15.401 Finance Theory I

15.40115.401 Finance Theory IAlex StomperMIT Sloan School of ManagementInstitute for Advanced Studies, ViennaLecture 4: Common StocksLecture Notes

Key concepts15.401Lecture 4: Common stocksIntroduction to stock marketsDiscounted Cash Flow Model (DCF)Modeling cash flowsEPS and ROEGrowth opportunities and growth stocksP/E and PVGOReadings:Brealey, Myers and Allen, Chapter 5Bodie, Kane and Markus, Chapter 18Lecture Notes2

Introduction to common stocks15.401Lecture 4: Common stocksCommon stock represents equity or an ownership position in acorporation.Payments to common stock are in the form of dividends:– cash dividend– stock dividend– share repurchaseContrary to payments to bondholders, payments to stockholdersare uncertain in both magnitude and timingTraded in open markets (public vs. private)Important characteristics of common stock: Residual claim - stockholders have claim to firm's cash flows/assets afterall obligations to creditors are met Limited liability - stockholders may lose their investments, but no more Voting rights - stockholders are entitled to vote for the board of directorsand on other major decisionsLecture Notes3

Dividends are “sticky”Lecture Notes15.401Lecture 4: Common stocks4

Dividends tend to follow earningsLecture Notes15.401Lecture 4: Common stocks5

15.401Organization of stock markets1. Primary market - underwritingLecture 4: Common stocks– Venture capital: A company issues shares to investment partnerships,investment institutions and wealthy individuals.– Initial public offering (IPO): A company issues shares to generalpublic for the first time (i.e., going public).– Secondary (seasoned) offerings (SEO): A public company issuesadditional shares– Stock issuing to the public is usually organized by investment bankwho act as underwriters.2. Secondary market (resale market) - Exchanges and OTC– Exchanges: NYSE, AMEX, ECNs,– OTC: NASDAQ3. Trading in secondary market– Trading costs: commission, bid-ask spread, price impact– Buy on margin– Long and shortLecture Notes6

Organization of stock marketsLecture Notes15.401Lecture 4: Common stocks7

Organization of stock marketsLecture Notes15.401Lecture 4: Common stocks8

This lecture15.401Lecture 4: Common stocksWe will analyze the relation between the stock price and dividends.There are three schools of thought on dividends: Dividends donʼt matter. Why? Because a company can always “undo”dividend payments by issuing stock. Or can it? Dividends are bad if they cause tax obligations. But how about stockrepurchases? Dividend are (perceived as) good if they “signal” the future prospects ofthe firm.In this lecture, we will take the investorsʼ view: how to value a stock based onexpectations about dividend payments.Lecture Notes9

Discounted cash flow model15.401Lecture 4: Common stocksBasic PV formula applies to the valuation of stocks. Need to knowExpected future dividendsDiscount rates for dividendsNotation:Pt -- expected stock price at t (ex-dividend)Dt -- expected cash dividend at trt -- risk-adjusted discount rate for cash flow at t.Dividend Discount Model (DCF)Stock price is the present value of future dividends: DtP0 t(1 r)t 1tLecture Notes10

Modeling cash flows15.401Lecture 4: Common stocksConstant GrowthDividends are expected to grow at a constant rate g in perpetuity:Dt 1 (1 g)DtMoreover: rt r. Then: DtD1P0 tr gt 1 (1 rt )This is the Gordon Model:D11 gP0 D0r gr gExample 1. Dividends are expected to grow at 6% per year and thecurrent dividend is 1 per share. The expected rate of return is 20%.1.06P0 7.570.2 0.06Lecture Notes11

Modeling cash flows15.401Lecture 4: Common stocksDCF with constant growth gives a relation between current stockprice, current dividend, dividend growth rate and the expectedreturn. Knowing three of the variables, we can determine thefourth.Example. Determine cost of capital (the discount rate). Suppose thedividend yield for Duke Power is D0/P0 0.052. Estimates of longrun growth:The cost of capital is given byD1(1 g)D0r g gP0P0Thus,Cost of capital Dividend yield dividend growth.Lecture Notes12

Modeling cash flows15.401Lecture 4: Common stocksExample. Estimate dividend growth rate. WSJ reported the followingdata on AT&T stock:What is market's estimate of AT&Tʼs dividend growth rate, if r 12%?Solving the valuation formula for g givesSinceWe haveLecture Notesr D0 / P0g 1 D0 / P0P0 (38.5 38.125) / 2 38.3125D0 / P0 1.32 / 38.3125 0.03445g 0.12 0.03445 8.27%1.0344513

Modeling cash flows15.401Lecture 4: Common stocksMulti-stage growthFirms evolve through different stages in their lifecycles. For example,1. Growth stage - rapidly expanding sales, high profit margins, andabnormally high growth in earnings per share, many new investmentopportunities, low dividend payout ratio.2. Transition stage - growth rate and profit margin reduced bycompetition, fewer new investment opportunities, high payout ratio.3. Maturity stage - earnings growth, payout ratio and average return onequity stabilizes for the remaining life of the firm.Lecture Notes14

Modeling cash flows15.401Lecture 4: Common stocksMulti-stage growth1. In most applications, the dividends are modeled explicitly until thefirm settles into steady-state growth.2. The firm value is computed as follows:D1D2Dt1Dt 1P0 . 2t1 r (1 r)(1 r) (1 r)t r gsteadyExample. In Example 1 (D0 1 and r 20%), suppose that thegrowth rate is 6% for the first 4 years and then drops to 2% steadystate growth. 1.06 1.06 2 1.06 31 1.06 4P0 6.412331.2(1.2)(1.2)(1.2) 0.2 0.02Notice: more than 60% of the firm value is due to the steady state growth.Lecture Notes15

EPS and ROE15.401Lecture 4: Common stocksActual forecast of dividends involves many practical factors.We need to understand the earnings process.Terminology:Earnings (E or EPS): total profit net of depreciation and taxesPayout ratio: dividend/earnings DPS/EPS pRetained earnings: (earnings - dividends)Plowback ratio: retained earnings/total earnings bBook value (BV): cumulative retained earningsReturn on book equity (ROE): earnings/BVLecture Notes16

EPS and ROE15.401Lecture 4: Common stocksExample. Texas Western (TW).Expected earnings 1.00 per share next year.Book value is 10.00 now.Plans an expansion to increase net book assets by 8% per year.Return on new investment is 10%.New investment is financed by retained earnings.Cost of capital is 10%, same as rate of return on new investments.Price TW's shares ifTW expands at 8% foreverTW's expansion slows down to 4% after year 5Here,Plowback ratio b (10)(0.08)/(1) 0.8Payout ratio p (1-0.8)/(1) 0.2ROE 10% r (cost of capital)Lecture Notes17

EPS and ROE15.401Lecture 4: Common stocksPlowback ratio b 0.8Payout ratio p 0.2ROE 10% r1. No expansion. D E 1.0 andP0 2. Continuing expansion.E 1 10r 0.1g ROE b 0.10 0.8 0.08D1 EPS1 p 0.2D10.2P0 10r g 0.1 0.08Why are the values the same under these scenarios?Lecture Notes18

EPS and ROELecture 4: Common stocks15.4013. 2-stage expansion. Forecast EPS, D, BVPS by year:b 80%b 40%10%5Dt10.88P0 5 5 101.1 0.1 0.04t 1 1.1Lecture Notes19

Growth opportunities15.401Lecture 4: Common stocksGrowth opportunities are investment opportunities that earn expectedreturns higher than cost of capital.Stocks of companies that have access to significant growthopportunities are considered growth stocks.The following may not be growth stocks– A stock with growing EPS– A stock with growing dividends– A stock with growing assetsThe following may be growth stocks– A stock with EPS growing slower than cost of capital– A stock with DPS growing slower than cost of capitalLecture Notes20

Growth opportunities15.401Lecture 4: Common stocksExample. ABC Software has the following data: Expected EPS nextyear is 8.33; Payout ratio is 0.6; ROE is 25%; and, cost ofcapital r 15%.Thus,D1 p EPS 0.6 8.33 5g b ROE 0.4 0.25 0.1Following a no-growth policy (g 0, p 1), its value isD1EPS1 8.33P0 55.56r gr0.15Following the growth policy, its price isD15P0 100r g 0.15 0.1The difference of 100-55.56 44.44 comes from the growthopportunities, which offers a return of 25% cost of capital 15%.Lecture Notes21

P/E and PVGO15.401Lecture 4: Common stocksStock price has two components:1. Present value of earnings under a no-growth policy2. Present value of growth opportunitiesEPS1P0 PVGOrTerminology: Earnings yield: E/P EPS1/P0 P/E ratio: P/E P0/EPS1(Note: In business media, E/P is often quoting EPS0/P0 rather than EPS1/P0. Butfinance is forward looking.)Lecture Notes22

P/E and PVGO15.401Lecture 4: Common stocksThus, If PVGO 0, P/E ratio equals inverse of cost of capital1P/E r If PVGO 0, P/E ratio becomes higher:1 PVGO 1P/E rEPS1r PVGO is positive only if firm earns more than the cost of capitalLecture Notes23

P/E and PVGO15.401Lecture 4: Common stocksConsider the simple case in which the plowback ratio b, ROE, and r areconstant forever.1ROE 1ROE PVGO EPS1b 1 EPS2b 1 .2 1 r r (1 r)r NPV1NPV2Since EPS2 (1 g) EPS1, we obtain:11 gPVGO NPV1 NPV1 .21 r(1 r)Lecture Notes24

P/E and PVGO15.401Lecture 4: Common stocksLooks like a growing annuity11 gNPV1PVGO NPV1 NPV1 . 21 r(1 r)r gLetʼs go back to the previous example:ROE 25%, r 15%, g 10%, b 40%EPS1 8.33ROE 0.25 NPV1 EPS1b 1 8.33 0.4 1 2.22 r 0.15 NPV1 2.22PVGO 44.44r g 0.25 0.15Lecture Notes25

Key concepts15.401Lecture 4: Common stocksIntroduction to stock marketsDiscounted Cash Flow Model (DCF)Modeling cash flowsEPS and ROEGrowth opportunities and growth stocksP/E and PVGOLecture Notes26

_Payout ratio: dividend/earnings DPS/EPS p _Retained earnings: (earnings - dividends) _Plowback ratio: retained earnings/total earnings b _Book value (BV): cumulative retained earnings _Return on book equity (ROE): earnings/BV 16 EPS and ROE