docFile
download 
Report Transcription
File
8/23/14 Learning Objec@ves 2 ¨ Understand basic concepts of corporate finance ¤ Capital structure, cost of equity, dividend policy ¨ Calculate rate cost of equity capital, kE ¨ Calculate unleveraged rate cost of capital, kU ¨ Systemic equity risk ¤ ¨ Capital Structure and Cost of Equity Simple Firm Assump@ons 3 4 ¨ Fairway Corp financial structure plus T = 0, ∆T = 0, IDI = 0, NOA = 0 ¤ C = IC ¤ τ ≥ 0, EB > 0, DB ≥ 0 ¤ ¨ M&M Assump@ons FCF is a perpetuity n FCF = NOPAT – ∆IC = EBIT(1-‐τ) n ∆ IC = CX – DX -‐ CC + ∆OWC = 0 n CX – DX = 0, CC=0, ΔOWC=0 ¤ Debt is constant (a perpetuity) n ∆DB = ∆D = 0 ¤ kTS = kD ¤ Capital Structure and Cost of Equity Miller and Modigliani ¤ Assump@ons ¤ ¨ Capital structure assuming no tax advantaged debt Proposi@ons Demonstrate that under M&M assump@ons the DCF valua@on methods are equivalent Firm Value -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Fair Value LE & TA -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ ----------------------NIBCL NIBCL NIBCL NIBCL Assume: NOA=0, T=0 OA = TA, NOCE = IS = 0 IC = EB + DB , LE = IC + NIBCL IC = OWC + NC = C V = PV(FCF) = Fair Value of IC V = IC + MVA MVA D -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Book Value LE & TA -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ CE AP ITP NIBCL NIBCL AR STD OWC V Value INV Value of TA DB of IC LTD TA VU IC E NC NC EB EB VTS 1 8/23/14 Simple Firm Example APV Valua@on with Constant FCF Growth 6 5 140 Fair Value [$M] V =D+E = D 120 100 CX − DX − CC = 0 ΔT = 0 ΔOWC = 0 APVM V = VU + VTS FCF1 = + VTS k U − g FCF 60 E 40 0 FCF1 k − g FCF VU 80 20 FCF = NOPAT − ΔN − ΔOWC = EBIT ⋅ (1 − τ) + ΔT − (CX − DX − CC) − ΔOWC FCFM 160 VTS FCF = EBIT ⋅ (1 − τ) EBIT ⋅ (1 − τ) V= + VTS kU EBIT ⋅ (1 − τ) = + τ ⋅D kU No assump@on yet on growth of debt, D, tax shield, TS, or present value of tax shield, VTS APV Valua@on with No FCF Growth (1-‐τ) kD D IX ΔT IDI Δ IC Without Debt 33% 67% 10% $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ With Debt 33% 67% 10% $ 100,000 $ 10,000 $ -‐ $ -‐ $ -‐ EBIT τ·∙EBIT EBIT·∙(1-‐τ) IX·∙(1-‐τ) NP $ 223,881 $ 73,881 $ 150,000 $ -‐ $ 150,000 $ 223,881 $ 73,881 $ 150,000 $ 6,700 $ 143,300 t IX·∙(1-‐τ) $ -‐ IDI·∙(1-‐τ) $ -‐ Δ T $ -‐ NOPAT M&M assump@ons including kTS = KD FCF $ 6,700 $ -‐ $ -‐ $ 150,000 $ 150,000 Δ IC $ -‐ $ -‐ $ 150,000 $ 150,000 Rates of Return on Equity 8 APVM : V = $180 FCF EBIT(1 − τ) + τ ⋅ D = + τ ⋅D kU kU ‘Trailing’ net profit on present equity book value $160 Fair Value [$M] $140 D $120 $100 VU $80 $60 E $40 $20 VTS $0 FCFM : V = FCF k = EBIT(1 − τ) k Capital Structure and Cost of Equity FCFE + D kE EBIT(1 − τ) -‐ k D ⋅ D ⋅ (1 − τ) = +D kE FCFEM : V = NP0 EB -‐1 (EBIT -‐ IX)(1 − τ) = EB roe = ‘Forward’ (expected) net profit on present equity fair value E[NP1 ] E0 E[(EBIT -‐ k D ⋅ D) ⋅ (1 − τ)] = E (EBIT -‐ k D ⋅ D) ⋅ (1 − τ) = E EBIT ⋅ (1 − τ) -‐ k D ⋅ D ⋅ (1 − τ) = E rE = 2 8/23/14 Cost of Equity: M&M Assump@ons Cost of Equity: General 9 10 V = EBIT ⋅ (1 − τ) + τ ⋅D = D + E kU rE = EBIT ⋅ (1 − τ) -‐ k D ⋅ D ⋅ (1 − τ) E ¨ Most common model is Capital Asset Pricing Model (CAPM) ¤ ¤ EBIT ⋅ (1 − τ) = (D + E − τ ⋅ D) ⋅ k U = ((1 -‐ τ) ⋅ D + E) ⋅ k U rE = Defines a measure of risk as a single parameter Remember: kE ≡ E[rE] = rE ((1 -‐ τ) ⋅ D + E)⋅ kU − kD ⋅ D ⋅ (1 − τ) ¨ E rE is a func@on of the ¤ D rE = k U + (1 − τ) ⋅ (k U − k D ) ⋅ E ¤ Risk free rate of return, rF Investor’s addi2onal expected return rate for the expected risk on equity investment n M&M Assumptions FCF and Debt are perpetuities D rE = rU + (1 − τ) ⋅ (k U − k D ) ⋅ E kE = kU + (1 − τ) ⋅ (kU − kD ) ⋅ ¨ D E The investor’s return rate is rela@ve to equity market value – not the firm’s equity book value kE ≡ rE = rF + f( risk[rE] ) But we s@ll don’t know kU Risk Free Rate of Return, rF 11 Capital Asset Pricing Model (CAPM) 12 ¨ Return rate is risk free (known) over some planning period and in some currency ¤ ¤ ¨ ¤ E[rM-‐rF] is the expected, excess risky return rate on the ‘market’ over some investment horizon (Market risk premium, MRP) E[rE − rF ] = β ⋅ E[rM − rF ] β is a risk parameter for an equity’s expected excess return rate rela@ve to the market’s expected excess return rate (Equity risk premium) Full return of principal ‘Nominal rate’ not real n Real rate of return may not be known n Future purchasing power of return and principal may not be known In the U.S. the risk free rate of return is the treasury debt zero coupon bond yield ¤ E[rE ] = rF + β ⋅ E[rM − rF ] 12 mo. treasury bill yield for 1 yr investment horizon 10 year zero coupon treasury strip yield might be used for a long term investment horizon Capital Structure and Cost of Equity Return rate is a random variable with expected value rE and rM Risk is an measure of return rate variance – actually the standard devia@on and usually annualized Beta for the market, βM = 1 Firm’s equity beta almost always 0.25 < β < 2 Examples: SO GG AAPL BIDU 3 8/23/14 Capital Asset Pricing Model (CAPM) More About Beta 13 14 ¨ • Plot historical excess return pairs rEi − rFi ,rMi − rFi 4.0% • i is index for historical sample pairs ( ) rEi − rFi • weekly or monthly historical samples are typical β calcs -3% Calcula@on ¤ Market: M 2.0% ¤ Correla@on of returns : ρiM 1.0% ¤ Standard devia@on of return rates: σi , σM (σi , σM > 0) n -1% 0% -1.0% • Linear (OLS) regression • Excess returns normally distributed about trend line • Trend line slope is β 1% 2% ¨ 3% -2.0% -3.0% β=.7 (1 ≥ ρiM ≥ -‐1) Annualized standard devia@on of return rate is called ‘vola@lity’ Insights ¤ Is β = +2 more risky than -‐2 ? ¤ Is ρ = +1 more risky than ρ = -‐1 ? ¤ Is a larger σ i more risky ? σM -4.0% Not enough info, investors care about ‘portfolio risk’ Yes -5.0% rMi − rFi More About Beta 15 σi σM Stock: i 0.0% -2% βi = ρiM ⋅ ¤ 3.0% Cost of Capital in Unleveraged Firm, kU 16 ¨ Yahoo ¤ ¨ Morningstar ¤ ¨ ¨ 3 years of monthly returns ¤ “Raw Beta” uses 2 years of weekly returns ¤ “Adjusted Beta” is .67 * Raw Beta + .33 * 1 ¨ Ibbotson ¨ Value Line ¨ Others – Standard and Poors, Barra ¤ ¤ ¤ 3 years of monthly returns Bloomberg 5 years of monthly returns 5 years of weekly returns Capital Structure and Cost of Equity βL for the actual, leveraged firm from linear regression βL = rE − rF rM − rF ¨ βU for unleveraged firm ¤ No tax advantaged debt βU = rU − rF rM − rF k U = rU = rF + βU ⋅ (rM − rF ) k E = rE = rF + βL ⋅ (rM − rF ) Unleveraging and leveraging does not involve ‘@me’ -‐ just transform one scenario to another e.g., ΔDB = 0 Typical to compare firm’s unleveraged β – risk due to business opera@ons 4 8/23/14 Beta Risk M&M Assump@ons M&M Assump@on: Relate k and kU 17 18 ¨ Compute βU from equivalence of D r = r + βL ⋅ (rM − rF ) rE = rU + (1 − τ) ⋅ (kU − kD ) ⋅ E F E General case ¨ ¨ rF + βL ⋅ (rM − rF ) = rU + (1 − τ) ⋅ (rU − rD ) ⋅ M&M assump@ons k = kE ⋅ D E Subs@tute r ≡ r + βU ⋅ (rM − rF ) U F (r − r ) D βL = βU + (1 − τ) ⋅ U D ⋅ (rM − rF ) E All firms with constant D/V E D + kD ⋅ (1 − τ) ⋅ V V k = kU ⋅ If firm’s debt is further assumed risk free debt, rD = rF kE = kU + (1 − τ) ⋅ (kU − kD ) ⋅ E D D + (1 -‐ τ) ⋅ (kU -‐ kD ) ⋅ + kD ⋅ (1 − τ) ⋅ V V V D E M&M restric@on of firms with constant D D ⎞ ⎛ k = kU ⋅ ⎜ 1 -‐ τ ⋅ ⎟ V ⎠ ⎝ D ⎞ ⎛ βL = βU ⋅ ⎜ 1 + (1 − τ) ⋅ ⎟ E ⎠ ⎝ M&M Assump@on: Hamada Equa@on 19 Capital Structure Scenario Analysis 20 D ⎞ ⎛ βL = βU ⋅ ⎜ 1 + (1 − τ) ⋅ ⎟ E ⎠ ⎝ rE = rF + βL ⋅ (rM − rF ) rE = rF + βU ⋅ (rM − rF ) ⋅ [1 + (1 − τ)]⋅ D E rE = rF + βU ⋅ (rM − rF ) + βU ⋅ (rM − rF ) ⋅ (1 − τ) ⋅ Risk free rate of return Business risk premium Sample Problem: ¨ A firm wants to determine its β risk and cost of capital, k, if it doubles its leverage (D/E ra@o) ¨ Miller & Modigliani ¤ D E Risk premium due to financial (leverage) risk ¤ ¤ ¨ Debt and FCF are constant over @me But different scenarios may have different levels of debt But ‘un-‐leveraging’ and ‘re-‐leveraging’ are scenario changes Given: rM = 12%, τ = 40%, D/E = .33, rF = 5% βL = 1.24 (from linear regression with D/E = .33) Assume rD = rF in this example Capital Structure and Cost of Equity 5 8/23/14 Capital Structure Scenario Analysis 21 Capital Structure Scenario Analysis 22 ¨ ¨ Calculate kE ¤ kE = rF + 1.24·∙(12% -‐ 5%) = 13.7% Calculate the unleveraged beta βU βU = βL ⋅ ¨ ¨ 1 1 = 1.24 ⋅ = 1.035 D ⎞ (1 + (1 − .40) ⋅ 0.33) ⎛ ⎜ 1 + (1 − τ) ⋅ ⎟ E ⎝ ⎠ ¨ kU = rF + βU·∙(rM -‐ rF) = 5% + 1.24·∙(12% -‐ 5%) = 12.2% Calculate the new cost of equity kE = rF + 1.445·∙(12%-‐5%) The Five Pillars rM τ = 15.1 Calculate the unleveraged cost of capital ¤ Calculate a new βL that reflects a D/E of .66 D ⎞ ⎛ βL = βU ⋅ ⎜ 1 + (1 − τ) ⋅ ⎟ = 1.035 ⋅ (1 + .4 ⋅ 0.66 ) = 1.445 E ⎠ ⎝ rF 12% 40% 5% Current Unlevered Prospective D/E 33% 0% 66% β 1.240 1.035 1.445 kE 13.7% 12.2% 15.1% The M&M Proposi@ons 23 Nobel Prize winner and former Univ. of Chicago professor, Merton Miller, published a paper called the “The History of Finance” Miller iden@fied five “pillars on which the field of finance rests” These include 1. 2. 3. 4. 5. Miller-‐Modigliani Proposi@ons • Merton Miller 1990 and Franco Modigliani 1985 Capital Asset Pricing Model • William Sharpe 1990 Efficient Market Hypothesis • (Eugene Fama, Paul Samuelson, …) Modern Por}olio Theory • Harry Markowitz 1990 Op@ons • Myron Scholes and Robert Merton 1997 Capital Structure and Cost of Equity Provide fundamental insights into corporate finance ¨ Franco Modigliani ¨ ¤ formerly professor at MIT ¤ 1985 Nobel Prize winner ¨ Merton Miller ¤ formerly professor at the University of Chicago ¤ 1990 Nobel Prize co-‐winner http://nobelprize.org/ nobel_prizes/economics/ laureates/ 24 6 8/23/14 Irrelevance or indifference ? M&M Proposi@on 1 (1-‐τ) kD D IX ΔT IDI Δ IC Assume no income tax: τ = 0 thus no tax shield ¤ These proposi@ons are also referred to as “Irrelevance Theorems” or “Indifference Theorems” “showing what doesn’t ma~er can also show, by implica@on, what does” Merton Miller ¤ The firm may have debt Capital structure and leverage are irrelevant to firm value FCF V = VU + VTS = + τ ⋅D kU FCF = ¤ ¤ EBIT τ·∙EBIT EBIT·∙(1-‐τ) IX·∙(1-‐τ) NP kU $ 450,000 $ -‐ $ 450,000 $ 50,000 $ 400,000 $ 450,000 $ -‐ $ 450,000 $ -‐ $ 450,000 IX·∙(1-‐τ) $ 50,000 $ -‐ IDI·∙(1-‐τ) $ -‐ $ -‐ Δ T $ -‐ $ -‐ The firm’s value is due to its asset’s expected free cash flow and risk, not how the assets are financed NOPAT The alloca@on of FCF between debt and equity providers is irrelevant to firm value 25 M&M Proposi@on 2 With Debt Without Debt 0% 0% 100% 100% 10% 10% $ 500,000 $ -‐ $ 50,000 $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ t $ 450,000 $ 450,000 Δ IC $ -‐ $ -‐ $ 450,000 $ 450,000 $ 400,000 $ 450,000 FCFF 26 FCFE Proposi@on 2: No income tax 28 27 • No income tax: τ = 0 thus no tax shield • Leverage does increase the expected return on equity, rE, due to increased risk to the shareholders, and thus increases the cost of equity, kE D kE = kU + (1 -‐ τ ) ⋅ (kU − kD ) ⋅ E if τ = 0 E D D kU = kE ⋅ + kD ⋅ kE = kU + (kU − kD ) ⋅ V V E ¤ But leverage does not change the cost of capital, k, from the unleveraged cost of capital, kU. Therefore leverage does not increase the value of the firm. D ⎞ ⎛ k = k U ⋅ ⎜ 1 -‐ τ ⋅ ⎟ V ⎠ ⎝ set τ = 0 k = k U Capital Structure and Cost of Equity 18% kE 16% kU 14% τ=0% k 12% kU=15% 10% kD=10% kD 8% 6% 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 D / E V= FCF FCF = VU = k kU kD is assumed not a func@on of D/E The rate cost advantage of using more debt capital is exactly offset by the increased rate cost of the equity due to increased risk 7 8/23/14 Example: No Income Tax ¨ ¨ ¨ ¨ M&M assump@ons τ=0%, kU=15%, kD=10%, D=$0 FCF = $450,000 FCF $450,000 V = VU = 15% = $3,000,000 Now the firm borrows $500,000 D=DB=$500,000 ¤ ¨ kU = t (1-‐τ) kD D IX ΔT IDI Δ IC EBIT With Debt Without Debt 0% 0% 100% 100% 10% 10% $ 500,000 $ -‐ $ 50,000 $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ $ -‐ $ 450,000 τ·∙EBIT $ -‐ τ EBIT·∙(1-‐ ) $ 450,000 IX·∙(1-‐τ) $ 50,000 NP $ 400,000 No Income Tax Example 30 ¨ ¤ ¤ $ 450,000 $ -‐ $ 450,000 $ -‐ $ 450,000 ¨ IX·∙(1-‐τ) $ 50,000 $ -‐ 29 FCFF FCFE the firm’s FCF remains at $450,000 and kU and rU remain at 15% n Is the firm’s value s@ll $3,000,000 or has IDI·∙(1-‐τ) $ -‐ $ -‐ it increased to $3,500,000 based on Δ T $ -‐ $ -‐ V = E + D ? NOPAT $ 450,000 $ 450,000 Δ IC The value remains $3,000,000 since ¨ $ -‐ $ -‐ $ 450,000 $ 450,000 $ 400,000 $ 450,000 kU is not a func@on of capital structure However the equity value is reduced to $2,500,000 (debt is senior to equity) FCF E = -‐ D kU $450,000 = -‐ $500,000 = $2,500,000 15% Actually a firm raising debt in this scenario intends to use it to buy back equity so that capital structure changes, but not total capital No Income Tax Example No Income Tax Example 31 Now compute the new cost of equity, kE ¤ ¤ ¨ ¨ kE is a func@on of capital structure, D/E D kE = kU + (kU − k D ) ⋅ E k = 15% + (15% − 10%) ⋅ $500,000 = 16.0% Increased E $2,500,000 Equity providers expect increase return due to increased risk E D + kD ⋅ (1 − τ) ⋅ V V = 16.0% ⋅ 0.833 + 10% ⋅ 0.167 = 15.0% k = kE ⋅ Capital Structure and Cost of Equity E = FCFE 400,000 = = $2,500,000 kE 16.0% $3,500,000 $3,000,000 D $2,500,000 $2,000,000 $1,500,000 VU EU E* $1,000,000 $500,000 And compute the new cost of capital, k Compute the equity value, E, using FCFE Value ¨ $-‐ No change D = $0 32 D = $500,000 8 8/23/14 M&M Proposi@on 1 M&M Proposi@on 2 33 34 ¨ Income tax included: τ > 0 • Income tax included: τ > 0 ¤ If the firm has debt, D>0, then the firm does have a tax shield ¤ Leverage increases the risk to shareholders and thus increases the expected (demanded) return on equity, rE , and the cost of equity, kE ¤ However the tax shield decreases the risk to shareholders rela@ve to the no tax scenario ¤ If the firm has debt, D>0, then the firm does have a tax shield ¤ Capital structure and leverage are relevant to firm value n The present value of the tax shield increases its unlevered value by τ·∙D n The firm’s value is due to its asset’s expected free cash flow and risk, as well as how the assets are financed n The alloca@on of FCF between debt and equity providers is relevant to firm value V = VU + VTS = kE = kU + (1 -‐ τ) ⋅ (kU − kD ) ⋅ ¤ FCF + τ ⋅D kU Leverage, D/V, decreases the cost of capital, k, from the unleveraged cost of capital, kU D ⎞ ⎛ k = kU ⋅ ⎜ 1 -‐ τ ⋅ ⎟ V ⎠ ⎝ Capital Structure Example Example with Income Tax (1-‐τ) kD DB=D IX ΔT IDI A: Tax / B: Tax / DB=$0 DB=$250,000 33% 33% 67% 67% 10% 10% $ -‐ $ 250,000 $ -‐ $ 25,000 $ -‐ $ -‐ $ -‐ $ -‐ C: Tax / DB=$500,000 33% 67% 10% $ 500,000 $ 50,000 $ -‐ $ -‐ D: Tax / DB=$750,000 33% 67% 10% $ 750,000 $ 75,000 $ -‐ $ -‐ kD EBIT τ·∙EBIT EBIT·∙(1-‐τ) IX·∙(1-‐τ) NP $ 450,000 $ 148,500 $ 301,500 $ -‐ $ 301,500 $ 450,000 $ 148,500 $ 301,500 $ 33,500 $ 268,000 $ 450,000 $ 148,500 $ 301,500 $ 50,250 $ 251,250 0.3 IX·∙(1-‐τ) $ -‐ $ 16,750 $ 33,500 IDI·∙(1-‐τ) $ -‐ $ -‐ $ -‐ ΔT $ -‐ $ -‐ $ -‐ NOPAT $ 301,500 $ 301,500 $ 301,500 $ 50,250 $ -‐ $ -‐ $ 301,500 36 35 t Determine costs of capital and value under four levels of debt 18% kE 16% kU tax % 33.0% kU 15.00% kD 10.0% 14% k 12% 10% 8% 6% 0.0 0.1 0.1 0.2 0.2 0.3 D / E 0.4 0.4 0.5 0.5 FCF FCFE Capital Structure and Cost of Equity D E $ 450,000 $ 148,500 $ 301,500 $ 16,750 $ 284,750 ΔIC $ -‐ $ -‐ $ -‐ $ -‐ $ 301,500 $ 301,500 $ 301,500 $ 301,500 $ 301,500 $ 284,750 $ 268,000 $ 251,250 9 8/23/14 Capital Structure AExample B Debt used to buy back equity so that IC remains constant kD 10.0% kU τ DB VU E EB 15.0% 33.0% $ -‐ $ 2,010,000 $ 2,010,000 $ 1,005,000 EBIT NOPAT FCF $ 450,000 $ 301,500 $ 301,500 D=DB EB IC VTS V E E/EB D/E D/V kE k V IX Capital Structure Example D $ 750,000 Input $ 255,000 $ 1,005,000 =EB+DB $ 247,500 τ·∙D $ 2,010,000 $ 2,092,500 $ 2,175,000 $ 2,257,500 =VU + τ·D $ -‐ $ 1,005,000 $ 1,005,000 $ -‐ C $ 500,000 $ 505,000 $ 1,005,000 $ 165,000 $ 250,000 $ 755,000 $ 1,005,000 $ 82,500 $2,400,000 $2,200,000 $ 2,010,000 $ 1,842,500 $ 1,675,000 $ 1,507,500 =VL -‐ D 2.00 2.44 3.32 5.91 0.000 0.136 0.299 0.498 0.000 0.119 0.230 0.332 15.00% 15.45% 16.00% 16.67% =kU+(1-‐τ)(kU-‐kD)·D/E 15.00% 14.41% 13.86% 13.36% =kU·(1-‐τ·D/V) FCFE $ 2,010,000 $ 2,092,500 $ 2,175,000 $ 2,257,500 = FCF / k $ -‐ $ 25,000 $ 50,000 $ 75,000 =kDD $ 301,500 $ 284,750 $ 268,000 $ 251,250 =FCF-‐(1-‐τ)·kD·D E roic EP MVA V rE roe $ 2,010,000 30.00% $ 150,750 $ 1,005,000 $ 2,010,000 15.00% 30.00% $ 1,842,500 30.00% $ 156,694 $ 1,087,500 $ 2,092,500 15.45% 37.72% $ 1,675,000 30.00% $ 162,186 $ 1,170,000 $ 2,175,000 16.00% 53.07% D D D $1,800,000 VU $1,600,000 VU VU E E $1,400,000 VU E E $1,200,000 $ 1,507,500 = FCFE / kE 30.00% =NOPLAT/IC $ 167,277 =IC·(roic-‐k) $ 1,252,500 = EP/k $ 2,257,500 =IC+MVA 16.67% =(EBIT-‐IX)(1-‐τ)/E 98.53% =(EBIT-‐IX)(1-‐τ)/EB $1,000,000 D=$0 D=$250,000 D=$500,000 D=$750,000 Essen@al Points Op@mal Capital Structure 39 VTS VTS VTS $2,000,000 40 V D/E V = Value according to simple firm assump@ons PV(financial distress) Actual firm value Value of unleveraged firm Op@mal D/E ra@os under each assump@on EBIT(1 − τ) + τ ⋅ D -‐ PV(Financial distress) kU Capital Structure and Cost of Equity ¨ Proposi@on 1 ¤ ¨ Firm value is due only to the expected return and risk on firm opera@ons, FCF, unless there is a tax shield due to debt and income tax. In that case the addi@onal value is due to the present value of the tax shield. Proposi@on 2 ¤ ¤ ¤ Debt (leverage) increases risk to shareholders and thus increases the cost of equity, kE, and the expected return on equity, rE The tax shield reduces the risk to the shareholder and thus the cost of equity. The tax shield increases the value of the firm. Leverage does not lower the cost of capital except in the case of tax advantaged debt 10 8/23/14 Essen@al Points Deriva@on of the Beta Risk Factor • Calculate cost of equity capital, kE • For any firm with a historical record of market equity price • Introduc@on to the CAPM model • Understand β risk and • Cost of equity capital and equivalence with expected return rate • Calculated unleveraged cost of capital, kU, from kE in the case of a simple firm • Explored the rela@onships between k, kU, kD, and kE for a simple firm • Differen@ated between risk free return, expected return on business opera@ons, and addi@onal expected return due to financial leverage ¨ 41 Calculate por}olio variance ¤ Split into market propor@onal variance and firm specific variance M M σP2 = ∑ ∑w ⋅ w ⋅ σ i=1 M σ P2 = ∑ i=1 M i j=1 j M ∑ w ⋅ w ⋅ (β ⋅ β ⋅ σ i j=1 j i j M σP2 = ∑ σ ij ≡ βi ⋅ β j ⋅ σ M2 + σ εij ij 2 M 2 M +σ εij ) M M i=1 j=1 σ εij ≡ σ ij − βi ⋅ β j ⋅ σM2 ∑w ⋅ w ⋅ β ⋅ β ⋅ σ + ∑ ∑w ⋅ w ⋅ σ i=1 i j=1 j i j i j εij 42 Deriva@on of the Beta Factor ¨ 2 M M 2 M Split σP = ∑ ∑ w i ⋅ w j ⋅ βi ⋅ β j ⋅ σM + ∑ i=1 j=1 i=1 Deriva@on of the Beta Factor M ∑ w ⋅ w ⋅ σ j=1 i j Market propor@onal Firm specific ⎞ ⎛ ⎛ M M M M M ⎜ ⎟ ⎜ M σP2 = ⎜ ∑ w2iβ2iσM2 + ∑ ∑ wi ⋅ w j ⋅ βi ⋅ β j ⋅ σM2 ⎟ + ⎜ ∑ w2i ⋅ σ2ε + ∑ ∑ wi ⋅ w j ⋅ σε i=1 j=1 i=1 j=1 ⎜ i=1 ⎟ ⎜ i=1 j≠ i j≠ i ⎠ ⎝ ⎝ variance covariance variance covariance ¨ Firm specific covariance is assumed zero. Split the variances and covariances i 2 P M 2 i 2 i 2 M 2 εi M σ = ∑ w ⋅ (β ⋅ σ + σ ) + ∑ i=1 Capital Structure and Cost of Equity 43 i=1 M j=1 j≠ i ⎞ ⎟ ij ⎟ ⎟ ⎠ 2 M ∑ wi ⋅ w j ⋅ βi ⋅ β j ⋅ σ M M i=1 i=1 σP2 = ∑ w2i ⋅ (β2i ⋅ σM2 + σ2εi ) + ∑ εij 2 i 2 i 2 M M j=1 j≠ i i j j Systemic risk only 2 M Systemic and σiM = βi ⋅ βM ⋅ σ non-‐systemic σiM = βi ⋅ σM2 risk i σij = βi ⋅ β j ⋅ σM2 2 εi σ = β ⋅σ + σ (firm specific) 2 M ∑w ⋅ w ⋅β ⋅β ⋅ σ βi = σiM σM2 44 11 8/23/14 Deriva@on of the Beta Factor Reference: More About Beta 46 V = VU + VTS = D + E σ βi = iM σM2 Use the following weighted averages when leverage (D/V and E/V) is constant Note that the sums below are for por}olios, not through @me Cannot use with M&M, but can use for M&E and H&P Sub into CAPM formula ri = rF + σiM ⋅ (rM − rF ) σM2 Price of risk ri − rF rM − rF = 2 σiM σM σi σM Capital Structure and Cost of Equity i=1 = w1 ⋅ β1 + w 2 ⋅ β2 VU V D E + β TS ⋅ TS = βD ⋅ + βE ⋅ V V V V assume β TS = βU D E βU = β D ⋅ + βE ⋅ V V βU ⋅ σiM = ρiM ⋅ σi ⋅ σM βi = ρiM ⋅ M βP = ∑ w i ⋅ β i 45 M rP = ∑ wi ⋅ ri i=1 = w1 ⋅ r1 + w2 ⋅ r2 rU ⋅ VU V D E + rTS ⋅ TS = rD ⋅ + rE ⋅ V V V V D E + rE ⋅ V V E D rE ⋅ = rU − rD ⋅ V V V D rE = rU ⋅ − rD ⋅ E E rU = rD ⋅ 12