Foundatons of Fnance Lecture 10: Valuaton Models (wth an Introducton to Captal Budgetng). I. Readng. II. Introducton. III. Dscounted Cash Flow Models. IV. Relatve Valuaton Approaches. V. Contngent Clam Valuaton. VI. Expected Return Determnaton. VII. Constant Growth DDM. VIII. Investment Opportuntes. 0
Foundatons of Fnance Lecture 10: Valuaton Models (wth an Introducton to Captal Budgetng). I. Readng. A. BKM, Chapter 18, except Secton 18.6. B. RWJ, Chapter 8, Secton 8.1 and skm Sectons 8.2-8.6. II. Introducton. A. Defnton of Valuaton. 1. Valuaton s the art/scence of determnng what a securty or asset s worth. a. sometmes we can observe a market value for a securty and we are nterested n assessng whether t s over or under valued (e.g., stock analysts). b. sometmes there s no market value and we are tryng to construct one for barganng or transacton purposes (e.e., a corporaton s nterested n sellng a dvson.). c. sometmes we have a project that we are decdng whether to accept or reject. 2. The value of a securty or asset s gong to depend crucally on the asset prcng model we choose. (The effect s through the approprate dscount rate.) 3. The most common knds of valuaton problem are a. equty valuaton. (1) seasoned equty. (2) IPOs. b. frm valuaton. c. captal budgetng: project valuaton. B. Three Valuaton Approaches. 1. Dscounted Cash Flow (DCF) Models: values an asset by calculatng the present value of all future cash flows 2. Relatve Valuaton: values an asset by lookng at the prces of comparable assets and usng multples such as prce/earnngs (P/E). 3. Contngent Clam Valuaton: uses opton prcng tools to value assets wth opton features. 1
Foundatons of Fnance III. Dscounted Cash Flow Models. A. General Approach. 1. The ntrnsc value of an asset P t s the present value of expected cash flows E[D t ] on the asset dscounted by the requred rate of return on the asset E[R ]: 0 E[CF 1 E[R ] E[CF2 ] (1 E[R ])... E[CFτ ]... 2 (1 E[R ]) τ P " τ1 R D 1 P 1 E[CF τ ] (1 E[R ]) τ B. Two tems affect the ntrnsc value of an asset. 1. Expected Return on the asset. 2. Stream of Expected Cash Flows on the asset. C. Dscusson. 1. Ths formula hghlghts the relaton between expected return and prce and why we call a model that tells us somethng about expected return an asset prcng model. 2. We can see that holdng expected cash flows fxed, asset prce today s decreasng n expected asset return; the hgher the expected return needed to compensate for the asset s rsk the lower the asset s prce. D. Equty Valuaton: Dvdend Dscount Model (DDM) 1. DDM s an example of a dscounted cash flow model. 2. DDM assumes that the stock s bought, held for some tme (dvdends are collected), and then sold. 3. The share s valued as the present value of the expected dvdends and the expected proceeds from the sale. 4. Assume that dvdends are pad annually and that the tme 0 dvdend has just been pad. 5. If the stock s held one year, the return on the stock s P 0 1 P 0 E[D 1 P. 1 E[R ] where D t s frm s dvdend per share at tme t and P t s the stock prce of the frm at t. Takng expectatons and rearrangng gves. 2
Foundatons of Fnance 6. Notce that E[R ] here apples to the frm s equty not the frm s assets. 7. If the stock s held for two years, the present value s gven by 0 E[D. 1 E[R ] E[D2 2 ] (1 E[R ]) 2 P P 8. If the stock s held untl the company s lqudated, the present value s gven by 0 E[D 1 E[R ] E[D2 ] (1 E[R ])... E[Dτ ]... 2 (1 E[R ]) τ " τ1 E[D τ ] (1 E[R ]) τ whch s known as a dvdend dscount model (DDM). E. Captal Budgetng Decsons. 1. A frm s constantly decdng whether to undertake varous projects avalable to t: these are captal budgetng decsons. 2. The frm s clamholders want the frm to undertake a project f ts value to the frm s postve. 3. The dscounted cash flow approach says to dscount the expected cash flows from the project to the present usng the approprate expected return for the cash flows. 4. The sum of present values (ncludng any ntal outlay) s known as the net present value NPV of the project: NPV 0 CF 0 E[CF " τ0 1 E[R ] E[CF E[CF τ ] (1 E[R ]) τ 2 ] (1 E[R ])... E[CF... 2 (1 E[R ]) τ 5. The frm should only undertake projects wth postve NPVs. 6. The project cash flows nclude all ncremental cash flows as a result of undertakng the project. 7. The approprate expected return for dscountng back the expected project cash flows depends on ther rskness. 8. Example. ZDF Co. s consderng an expanson nto a new lne of busness producng wdgets. The new lne wll requre an outlay of $20 mllon today and wll generate an expected net cash flow of $5 mllon 3. τ ].
Foundatons of Fnance per year for the next 10 years. Each year s cash flow wll be receved at the end of the year. The requred return on the frm s equty s currently 20% p.a. whle the requred return on the frm s assets s 18% p.a.. The requred return on the assets for frms currently producng wdgets s 15% p.a. Headquarters expects to use all ts current dle admnstratve capacty to oversee the new busness lne. Headquarter overhead s $6 mllon per year and dle capacty s currently 25% of total capacty. Should ZDF Co. expand nto the new lne of busness? a. Use the requred return on assets n the new busness lne of 15% p.a.. b. Ignore headquarter overhead snce t s a sunk cost. c. Calculate the NPV of the expanson: NPV 0 = -20 + 5 PVAF 15%,10 = -20 + 5 x 5.0187 = 5.09. d. Snce the NPV 0 >0, ZDF Co. should undertake the expanson. IV. Relatve Valuaton Approaches. A. Defnton of P/E rato. 1. The Prce/Earnngs or P/E rato s defned as the prce per share dvded by the earnngs per share (after nterest). 2. IBM Example. a. As of the end of December 2000, the P/E rato for IBM s gven as 19.1 by Bloomberg. Ths can be obtaned by dvdng the prce per share at the end of December 2000 by the earnngs per share for 2000: 85/4.44 = 19.1. 3. The P/E rato s sometmes used to descrbe the prce as IBM s sellng at 19.1 tmes earnngs. B. Use of P/E rato. 1. The P/E rato s sometmes used to get a rough measure of the ntrnsc value of a company that s not publcly traded. 2. When valung the equty of a frm, the approach requres a set of comparable frms to be dentfed. 3. An average P/E rato s calculated for the set of comparable frms. 4. The current earnngs of the frm are multpled by ths average P/E to obtan an estmate of the frm s ntrnsc value. C. Advantages of relatve valuaton. 1. Smple and quck. D. Dsadvantages of relatve valuaton. 1. Defnton of a comparable frm s subjectve. 2. Accountng earnngs are subject to dstortons across frms due to unstable accountng practces. 4
Foundatons of Fnance V. Contngent Clam Valuaton. A. Equty: 1. Can vew equty as a call opton on the assets of the frm wth: a. a strke prce equal to the promsed payment on the debt; and, b. an expraton date equal to the debt s maturty date. B. Debt: 1. Frm asset value equals equty value plus debt value. a. So can thnk of debt as a long poston n the frm s assets and a short poston n the frm s equty. 2. Can vew debt as: a. a long poston n the frm s asset value b. a short poston n a call on the frm s asset value wth a strke prce equal to the promsed debt payment and an expraton date equal to the debt s maturty date. C. Example: Suppose XYZ Co s assets pay off a random amount CF n 1 year s tme and XYZ has ssued debt wth a promsed payment of $100 n 1 year s tme, and equty. CF <100 60 80 100 >100 120 140 160 180 200 Debt CF 60 80 100 100 100 100 100 100 100 mn{cf,100} Equty 0 0 0 0 CF-100 20 40 60 80 100 max{0,cf-100} Frm CF 60 80 100 CF 120 140 160 180 200 CF D. Applcaton to captal budgetng. 1. Choosng a crteron for makng captal budgetng decsons. a. The approprate objectve when makng captal budgetng decsons s maxmzaton of frm value. b. A frm s manager however may nstead act n the best nterests of the frm s equtyholders. c. When the frm s debt s rskless, maxmzng equty value s the same as maxmzng frm value. But when the frm s debt s rsky, maxmzng equty value may not be the same as maxmzng frm value. d. A project could reduce frm value whle ncreasng equty value at the expense of debtholders:.e., V(0)' = S(0)& + B(0)'' where V s total frm value, S s equty value and B s debt value. e. Example: Project has a NPV(0) = -5 but ts acceptance ncreases equty value. 5
Foundatons of Fnance V(0) = S(0) + B(0) wthout project: 120 = 30 + 90 wth project: 115 = 35 + 80 2. Black-Scholes opton prcng model can be used to understand when equty value s lkely to postvely affected by acceptance of a project. a. It s possble to express frm value as follows: V(0) = S(0) + B(0) V(0) = C P,T (0) + {V(0) - C P,T (0)} where C P,T (0) s the value of a call opton on the frm s assets wth a strke equal to the debt promsed payment P, and T s the maturty date of the debt. b. Black-Scholes tells us that (1) current call prce s ncreasng n the current value of the underlyng asset. (2) current call prce s ncreasng n the volatlty of return on the underlyng asset. 3. Asset substtuton or rsk shftng. a. Consder a project wth a negatve NPV that ncreases the volatlty of the return on the frm s assets (σ V ). b. Frm debt s rsky. c. Know frm value V(0) drops snce NPV(0)<0. d. For the equty (whch s a call opton on the frm s assets): (1) reducton n V(0) causes equty value S(0) = C P,T (0) to drop; but (2) ncrease n σ V causes equty value S(0) = C P,T (0) to ncrease. (3) net effect could be to ncrease S(0) f ncrease n σ V s suffcently large relatve to the drop n V(0). e. Snce frm value V(0) drops, any ncrease n S(0) s more than offset by the drop n debt value B(0). f. A manager who cares about equty holders would accept ths project even though t has a negatve NPV. g. The manager s engagng n what s called rsk-shftng behavor. h. Rsk-shftng behavor s an example of the potental conflcts of nterest that can arse between equtyholders and debtholders. 6
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Foundatons of Fnance VI. Expected Return Determnaton. A. Approaches: 1. In a CAPM framework, use the SML; ths approach allows you to explctly make adjustments to your Beta estmate to reflect your assessment of the future Beta of the stock. 2. If valung exstng equty, can also use a hstorcal average return as an estmate of expected return. 3. Can also adjust the estmate to take nto account the predctablty of returns and to allow for the senstvty of the stock to other sources of rsk (n an I-CAPM) settng; we wll not focus on these adjustments here. 4. For smplcty, we wll gnore tax consderatons. B. Equty Beta versus Frm Beta. 1. Can thnk of the frm as a portfolo of assets/projects or a portfolo of clams on those assets: V = A 1 + A 2 +... + A J and V=S+B β V A 1 V β A1 A 2 V and β V S V β S B V β B where V s the value of the frm; A j s the value of the jth asset of the frm; S s the market value of the frm s equty; B s the market value of the frm s debt. 2. Recall that Beta wth respect to the market for a portfolo s a weghted average of the Betas of the assets that comprse the portfolo where the weghts are the portfolo weghts. In an I-CAPM context, the same s true for Beta wth respect to other varables ndvduals care about. 3. It follows that for Beta wth respect to any varable (whch of course ncludes Beta wth respect to the market): β A2... A J V β AJ. where β V s the Beta of the frm; β Aj s the Beta of the jth asset of the frm; β S s the Beta of the frm s equty; β B s the Beta of the frm s debt. 9
Foundatons of Fnance 4. Note a. If the frm s assets are unchanged, then frm Beta wth respect to any varable s unchanged. b. Each asset or project of the frm can have a dfferent Beta from the frm Beta. c. Equty Beta can be calculated by rewrtng the above formula: β S V S β V B S β B β V B S [β V β B ] d. Can see that equty Beta depends on: (1) the Betas of the frm s assets; (2) the level of debt of the frm; and (3) the Beta of the frm s debt. e. If the frm s debt s rskless, debt Beta wth respect to any varable s 0 and so equty Beta can be calculated: β S V S β V 5. Decdng whch Beta to use for a partcular valuaton problem. a. When usng DCF methods to value the frm drectly, use frm Beta to calculate the expected return on the frm s assets. b. When usng DCF methods to value the frm s equty drectly, use equty Beta to calculate the expected return on the frm s equty. c. When valung or evaluatng a specfc project, always use the Beta of the project (whch could be dfferent from the frm s Beta). C. Examples. 1. Suppose ZX company has a two assets. The frst has a Beta wth respect to the market of 1.5 whle the second has a Beta wth respect to the market of 0.9. The frst asset s worth $12M and the second s worth $8M. The frm has $4M of rskless debt. The CAPM holds for the economy, the rskless rate s 5% p.a. and the expected return on the market portfolo s 13% p.a. What s the expected return on ZX s equty? a. Frst, get the Beta of the frm: β V,M A 1 V β A1,M A 2 V β A2,M 12 128 1.5 8 0.9 1.26. 128 b. Second, get the Beta of the equty: β S,M V S β V,M 20 204 1.26 1.575. 10
Foundatons of Fnance c. Thrd, use the SML to get the expected return on the equty: E[R S ] = R f + {E[R M ]- R f }β S,M = 5% + {13%-5%} 1.575 = 17.6%. 2. Project Beta s lkely to dffer from frm Beta when: a. The frm s a conglomerate. b. The project represents an entry nto a new ndustry by the frm. 3. IBM Example: Value IBM equty as of the end of 12/00. a. To use DCF technques, need an estmate of the expected return on IBM stock: E[R S-IBM ] b. CAPM (1) Inputs: (a) market expected excess return (E[R M ] -R f ) ) average monthly excess return on the S&P 500 for the perod 1/26 to 12/00 s 0.6776% ) annualzed gves 12 x 0.6776% = 8.131%. (b) R f : based on yeld curve at end of 12/00, use 5%. (c) (2) Usng the SML: E[R S-IBM ] = 5% + 1.07 x 8.131% = 13.70% β S-IBM,M can be obtaned from the Bloomberg screen: 1.07 s the Beta obtaned usng monthly data from 1/91 to 12/00. c. Could also use an estmate of expected equty return based on hstorcal average return. 11
Foundatons of Fnance VII. Constant Growth DDM. A. Model. 1. Suppose E[ D = D 0 {1 + g }, E[ D 2 ] = E[D {1 + g },..., E[ D τ+ = E[D τ ] {1 + g }. 2. So g s the growth rate of the expected dvdend whch s assumed constant. 3. Can show that the DDM can be wrtten: P 0 D 0 {1 g } E[D 1 ] whch s vald so long as E[R ] > g. E[R ] g E[R ] g B. IBM Example. 1. Am s to value IBM stock as at 12/31/00. 2. Inputs. a. The total dvdends pad n 2000 were $0.51 per share. b. Usng the CAPM gves a dscount rate of 13.70% p.a. c. The Earnngs Estmates table ndcates a growth rate n annual earnngs over the next 5 years of 13.18%: ths wll be our estmate of g IBM. 3. Usng the constant growth DDM, IBM IBM P 0 = D 0 {1 + g IBM } / {E[R IBM ] - g IBM } = $0.51x (1+0.1318) / (0.1370-0.1318) = 111.00. 4. Compare ths to the prce of IBM at the end of December 2000 of $85.00. If we had full fath n our valuaton we would consder IBM to be undervalued and ssue a buy recommendaton. C. Other Implcatons of the Constant Growth DDM. 1. Can rewrte the basc model: E[R ] E[D P 0 g. E[P E[D {1 g } E[R ] g a. Ths formula breaks requred return nto the expected dvdend yeld plus expected captal gan. 2. So g s the expected captal gan on the stock (assumng no stock splts or stock dvdends); can show ths explctly: P 0 {1 g }. 3. If we assume the stock s correctly valued, we can use the stock s dvdend yeld and earnngs growth rate to calculate an estmate of expected return. 12
Foundatons of Fnance VIII. Investment Opportuntes. A. Introducton. 1. Let K τ be the book value of a share of equty at tme τ. 2. The book value per share evolves through tme n the followng way: K τ = K τ-1 + (E τ -D τ ) where E τ are frm s earnngs (after nterest) per share n perod τ. Any earnngs not pad out as a dvdend get added to the book value. B. Assumptons. 1. The constant growth DDM correctly values stock. 2. Each year frm s assets generate an expected after nterest cash flow whch s a constant fracton ROE of the book value of the equty. Ths ROE s known as the expected return on book equty. So the frm s expected earnngs after nterest for perod (τ+1) are equal to the book value of the equty at the start of the perod multpled by ROE. In per share terms: E[E τ+ = K τ ROE. 3. Frm pays a constant fracton (1-b ) of ts earnngs as a dvdend. So D τ+1 = (1-b ) E τ+1 for any τ. a. (1-b ) s called the payout rato. b. b s called the plowback or retenton rato. 4. IBM Example: a. Inputs. (1) Earnngs per share for IBM for 2000 was $4.44. (2) IBM D 0 = $0.51. b. Can calculate b IBM : (1-b ) = D 0 / E 0 = 0.51/4.44 = 11.49% and b = 88.51%. 13
Foundatons of Fnance E[E E 0 C. Implcatons. 1. Snce dvdend per share s a fxed fracton of earnngs per share, t follows that expected earnngs per share also grow at g : E[D {1 b } {1 b }D 0 E[D D 0 {1 g } 2. IBM Example. a. Takng the earnngs growth estmate as our estmate of g IBM s consstent wth ths constant payout model. b. Inputs: (1) g IBM = 13.18%. (2) IBM E 0 = 4.44. c. IBM Can calculate E[E : IBM IBM E[E = E 0 [1+g IBM ] = 4.44 [1+0.1318] = 5.025. 3. What s the expected book value per share at tme 1? E[K = E[K 0 + (E 1 -D 1 )] = K 0 + K 0 ROE - K 0 ROE (1-b ) = K 0 (1 + ROE b ). E[K K 0 E[E 2 ] ROE ROE E[E Can show that the book value per share s also expected to grow at g : E[E 2 ] 1 g. E[E Thus, have shown that b ROE = g. 4. IBM Example. a. Inputs: (1) b IBM = 88.51%. (2) g IBM = 13.18%. (3) IBM E[E = $5.025. b. Can calculate ROE IBM ROE IBM = g IBM / b IBM = 0.1318/0.8851 = 14.89%. c. Can then calculate K 0 IBM mpled by the model: K 0 IBM = E[E 1 IBM ] / ROE IBM = $5.025/0.1489 = $33.75 whch can be compared wth the actual book value at the end of 2000 of $11.56. The dfference between the two s a measure of the extent to whch the assumptons about the evoluton of book value hold for IBM. 14
Foundatons of Fnance D. Uses of the Model. 1. Valuaton. a. Can easly show that the followng formula must hold for the stock prce of frm : 0 D 0 {1 g } E {1 g }{1 b }. E[R ] g 0 E[E {1 b } E[R ] b ROE E[R ] b ROE P P 2. Optmal Plowback Rato. a. If frm pad out all ts earnngs as a dvdend (b =0), ts stock prce at tme zero would be E[E /E[R ]. The dfference between ths value and the constant growth DDM value s due to growth. Thus, 0 E[E E[R ] PVGO 0 E 0 {1 g } E[R ] PVGO 0 where PVGO 1 s the value at tme 0 of frm s growth opportuntes. b. Note that: (1) If E[R ] > ROE : (a) PVGO 1 0; and, (b) b = 0 maxmzes P 1. (2) If E[R ] < ROE : (a) PVGO 1 0; and, (b) P 1 s ncreasng n b. (3) If E[R ] = ROE : (a) PVGO 1 = 0; and, (b) P 1 s unaffected by choce of b. c. IBM Example. (1) Inputs. (a) IBM P 0 = $111.00. (b) IBM E[E = $5.025. (c) E[R IBM ] = 13.70%. (d) ROE IBM = 14.89%. (2) IBM Can calculate PVGO 0 : IBM IBM IBM PVGO 0 = P 0 - {E[E / E[R IBM ]} = $111.00 - $5.025/0.1370 = $111.00 - $36.68 = $74.32. (3) IBM Note that PVGO 0 0 as would be expected snce 13.70% = E[R IBM ] < ROE IBM = 14.89%.. 15
Foundatons of Fnance Lecture 10: Market Effcency I. Readng. II. Defnton of Market Effcency. III. Features of Market Effcency. IV. Levels of Market Effcency V. Costly Informaton Acquston and Costly Tradng. VI. How effcent are U.S. fnancal markets. VII. Jont Test Problem. VIII. Predctablty of Returns. IX. Example of Sem-strong Form Ineffcency 16
Foundatons of Fnance Lecture 10: Market Effcency I. Readng. A. BKM, Chapter 12. Read Sectons 12.1 and 12.2 but only skm Sectons 12.3 and 12.4. II. Defnton of Market Effcency. A. In an effcent market, the prce of a securty s an unbased estmate of ts value. B. Notce that the level of effcency n a market depends on two dmensons: a. The amount of nformaton ncorporated nto prce. b. The speed wth whch new nformaton s ncorporated nto prce. III. Features of Market Effcency. A. To assess the level of market effcency need to know the securty s value; whch requres knowng how assets are prced. B. Market effcency says that: 1. f a pece of news s always followed by a another pece of news than the market ncorporates the lkely mpact of the second pece of news at the tme that the frst pece of news becomes avalable. 2. so even f news s correlated, prce changes wll not be. 3. Tomorrow s Prce = Today s Prce (1 + Expected Return) + Unpredctable Dsturbance. 17
Foundatons of Fnance IV. Levels of Market Effcency A. Weak form. 1. Prce reflects all nformaton contaned n past prces. 2. So an nvestor can not use past prces to dentfy msprced securtes. 3. Techncal analyss: a. refers to the practce of usng past patterns n stock prces to dentfy future patterns n prces. b. s not proftable n a market whch s at least weak form effcent. B. Sem-strong form. 1. Prce reflects all publcly avalable nformaton. 2. So an nvestor can not use publcly avalable nformaton to dentfy msprced securtes. 3. Fundamental analyss: a. refers to the practce of usng fnancal statements and other publcly avalable nformaton about frms to pck stocks. b. s not proftable n a market whch s at least sem-strong form effcent. 4. If a market s sem-strong form effcent, then t s also weak form effcent snce past prces are publcly avalable. C. Strong form. 1. Prce reflects all avalable nformaton. 2. So an nvestor can not use any avalable nformaton to dentfy msprced securtes. 3. Insder tradng: a. refers to the practce of usng prvate nformaton about frms to pck stocks. b. s not proftable n a market whch s at least strong form effcent. c. s llegal. 4. If a market s strong form effcent, then t s also sem-strong and weak form effcent snce all avalable nformaton ncludes past prces and publcly avalable nformaton. 18
Foundatons of Fnance V. Costly Informaton Acquston and Costly Tradng. A. A Contradcton 1. If markets are effcent, all nformaton s reflected n prce. 2. But then there s no ncentve to gather costly nformaton and trade on t. 3. So how does the nformaton get nto prce?!. B. An Alternate Argument. 1. Could have an equlbrum where some nvestors choose to gather nformaton and some do not. 2. Those that do earn better returns whch offset the costs of acqurng the nformaton and tradng on t. 3. The market s not fully effcent n the sense dscussed above. VI. VII. VIII. How effcent are U.S. fnancal markets. A. Probably sem-strong form effcent but not strong form effcent. B. Can fnd rare examples of sem-strong form neffcency. Jont Test Problem. A. The queston whether prce fully reflects a gven pece of nformaton always depends on the model of asset prcng that the researcher s usng. It s always a jont test. B. Example: Takng the CAPM as the model of asset prcng, fndng a relaton between expected return and sze after controllng for Beta wth respect to the market mples semstrong market neffcency snce sze s publcly avalable. However, takng a multfactor model as the model of asset prcng, the relaton between a sze and expected return may be due to a stock s sze beng correlated wth the stock s rsk loadng for a relevant factor. Predctablty of Returns. A. Can forecast long horzon returns usng: 1. past long horzon returns (negatve relaton) (p 29). 2. nformaton varables related to the busness cycle (p 29); a. aggregate dvdend yeld at the start of the return perod (postve relaton). b. term spread (long term hgh grade corporate bond yeld less one month T-bll rate) whch s known at the start of the return perod (postve relaton). c. these nformaton varables are counter cyclcal. B. These fndngs are consstent wth two stores: 1. tme varyng expected returns and semstrong market effcency. 2. constant expected returns and semstrong market neffcency. 19
Foundatons of Fnance IX. Example of Sem-strong Form Ineffcency A. Stocks added and deleted from the S&P 500. 1. see pp 30-32. 20
Foundatons of Fnance