: sales, profits and capitalisation Market cap ($bn) Google Alibaba US v China stock performance Share price performance since start 2015 ($bn) Amazon Google Baidu Alibaba Baidu Tencent Facebook Amazon Netflix Revenue ($bn) FT graphic Sources: FT Research, Thomson Reuters Datastream; S&P Capital IQ Stock Valuation 7

9 From Textbook Source: Brealey-Myers-Allen, 11th ed., Chapter 4 Stock Valuation 8

10 Price/Dividend Ratio Look at GPS/AEO data online Stock Valuation 9

12 Price/Earnings Ratio P/E ratio: more common multiple. :: But what is the interpretation? Stockholders get dividends, not earnings. :: Answer coming soon. First, Comps Spreadsheet Stock Valuation 10

13 Recursive Valuation of Dividends (Basis of the Dividend Discount Model ) Stock Valuation 11

14 Conundrum? (1) Share prices equal the present value of all future dividends. (2) Investors hope for capital gains, in addition to dividends. :: i.e., investors hope to buy low, sell high :: Why doesn t the share price in (1) depend on capital gains? Stock Valuation 12

15 Numerical Examples :: What is the value of the stock? :: [risk-free] dividends of :: $10 per share at year 1, :: $10 per share at year 2, :: $10 per share at year 3 :: Zero ($0) per share at year 4, 5, 6 and so on :: The discount rate, r, is 18%. Constant (simplification). :: What is the value of the stock? :: What if you plan to hold the stock for only 1 year? Stock Valuation 13

16 Numerical Examples $10 per share at year 1. $10 per share at year 2. $10 per share at year 3. Zero ($0) per share at year 4, 5, 6 and so on. The discount rate is 18% Stock Valuation 14

17 One Year Only Price at date 1 = price at date 0 = PV of Stock Valuation 15

18 Recursive Valuation General case: :: What is the value of the stock? :: Dividends of $d t (riskless) :: The discount rate is r :: Does it matter how long you plan on holding the stock? Stock Valuation 16

19 Recursive Valuation Stock Valuation 17

20 Recursive Valuation: Point Decompose return into capital gain and dividend yield :: Stock valuations are determined by the value of the cash-flow that accrues to the owner of the stock. :: Value of cash flows = present discounted value of sum of the dividends (or payouts ) :: Value of cash flows = present discounted value of (tomorrow s dividend + tomorrow s price) P t = i=0 E(d t+i ) (1 + r) i = E (P t+1 + d t+1 ) 1 + r Stock Valuation 18

21 Recursive Valuation: Point Decompose return into capital gain and dividend yield :: Stock valuations are determined by the value of the cash-flow that accrues to the owner of the stock. :: Value of cash flows = present discounted value of sum of the dividends (or payouts ) :: Value of cash flows = present discounted value of (tomorrow s dividend + tomorrow s price) P t = i=0 E(d t+i ) (1 + r) i = E (P t+1 + d t+1 ) 1 + r = 1 + r = E P t+1 P t + E d t+1 P t Stock Valuation 18

22 Earnings, Growth and Reinvestment (The Link Between Earnings and Dividends) (Understanding the P/E Ratio) Stock Valuation 19

23 Dividends Stock Valuation 20

24 Understanding the P/E Ratio Motivation :1: Earnings, not dividends? :2: P/E ratio is most common valuation ratio. Stock Valuation 21

25 Problem Stock valuation P t = i=0 E t [ d t+i ] (1 + E[r]) i But wait... some firms don t pay dividends? Stock Valuation 22

26 Problem Stock valuation P t = i=0 E t [ d t+i ] (1 + E[r]) i But wait... some firms don t pay dividends? :: Can we stick in earnings? Stock Valuation 22

27 Problem Stock valuation P t = i=0 E t [ d t+i ] (1 + E[r]) i But wait... some firms don t pay dividends? :: Can we stick in earnings? No. Earnings are not the payments to stockholders. Stock Valuation 22

28 Problem Stock valuation P t = i=0 E t [ d t+i ] (1 + E[r]) i But wait... some firms don t pay dividends? :: Can we stick in earnings? No. Earnings are not the payments to stockholders. :: Two approaches 1. Model how earnings affects dividends 2. V = D + E: Value the firm s FCF, subtract the debt, divide by shares outstanding. Stock Valuation 22

29 Problem Stock valuation P t = i=0 E t [ d t+i ] (1 + E[r]) i But wait... some firms don t pay dividends? :: Can we stick in earnings? No. Earnings are not the payments to stockholders. :: Two approaches 1. Model how earnings affects dividends 2. V = D + E: Value the firm s FCF, subtract the debt, divide by shares outstanding. :: Key thing: :: Dividend policy ( payout policy ) is a financial decision. Stock Valuation 22

30 Why? [Source: google.com but lots (lots!) of places have this information.] Why the differences in P/E? Stock Valuation 23

31 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. Stock Valuation 24

32 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. :: EPS t = DIV t + RE t Stock Valuation 24

33 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. :: EPS t = DIV t + RE t :: BVE t = book-value of equity, at the beginning of Year t. Stock Valuation 24

34 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. :: EPS t = DIV t + RE t :: BVE t = book-value of equity, at the beginning of Year t. :: Return on Equity: ROE = EPSt BVE t. Stock Valuation 24

35 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. :: EPS t = DIV t + RE t :: BVE t = book-value of equity, at the beginning of Year t. :: Return on Equity: ROE = EPSt BVE t. :: Plowback ratio: PLOW = REt EPS t Stock Valuation 24

36 Accounting Definitions Most variables are per share in Year t. :: P t ex-dividend price per share. :: EPS t = DIV t + RE t :: BVE t = book-value of equity, at the beginning of Year t. :: Return on Equity: ROE = EPSt BVE t. :: Plowback ratio: PLOW = REt EPS t :: Payout ratio: PAY = DIVt EPS t = 1 PLOW Stock Valuation 24

37 Engine of Growth Assume ROE is constant over time :: EPS t = ROE BVE t :: Just the definition of ROE, rewritten. To figure out earnings, just multiply ROE times BVE t Stock Valuation 25

38 Engine of Growth Assume ROE is constant over time :: EPS t = ROE BVE t :: Just the definition of ROE, rewritten. To figure out earnings, just multiply ROE times BVE t :: BVE t = BVE t 1 + EPS t 1 PLOW :: BVE grows by plowing back earnings. Same as saying BVE this year equals BVE last year plus retained earnings. Stock Valuation 25

39 Engine of Growth Assume ROE is constant over time :: EPS t = ROE BVE t :: Just the definition of ROE, rewritten. To figure out earnings, just multiply ROE times BVE t :: BVE t = BVE t 1 + EPS t 1 PLOW :: BVE grows by plowing back earnings. Same as saying BVE this year equals BVE last year plus retained earnings. :: Combine these two equations and arrive at growth rate, g: BVE t = BVE t 1 + ROE BVE t 1 PLOW = BVE t 1 ( 1 + ROE PLOW ) }{{} growth=g = g = ROE PLOW Stock Valuation 25

40 Engine of Growth Assume ROE is constant over time :: EPS t = ROE BVE t :: Just the definition of ROE, rewritten. To figure out earnings, just multiply ROE times BVE t :: BVE t = BVE t 1 + EPS t 1 PLOW :: BVE grows by plowing back earnings. Same as saying BVE this year equals BVE last year plus retained earnings. :: Combine these two equations and arrive at growth rate, g: BVE t = BVE t 1 + ROE BVE t 1 PLOW = BVE t 1 ( 1 + ROE PLOW ) }{{} growth=g = g = ROE PLOW :: Makes sense: if each dollar of BVE earns an ROE of 12 cents (or 12%), and then 40% of these cents are PLOWED back in, you will have grown by = 4.8 cents, per dollar of BVE (or 4.8%). Stock Valuation 25

41 Growth :: Since EPS t is proportional to BVE t, EPS t must grow at rate g. EPS t = ROE BVE t :: Same, then, applies for DIV t and RE t: DIV t = PAY EPS t RE t = PLOW EPS t :: Growth: BVE t+1 = EPS t+1 = ( ) t BVE g ( ) t EPS g = BVE 1 ROE ( 1 + g ) t DIV t+1 = ( ) t DIV g = EPS 1 PAY ( 1 + g ) t = BVE 1 ROE PAY ( 1 + g ) t Stock Valuation 26

43 Valuation Recall, growing perpetuity: P 0 = DIV 1 r g where r is the cost of capital. = PAY EPS 1 r g = PAY ROE BVE 1 r ROE PLOW :: This is a model of how earnings maps into dividends. :: We can use it to get some important insights Stock Valuation 27

44 NPV Suppose that ROE = r P 0 = PAY r BVE 1 r r PLOW = BVE 1 Stock Valuation 28

45 NPV Suppose that ROE = r NPV = 0 P 0 = PAY r BVE 1 r r PLOW = BVE 1 :: Makes sense Stock Valuation 28

46 NPV Suppose that ROE = r NPV = 0 P 0 = PAY r BVE 1 r r PLOW = BVE 1 :: Makes sense :: If ROE > r, NPV > 0 :: If ROE < r, NPV < 0 Stock Valuation 28

47 Growth PVGO = Present Value of Growth Options PVGO = P 0 EPS 1 r Stock Valuation 29

48 Growth PVGO = Present Value of Growth Options PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r Stock Valuation 29

49 Growth PVGO = Present Value of Growth Options Special cases: PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r No growth (PLOW=0): PVGO = 0. But, if ROE > r, NPV is still positive. Just none from growing! Stock Valuation 29

50 Growth PVGO = Present Value of Growth Options Special cases: PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r No growth (PLOW=0): PVGO = 0. But, if ROE > r, NPV is still positive. Just none from growing! Growth and investing in loser projects. PLOW > 0 and ROE < r. Here, you can verify that PVGO < 0. The firm is growing, but in doing so it is wasting the money of its owners. Recall that if ROE < r then the firm represents a negative NPV project. By growing the firm through plowing back earnings, the managers are taking a dumb idea and exacerbating it. Stock Valuation 29

51 Growth PVGO = Present Value of Growth Options Special cases: PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r No growth (PLOW=0): PVGO = 0. But, if ROE > r, NPV is still positive. Just none from growing! Growth and investing in loser projects. PLOW > 0 and ROE < r. Here, you can verify that PVGO < 0. The firm is growing, but in doing so it is wasting the money of its owners. Recall that if ROE < r then the firm represents a negative NPV project. By growing the firm through plowing back earnings, the managers are taking a dumb idea and exacerbating it. PLOW > 0 and ROE > r. Well done! Stock Valuation 29

52 Growth PVGO = Present Value of Growth Options Special cases: PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r Growth but no growing value. If PLOW > 0 but ROE = r then PVGO = 0. Competitive markets make us consider this situation seriously. The firm s growth represents a series of investments in NPV = 0 projects. Growth, per-se, does not give a high P/E. Stock Valuation 30

53 Growth PVGO = Present Value of Growth Options Special cases: PVGO = P 0 EPS 1 r = PAY ROE BVE 1 r ROE PLOW ROE BVE 1 r Why do P/E ratios vary in the cross-section? One last way to express the main point is to write the definition of the PVGO as P 0 = PVGO + 1 EPS 1 EPS 1 r A high P/E ratio is indicative of either a high PVGO, a low cost-of-capital, or a bit of both. The link between the stock price and earnings per share is that the price will be high, relative to earnings, if either (or both) of these things hold. Stock Valuation 31

54 Hidden Assumptions :: ROE, PAY and PLOW are time invariant :: Constant growth in all variables (earnings, dividends, BVE, etc.) :: No capital structure (yet) :: Constant discount rate Stock Valuation 32

55 Summary Stock Valuation 33

56 Summary: Where do Stock Prices Come From? :: Where do stock prices come from? DCF :: PV of all future dividends :: PV of tomorrow s dividend and tomorrows stock price: dividend and capital gain :: Hardest part is getting the discount rate right Stock Valuation 34

57 Summary: Where do Stock Prices Come From? Valuing a stock is similar to valuing a bond: :: DCF the cash flows: dividend discount model :: If dividends are risky, DCF the expected dividends, discount by appropriate expected return Stock Valuation 35

58 Summary: Where do Stock Prices Come From? Valuing a stock is similar to valuing a bond: :: DCF the cash flows: dividend discount model :: If dividends are risky, DCF the expected dividends, discount by appropriate expected return But the cash flow to the stockholder depends on the financial policy of the firm... it s payout policy. So, Stock Valuation 35

59 Summary: Where do Stock Prices Come From? Valuing a stock is similar to valuing a bond: :: DCF the cash flows: dividend discount model :: If dividends are risky, DCF the expected dividends, discount by appropriate expected return But the cash flow to the stockholder depends on the financial policy of the firm... it s payout policy. So, :1: If you have a good handle on dividends, directly, then P = d/(r g) or P = E t dt/(1 + r)t or something similar Stock Valuation 35

60 Summary: Where do Stock Prices Come From? Valuing a stock is similar to valuing a bond: :: DCF the cash flows: dividend discount model :: If dividends are risky, DCF the expected dividends, discount by appropriate expected return But the cash flow to the stockholder depends on the financial policy of the firm... it s payout policy. So, :1: If you have a good handle on dividends, directly, then P = d/(r g) or P = E t dt/(1 + r)t or something similar :2: If you d like to go slightly deeper, and model where growth comes from, then P = (PAY ROE BVE)/(r ROE PLOW ). Stock Valuation 35

61 Summary: Where do Stock Prices Come From? Valuing a stock is similar to valuing a bond: :: DCF the cash flows: dividend discount model :: If dividends are risky, DCF the expected dividends, discount by appropriate expected return But the cash flow to the stockholder depends on the financial policy of the firm... it s payout policy. So, :1: If you have a good handle on dividends, directly, then P = d/(r g) or P = E t dt/(1 + r)t or something similar :2: If you d like to go slightly deeper, and model where growth comes from, then P = (PAY ROE BVE)/(r ROE PLOW ). :3: Or model the FCF, PV it, subtract the debt and divide by number of shares. This is next. It makes less stringent assumptions about constant growth, but requires many alternative assumptions. Stock Valuation 35

62 Summary: Link Between Dividends and Earnings :: Strictly speaking, stock holders get dividends, so stock prices derive from dividends :: But dividend policies vary a lot across firms, time. Dividends take many forms. Earnings, in contrast, are not a financial policy. They are the outcome of business operations. So what s the link? :: If plowback = 0, then EPS=DPS and the link is trivial :: If plowback > 0, then DPS<EPS. But we can use ROE and plowback to estimate D-growth :: If plowback > 0, and if its being plowed into NPV>0 projects, then part of firm value is PVGO: growth firm. E/P ratio is smaller than cost-of-capital: growth firms have bigger P/E ratios than non-growth firms with same cost-of-capital. Stock Valuation 36

Valuing the Firm Sometimes called financial modeling

70391 - Finance Valuing the Firm Sometimes called financial modeling 70391 Finance Fall 2016 Tepper School of Business Carnegie Mellon University c 2016 Chris Telmer. Some content from slides by Bryan