BUS 106 M3 (Ch. 12, 13, 16)
Capital Structure and Taxes
- MM Propositions 1 and 2 - assume no corporate taxes - tax deductible interest expense - how does this change things
Measuring market risk example
- When the market is up 1%, Turbot average increase is +0.8% - When the market is down 1%, Turbot average decrease is -0.8% - The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8 example: Beta = (average changes of -0.8 to 0.8) / (-1.0 to 1.0 change in market ) = 1.6%/2%
If you invest in a market index your expected return will be 12% with a standard deviation of 20%. You can also borrow at a rate of 4% (risk-free) to invest in the market. Suppose you have $100 to invest, but you decide to borrow an additional $50, and invest $150 in the index. What happens to the expected return and risk of your equity investment?
- With a $100 investment, expected dollar return is $12 and risk is a 20% standard deviation. - With $150 invested, the total expected dollar return is $18 and risk is $30 - Since you have to pay $4 of interest on the riskless loan, the expected dollar equity return is $14 (14% on equity), but your equity bears all of the risk, so standard deviation of the equity return is $30, or 30% of the equity investment
Issues in using COC and WACC
- debt has two costs 1. return on debt 2. increased cost of equity demanded due to increase in risk - betas change with capital structure Beta assets = [D/V * Beta debt]+[E/V *Beta equity] - corporate taxes complicate the analysis of WACC and may change our decisions
portfolio betas
- diversification decreases variability from unique risk (part of standard deviation), but not market risk - the beta of your portfolio will be a weighted average of the betas of the securities in the portfolio - if you owned all the S&P composite index stocks, you would have a weighted average of beta of 1.0
FCF and PV
- free cash flows (FCF) should be the theoretical basis for all PV calculations - FCF is a more accurate measurement of PV than either Div or EPS - when valuing a business for purchase, always use FCF -- if using WACC, compute after tax FCF as if all equity financed -- if using COC, include the tax benefit of debt in determining after tax FCF
capital structure and financial distress
- if debt is beneficial, why don't firms operate with very high debt ratios? costs of financial distress - costs arising from bankruptcy or distorted business decisions before bankruptcy market value = value if all equity financed + PV Tax shield - PV Costs of financial distress
capital structure
- mix of long-term (funded debt) and equity financing - capital structure doesn't include spontaneous financing (e.g. accounts payable) but doesn't include notes payable etc..
cost of capital
- return the firm's investors could expect to earn if they invested in other assets with comparable degrees of risk - the expected return to the forgone opportunity to invest in another asset of equivalent market risk - opportunity cost of investing in firm
examining financial choices
- trade off theory: debt levels are chosen to balance interest tax shields against the costs of financial distress - pecking order theory: theory stating that firms prefer to issue debt rather than equity if internal finance is insufficient - financial slack: ready to access to cash or debt financing that can be used to finance projects - free cash flow: liquidity in excess of the amount that can beneficially be invested
cost of capital and WACC
- why do we care about the distinction between cost of capital and WACC? because we don't want to double count tax benefit of debt - if we are valuing actual after-tax cash flows, we need to use cost of capital to avoid double counting V = Actual Free cash flow / cost of capital - if we tax-adjust actual cash flows as if there were no interest expense, we need to use WACC V = Unlevered free cash flow / WACC - (tax benefit reflected in discount rate)
stock 1 has a beta of 0.6 and is 40% of the portfolio. Stock 2 has a beta of 1.2 and is 60% so the portfolio beta is
= (40%*0.6)+(60%*1.2) = 0.96 Beta of a Portfolio = (% of Portfolio in First Stock) × (Beta of First Stock) + (% of Portfolio in Second Stock) × (Beta of Second Stock)
high beta stocks have ...
A ... higher total risk than low beta stocks B... higher diversifiable risk than low beta stocks C... higher non-diversifbale (higher systematic/market risk) risk than low beta stocks. YES D... none of the above
fora firm that's partly debt financed
A. if WACC is used, unlevered free cash flows should be valued. YES B. if WACC is used, actual free cash flows should be valued C. if cost of capital us used, unlevered free cash flows should be valued D. if cost of capital is used, actual free cash flows should be valued. YES E. both A and D are correct. YES
Because the capital market line is based on total risk (standard deviation)
A.. individual stocks will plot above the CML B.. individual stocks will plot on the CML C.. individual stocks will plot below the CML. YES D... A.. individual stocks could plot above or below the CML E.. none of the above
because the security market line is based only on non-diversifable risk (i.e. market risk)
A.. individual stocks will plot above the SML (positive Alpha if lucky) B.. individual stocks will plot on the SML. YES because buying/selling will occur until they plot on SML C.. individual stocks will plot below the SML (negative Alpha) D.. individual stocks could plot above or below the SML E... non of the above
If you borrow at the risk-free rate and use the borrow money plus your own money to invest in the market...
A.... the expected return and risk of your equity investment will not change. B.... the expected return on your equity will go down and the risk will go up. C.... the expected return on your equity will go down but the risk will go down. D..... the expected return on your equity will go up and the risk will go down. E..... the expected return on your equity will go up but the risk will go up. YES
The expected return on a stock depends on...
A.... the total risk of the stock. NO this is standard deviation B.... the diversifiable risk of the stock. C.... the non-diversifiable risk of the stock. YES D.... how well-diversified the portfolio will be. E.... none of the above.
Capital budgeting & project Risk example
Based on CAPM, ABC company has three divisions and an overall cost of capital of 17%. [4+1.3*(10)]. A breakdown of the company's investments is listed below. When evaluating a new dog food production investment, which cost of capital should be used? 1/3 nuclear parts mfr. Beta=2.0 1/3 computer hard drive mfr. beta=1.3 1/3 dog food production Beta=0.6 Average company Beta of assets = 1.3 use beta of 0.6 to determine r = 4+0.6(14-4)=10% 10% reflects the opportunity cost of capital on an investment given the unique risk of project
cost of capital and WACC exam example
Big oil has an equity beta of .85. the risk free rate is 6% and the market risk premium is 7%. the corporate tax rate is 35%. determine the cost of capital and WACC for big oil Re =0.6+0.85*(0.7) =0.1195 R assets = [0.243*0.9]+(0.757*.1195) = 0.0219+0.0905 = 11.23% WACC = [0.243*(1-0.35)*0.09]+(.757*.1195) = 0.0142+0.0905 = 10.47%
measuring market risk: fundamentals
Bj,m = ? Bj,m = ? §β_(j,m)=〖Cov〗_(j,m)/〖Var〗_m §β_(j,m)=(ρ_(j,m) σ_j σ_m)/(σ_m σ_m )=(ρ_(j,m) σ_j)/σ_m
Cost of Capital v. WACC
Cost of Equity: Re = Ra + D/E *(Ra -Rd) Cost of Capital: Ra = Rd*(D/(D+E)) + Re*(E/(D+E)) WACC = (1-Tc)*Rd*(D/(D+E)) + Re*(E/(D+E)) WACC = (1-Tc)*Rd*(D/Vl) + Re*(E/Vl)
capital budgeting example concatenation manufacturing
FCF = -32.8. -71.0. -85.2. -54.8. 183.4. 303.8 PV(FCF) = -32.8/(1.085) + -71.0/(1.085)^2. +. -85.2/(1.085)^3 + 54.8/(1.085)^4. + 183.4/(1.085)^5 + 8,680/(1.085)^5 Horizon value = (303.8/0.085-0.05) = 8,680
Cap. Struc. & Corporate Taxes
In a corporate tax environment, river cruise DOES create value by using debt financing. this is done by maximizing the cash flows to both equity and bondholders
Modigliani Miller (no taxes)
MM 1 - firm value doesn't depend on capital structure V unlevered = V levered = V equity + V debt MM 2 - required return on assets is a capital-structure weighted average of the returns on debt and equity R assets = D/V *R debt + E/V *R equity R equity = R assets + D/E *(R assets - R debt)
geothermal inc. has the following structure. given that geothermal pays 8% for debt and 14% for equity, what's the company cost
Market value of Debt = $194 | 30% Market value of equity = $435 | 70% Market value of assets = $647 | 100% Portfolio return = (.3*8%)+(.7*14%)=12.2% Terminology: this portfolio return can be referred to as 1. the required return on capital (or assets) 2. the Unlevered cost of equity 3. the cost of capital note: the required return on equity takes account of the capital structure choice (30% debt) - Geothermal's debt holders account for 30% of capital structure, but get a smaller share of income because their return is guaranteed by company - stockholders bear more risk and receive a greater expected return - if you buy all the debt and all equity, you get all income
market value of bonds
PV of all coupons and par value discounted at the current YTM - note: YTM implicitly factos in default risk. however, unless the cost of debt since it assumes no default
Capital structure
PV of tax shield = (D*Rd*Tc)/Rd = D * Tc (assume perpetuity) e.g. annual tax benefit = 500,000*0.10*0.35 = $17,500 annual tax benefit = $142,500-$125,00 = $17,500 PV of $17,500 perpetuity = $17,500/0.10 = $175,000
geothermal inc. has the following structure. given that geothermal pays 8% for debt and 14% for equity, what's the company cost pt 2
Portfolio return = (.3*8%)+(.7*14%)=12.2% this is the "unlettered cost of equity" as if no debt interest is tax deductible. given a 35% tax rate, debt only costs 5.2% after tax (i.e. 8% * (1-0.35)) this is the after tax cost of debt After tax cost of capital is the "weighted average cost of capital" WACC = (.3*5.2%)+(.7*14%)=11.4%
Security Market Line equation
R = Rf + Beta*(Rm -Rf) Required return for a a stock that is held in well-diversified portfolio = Risk-free rate + Beta of stock*(Return on market - risk free rate) R = Rf +Beta*(Market risk premium) Market risk premium = return on market - risk free rate R = Rf + stock's risk premium stock's risk premium = Beta of stock*(Return on market - risk free rate) - the more market risk you are taking, the higher the return you expect - upward slope
CAPM and Company cost of debt pt 2
R assets = R debt*(D/V) + R equity*(E/V) V=D+E D= market value of debt E= market value of equity = # shares * price per share ex: market value of equity is $8MM and market value of debt is 4$MM. given 11.5% cost of equity and 5.5% cost of debt, find the company cost of capital R assets = 0.55*(4/12) + 0.115*(8/12) = 9.5%
cost of capital equations
R assets = total income / value of investments R assets (D* R debt)+(E*R equity)/V ---- R assets = (amount of Debt * Required rate of return on debt)+(amount of Equity or stock outstanding * Return on equity or required return on stocks) / total Value of investments R assets = (D/V * R debt) + (E/V * R equity)
CAPM and Company cost of debt
R debt = CAPM = Rf + Beta debt *(Rm - Rf) ex: the risk free rate is 4%, expected return on market is 10%. company's debt beta is 0.25. find the cost of debt R debt = 0.4+0.25*(0.10-0.04) = 0.055 Practical approaches to estimating the cost of debt - market-adjusted return of equivalently risky debt portfolios - estimated IRR of future cash flows taking account of default risk
a company that's similar to the one you want to value (same capital structure and risk) just paid its annual dividend of $2.50. the dividend is expected to grow at a rate of 5% per year. and the stock is currently selling for $20. estimate the cost of equity for your firm
Re = (Div1/P0)+g = [Div0*(1+g)/P0]+g = 2.50*(1.05)/20 +0.05 = 2.625/20 +0.05 = 18.125%
weighted average cost of capital with preferred stock
WACC = [D/V*(1 - Tc)*R debt]+[P/V *R preferred]+[E/V *R equity] ex: executive fruit has issued $4M debt, $2M preferred stock and $6M common stock. the required returns are 6%, 12%, 18%, respectively. tax rate is 35%. determine the WACC V = 4+2+6 = $12M WACC = [4/12 *(1 - 35%)*6%]+(2/12 *12%)+(6/12 *18%) = 12.3%
cost of capital example
a company's equity beta is 1.2. market rate is 10% and debt is 30% of its market-valued capital structure. the corporate tax rate is 35%. what're the company's cost of capital and WACC? cost of equity capital = R e = 4%+1.2*[10%-4%] = 11.2% cost of capital = R a = 30%*6% +70%*11.2% = 9.64% WACC = 30%*(1-35%)*6%+0.7*11.2 = 9.01%
value and capital structure
assets value of cash flows from firm's real assets and operations value of firms liabilities and stockholders' equity market value of debt market value of equity value of firm
Modigliani Miller Debt Policy Doesn't Matter theory - no taxes
assumptions - no taxes - well-functioning capital markets - no information asymmetry - no incentive effects - costless bankruptcy Financial managers cannot increase value by changing mix securities used to finance the company capital structure doens't affect value
Testing the CAPM
beta vs average risk premium graph Over the long run, low beta stocks have done better than expected
required rates of return
bonds - Rd = YTM or Rf + Beta debt (Rm - Rf) common stock - Re = CAPM = Rf + Beta equity (Rm - Rf)
Estimating cost of equity by discounting dividends
dividend cost of equity by discounting dividends growing perpetuity model = P0 = Div1/(Re - g) solve for Re: Re = (Div1/P0) +g
risk and return
graph of return on S&P 500 and return on investment
measuring market risk example graph slide 4/5
graph stock with a 0.5 beta as well as a stock with a beta of 0.2 and market portfolio - calculate expected return and plot it?
stock betas
graphs that show linear distribution and slope of beta
standard deviations and beta
high standard deviations or high volatility may become a lot less risky if held in diversified portfolio beta helps determine whether or not you should add it to diversified portfolio
A company's equity beta is 1.2. the market rate is 10%, and the risk-free rate is 4%. the company's cost of debt is 6% and debt is 30% of its market valued capital structure. the corporate tax rate is 35%. what happens to the equity beta, the cost of equity, the company's cost of capital and WACC if debt is increased to 40%
how leverage affects cost of capital and WACC R a remains 9.64% and R d remains at 6% Find Re and Beta equity for the new capital structure Re = (Ra - Rd*Wd)/We = (9.64-6*0.4)/0.6 = 12.067 Beta equity = (Re-Rf)/(Rm-Rf) = (12.067-4)/(10-4)=1.334 WACC = 0.4*0.65*6 + 0.6*12.067 = 8.8%
The Capital Market Line slide graph
how to get expected return that's greater than market portfolio - borrow at risk free rate and use that money to put into the market portfolio to leverage up -- expected return is higher because you're taking more risk -- standard deviation is higher because you can lose money in stocks and have to pay back money borrowed
capital structure choices with financial distress
if financial distress is costly, the benefits of high leverage are reduced
market value of equity
market price per share multiplied by the number of outstanding shares
security market line
market risk premium ([=return on stock market - return on treasury bills] OR [return on stock market=market risk premium+return on treasury bill or risk-free rate]). RMp = (Rm-Rf) or Rm = RMp + Rf - suppose the historical average risk premium on the market portfolio is 8.2% and the current Treasury bill (risk-free) rate is 4%. What is the expected return on the market portfolio? Expected return on market portfolio (Rm) = risk premium on market portfolio + current Treasury bill (risk-free rate) = 8.2% + 4% = 12.2%
how to compute portfolio beta
portfolio beta = (fraction of money in stock 1 * beta of stock 1) + (fraction in stock 2 * beta of stock 2) = (40% of money * 2.34) + (60%*0.17)
market portfolio
portfolio of all assets in the economy - practice a broad stock market index is used to represent the market
beta
sensitivity of a stock's return to the return on the market portfolio - the non-diversifable portion of the stock's risk relative to the risk of the market
measuring capital structure
since bank debt is floating rate, book value = market value if the long term bonds pay an 8% coupon and mature in 12 years, assuming a 9% YTM, what's their market value PV = 16/1.09 + 16/1.09^2 + 16/1.09^3 + ... + 216/1.09^12 Market value of LT debt = $185.7M common stock is selling for $12 per share. market value of equity = 12*100M = $1,200M
Matching FCF and COC and WACC
suppose in concatenato example from text, year 1 interest expense is $50. compute the year 1 unlevered FCF to use with WACC and actual FCF to use with COC
after tax cost of debt
taxes are an important consideration in the company cost of capital because interest payments are deducted from income before tax is calculated After-tax cost of debt = pretax cost * (1 - tax rate) = R debt * (1 - Tc)
Weighted average cost of capital (WACC)
the expected rate of return on a portfolio of all the firm's securities, adjusted for tax savings due to interest payments (11.4%)
which projects are worth pursing
the firm's beta=0.9 and expected return=9.4% so which projects are worth pursing A. pursue only project 3 B. pursue projects 3 and 4 C. pursue projects 2,3,4 D. pursue projects 1 and 3. YES because they plot above firm's security market line E. pursue all four projects use project beta to determine
Capital Budgeting & Project risk
the project cost of capital depends on the use to which capital is being put - therefore, it depends on the risk project and not the risk of the company company cost of capital - opportunity cost of capital for investment in the firm as a whole - company cost of capital is the appropriate discount rate for an average risk investment project undertaken by the firm
measuring market risk example graph slide pt 2
the return on stock market is 10% and risk free rate of return is 3%. What is the risk premium for a stock (j) that has a beta of 0.5? What is the expected return of the stock? The market standard deviation is 20%. Stock j has a standard deviation of 25%. How much of the risk of stock j is market risk and how much is diversifiable Expected return = 3%+0.5*(10%-3%) = 6.5% nondiversifiable risk of stock j = Beta j * standard deviation of market = 0.5*20 = 10% diversifiable risk of stock j = 25%-10% = 15%
example of CAPM measuring market risk
the return on stock market is 10% and risk free rate of return is 3%. What is the risk premium for a stock (j) that has a beta of 0.5? what is the expected return of the stock Market risk premium = Rm - Rf = .10-0.3=0.7 Risk premium on any asset = Bj*(Rm-Rf) = 0.5*0.7=0.035 Expected return = Rf + Bj*(Rm-Rf) = 0.03+0.035=0.065
Capital Asset Pricing Model (CAPM)
theory of the relationship between risk and return - only undiversifiable (market) risk matters - Expected risk premium on any security = beta*market risk premium Market risk premium = Rm - Rf Risk premium on any asset = Bj*(Rm-Rf) Expected return = Rf + Bj*(Rm-Rf)
stock expected returns table slide
through diversification you can eliminate market risk
you own all equity of personal company. company has no debt. it has annual cash flow of $10,000 before interest and taxes. corporate tax rate is 35%. have option to exchange part of your equity position for 6% bonds with a face value of $50,000. your personal tax rate is zero. should you do this?
total cash flow all equity = 6,500 *1/2 debt = 7,550 (4,550+3,000 - 1,050) = 6,500 after personal taxes
capital budgeting
valuing a business - value of a business or project is usually computed as the discounted value of FCF out to a valuation horizon (H) - the valuation horizon is sometimes called the terminal value and is calculated like a perpetuity PV = FCF1/(1+WACC)^1 + FCF2/(1+WACC)^2 + FCF3/(1+WACC)^3 + ... + PVh/(1+WACC)^h
WACC
weighted average cost of capital = [D/V * (1 - Tc)*R debt] + [E/V* R equity] ex: market value of equity is $8MM and market value of debt is 4$MM. the corporate tax rate is 30%. given the 11.5% cost of equity and 5.5% cost of debt, find the company weighted average cost of capital (WACC) WACC = 0.55*(1-0.3)*4/12 +0.115* 8/12 WACC = 0.55*0.7*0.333+0.115*0.667 = 8.95%
company cost of capital (unlevered cost of equity)
weighted average of debt and equity returns (12.2%)
M&M (Debt policy doesn't matter)
when firm is doing better it makes more sense to have debt because it is fixed whereas when its not doing well debt is still fixed and need to be repiad firm is not doing anything that investor cannot do themselves since they can do structuring
financial choices
why don't firms operate with very high debt ratios? - trade-off theory: debt levels are chosen to balance interest tax shields against the costs of financial distress - pecking order theory: theory stating that firms prefer to issue debt rather than equity if internal finance is insufficient -- financial slack: ready to access to cash or debt financing that can be used to finance projects -- free cash flow: liquidity in excess of the amount that can beneficial be invested
financial distress slide graph
x: debt y: market value of the firm the reason why market value of firm starts to decrease after optimal amount of debt is that those present value financial distress costs start to outweigh the present value of the interests tax shield and that starts to decrease the market value of the firm there - so firms will lever up up to point where present value of interests tax shields equal the present value financial distress and this is called the optimal capital structure which is the right mix of debt and equity to maximize firm value
