finance chap 11-13
How much cash flow before tax and interest is necessary to support a project that requires $4 million annually for equity investors and $2 million annually in interest payments if the firm's tax rate is 35%?
$8.15 million working from the bottom up: cash flow b4 interest and tax 8.15m interest 2m ----- pretax cash flow 6.15m tax 2.15m ------ after tax cash flow 4m
market risk premium with two stocks =
(E(r)1- E(r)2)/(beta1-beta2)
project valuation--steps
1.find another project with the same systematic risk characters, and use hat projects return as the discount rate 2.if the project has the same level of riskiness as the rest of the company's business, we will find the cost of capital for the entire firm and use the discount rate for the new project.aka WACC- weighted average cost of capital
assume you found an alternative investment, which has the same level of systematic risk as your project of interest. if the alternative investment offers a return of 10%, what is the appropriate rate for you project?
10% --bc has the same systematic risk characters
The yield-to-maturity of a firm's bond is 8.5%. The firm has a beta of 1.3 and a tax rate of 34%. The market risk premium is 8.4% and the risk-free rate is 3.8%. What is the firm's WACC if the firm has a capital structure that is 40% debt financed?
11.08% re = 3.8% + 1.3(8.4%) = 14.72% WACC = (1 - 0.40)(0.1472) + 0.40(.085)(1 - 0.34) = 0.1108, or 11.08%
A stock is expected to return 11% in a normal economy, 19% if the economy booms, and lose 8% if the economy moves into a recessionary period. The economists predict a 65% chance of a normal economy, a 25% chance of a boom, and a 10% chance of a recession. What is the expected return on the stock?
11.10% E(R) = (0.65 × 0.11) + (0.25 × 0.19) + (0.10 × -0.08) = 0.1110, or 11.10%
What is the WACC for a firm with 40% debt, 20% preferred stock, and 40% equity if the respective costs for these components are 9.23% before tax, 12% after tax, and 18% before tax? The firm's tax rate is 35%.
12% WACC = [0.4 × (1 - 0.35 × 9.23%)] + (0.2 × 12%) + (0.4 × 18%) = 12.0%
What is the approximate standard deviation of returns if over the past 4 years an investment returned 8%, -12%, -12%, and 15%?
12.01% Mean = (8% - 12 - 12 + 15)/4 = -0.25% Variance = {[8 - (-0.25)]2 + [-12 - (-0.25)]2 + [-12 - (-0.25)]2 + [15 - (-0.25)]2}/4 = 144.1875 Std dev = 144.1875.5 = 12.01%
What is the variance of returns of a 3-stock portfolio (with unequal weights 25%, 50%, and 25%) that produced returns of 20%, 25%, and 30%, respectively?
12.50 Mean = .25 × 20% + .50 × 25% + .25 × 30% = 25% Variance = .25 × (20 - 25)2 + .50 × (25 - 25)2 + .25 × (30 - 25)2 = 12.50
A firm with a beta of 1.22 just paid its annual dividend of $5.64 a share. The dividends increase at a rate of 2% annually. The risk-free rate is 3.5%, the market rate of return is 12.4%, and the dividend discount rate is 11.6%. What is the best estimate of the firm's cost of equity if the firm's stock currently sells for $60 a share using an average of methods?
12.97% re = 0.035 + 1.22(0.124 - 0.035) = 0.14358, or 14.358% re = ($5.64 × 1.02)/$60 + 0.02 = 0.11588, or 11.588% Average = (14.358% + 11.588)/2 = 12.97%
What proportion of a firm is equity financed if the WACC is 14%, the after-tax cost of debt is 7%, the tax rate is 35%, and the required return on equity is 18%?
14% = (1 - x)(7%) + (x)18%; x = 63.64%
minimal risk requirements
2 or more securities weights of the securities in the portfolio
Company X has 2 million shares of common stock outstanding at a book value of $2 per share. The stock trades for $3 per share. It also has $2 million in face value of debt that trades at 90% of par. What is the weight of debt for WACC purposes?
23.08% Weight of debt = (0.90 × $2m)/[(2m × $3) + (0.90 × $2m)] = 0.2308, or 23.08%
A firm has 12,500 shares of stock outstanding that sell for $42 each. The book value of equity is $400,000. The firm has also issued $250,000 face value of debt that is currently quoted at 101.2. What value should be used as the weight of equity when computing WACC?
67.48% We = (12,500 × $42)/[(12,500 × $42) + 1.012($250,000)] = 0.6748, or 67.48%
The weighted-average cost of capital for a firm with a 65/35 debt/equity split, 8% pre-tax cost of debt, 15% cost of equity, and a 35% tax rate would be:
8.63%. WACC = [0.65 × .08 × (1 - 0.35)] + (0.35 × 0.15) = 0.0863, or 8.63%
Which one of the following companies is most apt to be exposed to the least amount of macro risk? A machine tool manufacturer A large producer of flour A major commercial bank A regional airline
A large producer of flour
project valuation equity financing: cost of equity =
CAPM E(R) expected return on equity (Stock) 1. CAPM E(R) = rf + β*(rm − rf) 2. NPV= -investment+ all (CF/CAPM E(R) ^t)
What is the after-tax cost of preferred stock that sells for $10 per share and offers a $1.20 dividend when the tax rate is 35%?
Cost of preferred = $1.20/$10.00 = 0.12, or 12%
What appears to be the targeted debt ratio of a firm that issues $15 million in bonds and $35 million in equity to finance its new capital projects?
Debt ratio = $15m/($15m + 35m) = 0.30, or 30%
Stock A has a beta of .5, and investors expect it to return 5%. Stock B has a beta of 1.5, and investors expect it to return 13%. Use the CAPM to calculate the market risk premium and the expected rate of return on the market. ***practice this
Market risk premium 8% ± 1% Expected market rate of return 9% ± 1% Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. r = rf + β(rm − rf) Using the CAPM relationship, we can see that a change in beta will change the rate of return by the change in beta × market risk premium. So, solving for the market risk premium: MRP = (13% - 5%) / (1.5 - .5) = 8% Given the market risk premium, we can now solve for the risk-free rate using Stock A (It doesn't matter which stock you use.): .05 = rf + .5(.08) rf = .01, or 1% We know the beta of the market is 1,so the market rate of return is: Market return = 1% + 1(8%) = 9%
Which one of the following statements is incorrect concerning stock indexes? Most indexes include all of the publicly-traded common stocks. Some indexes cover only a specific market sector. Some indexes are equally weighted. Indexes have been developed for foreign stocks.
Most indexes include all of the publicly-traded common stocks.
project valuation equity financing: when asked if company should invest look at
NPV>0... if it is you invest calculate 1.CAPM E(R) 2. NPV (the value from 1 is on the bottom of the NPV equation
A share of stock with a beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 3 decimal places.) chapter 12 problem 6
P1 = $52.625 From the CAPM, the appropriate discount rate is: r = rf + β(rm - rf) = 4% + (.75 × 7%) = 9.25% r = .0925 = Dividend + Capital gain = $2 + (P1 - $50) 2formula17.mml P1 = $52.625 Price $50
Suppose an analyst estimates that free cash flow will be $2.43 million in year 5. What is the present value of this free cash flow if the company cost of capital is 12%, the WACC is 10%, and the equity cost of capital is 15%?
PV = $2.43m/1.105 = $1,508,839
According to CAPM estimates, what is the cost of equity for a firm with a beta of 1.5 when the risk-free interest rate is 6% and the expected return on the market portfolio is 15%?
Re = 6% + 1.5(15% - 6) = 19.5%
In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10%, and Treasury bills offered 7%. The risk premium for common stocks was:
Risk premium = 18% - 7% = 11%
Why is debt financing said to include a tax shield for the company? Taxes are reduced by the amount of the debt. Taxable income is reduced by the amount of the debt. Taxable income is reduced by the amount of the interest. Taxes are reduced by the amount of the interest.
Taxable income is reduced by the amount of the interest.
Which one of the following statements is correct when Treasury bills yield 7.5% and the market risk premium is 9.5%? The S&P 500 would be expected to yield about 12.68%. The S&P 500 would be expected to yield about 17.00%. The S&P 500 would be expected to yield about 8.50%. The S&P 500 would be expected to yield about 9.50%.
The S&P 500 would be expected to yield about 17.00%. E(R) = 7.5% + 1(9.5%) = 17%
What will be the effect of using the book value of debt in WACC decisions if interest rates have decreased substantially since a firm's long-term bonds were issued? The debt-to-value ratio will be understated. The debt-to-value ratio will be overstated. It cannot be determined without knowing interest rates. There will be no effect on WACC decisions.
The debt-to-value ratio will be understated.
Which one of the following statements best explains the fact that cyclical firms tend to have high betas? Their profit margins are small. Their earnings are less diversifiable. Their stocks are overpriced. Their earnings are not stable.
Their earnings are not stable.
Which one of these is considered to be the safest investment? U.S. Treasury bonds Common stock U.S. Treasury bill Preferred stock
U.S. Treasury bill
Which one of the following risk types can be most eliminated by adding stocks to a portfolio? Inflation rate risk Unique risk Systematic risk Market risk
Unique risk
treasury bills what is the time line and what kind of asset is it?
a portfolio of 3 month loans issued each week by the us government they are risk free assets
treasury bonds what is it and when does it mature?
a portfolio of long term bonds issued by the government and maturing in about 10 years
The risk-free rate is 6% and the expected rate of return on the market portfolio is 13%. a. Calculate the required rate of return on a security with a beta of 1.25. b. If the security is expected to return 16%, is it overpriced or underpriced?
a. Required return = rf + β(rm − rf) = 6% + [1.25 × (13% − 6%)] = 14.75% b. underpriced. Its expected return is greater than the required return given its level of risk.
We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, −.2. a. If the interest rate on Treasury bills is 5% and the expected return on the market portfolio is 15%, what is the expected return on the shares of the law firm according to the CAPM? b. Suppose you invested 90% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio?
a. r = rf + β(rm − rf) = 5% + [(−.2) × (15% − 5%)] = 3% b. Portfolio beta = (.90 × βmarket) + (.10 × βlaw firm) = (.90 × 1.0) + [.10 × (−.2)] = .88
In 2013 Caterpillar Inc. had about 759 million shares outstanding. Their book value was $35 per share, and the market price was $94.50 per share. The company's balance sheet shows that the company had $32.5 billion of long-term debt, which was currently selling near par value. a. What was Caterpillar's book debt-to-value ratio? b. What was its market debt-to-value ratio? c.Which measure should you use to calculate the company's cost of capital?
a. Book debt-to-value ratio = Debt / (Debt + Equity) = $32.5b / [$32.5b + (.759b × $35)] = .55 b. Market debt-to-value ratio = Debt / (Debt + Equity) = $32.5b / [$32.5b + (.759b × $94.50)] = .31 c. Market value is the proper measure, as it is determined by cash flows and forecasts, rather than accounting rules.
project valuation with equity financing: if the project is financed 100% equity, then the required rate of return of the project is equal to?
a. cost of equity of the firm->if new project has the same level of systamtic risk of company's equity or b.opportunity cost of capital->other equity investment opportunities with similar risk level (aka stocks)
Olympic Sports has two issues of debt outstanding. One is a 8% coupon bond with a face value of $31 million, a maturity of 10 years, and a yield to maturity of 9%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 9%. The face value of the issue is $36 million, and the issue sells for 93% of par value. The firm's tax rate is 35%. a. What is the before-tax cost of debt for Olympic? b. What is Olympic's after-tax cost of debt?
a.9.49% b.6.17% a. First, compute the price of the 8% coupon bonds for each $1,000 of face value: PV = [(.08 × $1,000) × (1 / .09 - {1 / [.09(1 + .09)10]})] + $1,000 / (1 + .09)10 = $935.82 This means that each 8% coupon bond is selling for 93.582% of face value. Thus, the total market value of the issue is: Market value = .93582 × $31m = $29,010,526 The 9% coupon bonds are selling at 93% of face value, thus the market value of that issue is: Market value = .93 × $36m = $33,480,000 Total market value = $29,010,526 + 33,480,000 = $62,490,526 We also need to know the yield to maturity for the 9% bonds: PV = $930 = [(.09 × $1,000) × ((1 / r) - {1 / [r(1 + r)15]})] + $1,000 / (1 + r)15 Using trial-and-error, a financial calculator, or a computer, we find that: r = 9.9159% We can now calculate the before-tax cost of debt: Before-tax cost of debt = WA × rA + WB × rB = [($29,010,526 / $62,490,526) × .09] + [($33,480,000 / $62,490,526) × .099159] = .0949, or 9.49% b. After-tax cost of debt = Before-tax cost of debt × (1 - Tc) = 9.49% × (1 - .35) = 6.17%
project valuation debt financing: if the project is financed 100% debt, then the required rate of return of the project is equal to?
a.cost of debt of the firm->if new project has the same level of systematic risk of company's debt or b.opportunity cost of capital->other debt investment opportunities with similar risk level (aka bonds)
Although Standard and Poor's Composite Index contains a limited number of U.S. publicly traded stocks, the Index represents: approximately 75% of U.S. stocks traded, in market value. all stocks priced at $50 a share or more. approximately 50% of U.S. stocks traded, in market value. all stocks in the industrial sector.
approximately 75% of U.S. stocks traded, in market value.
expected returns
are a reflection of how much risk is involved with investing in the securities
actual returns
are a reflection on how well the firm has done (the price moves to reflect changes in firm value)
unsystematic risk
arises due to random events that only affect a single company or a small group of companies ie. CEO resignation, lawsuits, strikes
diversification what it does and to what kind of risk does it affect?
as long as the stock in the portfolio don't move perfectly together, as one stock experiences an increase in price, the other stock may experience a decrease in price, and the total volatility of the portfolio is less affected than the volatility of each security in the portfolio you can not diversify all the risk, only to an extend can only reduce or eliminate unsystematic risk
variance
average value of squared deviations from the mean
if you are just given beta and sd of market return.. to find the new sd.. you
b* sdtotal risk of the market portfolio look at connect to see an example in chapter 12
why cant systematic risk be diversified?
because it arises from economy wide influences that affect all assets
project valuation equity financing: when looking to find CAPM E(R).. teacher can say find:
cost of equity discount rate for valuing the project
compare t-bills and t-bonds they have different-----
different maturities
t-bills and stocks have different----
different risk levels
Risk factors that are expected to affect only a specific firm are referred to as: risk premiums. market risk. systematic risk. diversifiable risk.
diversifiable risk.
rational investors prefer highest expected return with lowest possible risk. how do we lower the risk?
diversification
the market portfolio is made up of individual stocks, so why isn't its variability equal to the average variability of its components?
diversification reduces variability of the portfolio returns. as long as you find stocks that are not perfectly positively correlated your portfolio will have lower variation than each stock
what is: non-diversifiable/ systematic/ market risk? what do they affect?
economy wide sources of risk that affect the entire stock market
tf: the firms beta measure the total risk of the firm
false it measures the market systematic risk
diversifiable/ unsystematic/ specific/ idiosyncratic risk..what do they affecr
firm or industry specific risk factors only affect some stocks or small group of stocks
If the slope of the line measuring a stock's historic returns against the market's historic returns is positive, then the stock: has a beta greater than 1.0. has no unique risk. has a positive beta. plots above the security market line.
has a positive beta
what does beta measure
how sensitive a security is to market movements b>1: amplify the overall market movements(aggressive stock which is good when the market goes up) 0>b>1: move in the same direction as the market but not a lot (defensive stock which is good when the market goes down) b<0: moves in opp. direction of the market b=0: independent from market movements-risk free asset b=1: move exactly the same as the market-the market itself ie. stocks beta is 1.41, then when the market goes up by 1%, the return on the stock goes up by 1.41% on average
SML line if stock is below? if stock is above?
in equilibrium, all stock should lie on the SML. this means all stocks are correctly priced. underpricese(r)>capm e(r) overprised e(r)<capm e(r)
historical return patters
in the finance market as proxies to make predictions on the expected returns of a stock in the future
risk premium stock
is a function of the market risk premium and the stock's sensitivity to market movements (beta) =beta*market premium
investment risk
is related to the probability of earning a low or negative actual return the greater the chance of lower than expected, or negative returns, the riskier the investment the wider spread the return indicates higher risk
Rate of Return Scenario Probability Stocks Bonds Recession .20 −5 % +14 % Normal economy .60 +15 +8 Boom .20 +25 +4 Consider a portfolio with weights of .60 in stocks and .40 in bonds.
look for the answers on connect chapter 11 problem 12
Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $50. The stock will pay a dividend at year-end of $2. Assume that risk-free Treasury securities currently offer an interest rate of 2%. Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013 (figures in percent per year) are as follows. Portfolio Average Annual Rate of Return Average Premium (Extra return versus Treasury bills) Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6
look for the answers on connect chapter 11 problem 13 What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.) Discount rate 9.60 ± 1% % What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Stock price $ 47.45 ± 1%
When the overall market experiences a decline of 8%, investors with portfolios of aggressive stocks will probably experience portfolio: losses greater than 8%. gains of less than 8%. losses of less than 8%. gains greater than 8%.
losses greater than 8%.
market index
measures of the investment performance of the overall market
The company cost of capital: measures what investors require from the company. depends on historical profits and cash flows. depends on current profits and cash flows. is measured using security book values.
measures what investors require from the company.
what do future scenarios do?
model future uncertainty
If a security plots below the security market line, it is: offering too little return to justify its risk. ignoring all of the security's unique risk. a defensive security, which expects to offer lower returns. underpriced, a situation that should be temporary.
offering too little return to justify its risk.
CAPM e(r)> e(r)
overpriced
market portfolio
portfolio of all assets in the economy
The appropriate opportunity cost of capital is the return that investors give up on alternative investments that: earn the average market rate of return. are included in the S&P 500 index. possess the same level of risk. earn the risk-free rate of return.
possess the same level of risk.
The basic tenet of the CAPM is that a stock's expected risk premium should be: greater than the risk-free rate of return. proportionate to the stock's beta. greater than the expected market return. proportionate to the market return.
proportionate to the stock's beta.
XYZ Company issues common stock at a price of $25 a share. The firm expects to pay a dividend of $2.20 a share next year. If the dividend is expected to grow at 2.5% annually, what is XYZ's cost of common equity?
re = $1.20/$25 + 0.025 = 0.113, or 11.3%
respected return of an individual stock =
risk free rate+ risk premium specific risk is diversifiable but market risk is not
market risk premium
risk premium of market portfolio. difference between market return and return on risk free t- bill
correlation coefficient
shows the strength of the relationship between two series -1: perfectly negative related 0: independent of each other 1: perfectly positively related
risk=
specific risk+ unsystematic risk
market risk premium =
stock return- t bill return
The slope of the regression line that exhibits the past relationship between a stock's returns and the market's returns is the: market's beta. stock's beta. stock's standard deviation. market risk premium.
stock's beta.
market premium=
t bond return- t bill return
expected return (current year)=
t-bill yield+ historical market risk premium
covariance
tells us the direction of the relationship, between two series. it does not say the strength of the relationship
For a company that pays no corporate taxes, its WACC will be equal to: the total value of its assets. the expected return on its equity. the expected return on its debt. the expected return on it assets.
the expected return on it assets.
The slope of the security market line equals: one. the market risk premium. the expected return on the market portfolio. beta.
the market risk premium.
opportunity cost of capital
the rate of return that the firm's shareholders are giving up by investing in the project rather than in comparable risk alternative
what kind of stock will A diversified investor want the stock with the lowest beta the stock with the highest beta the stock with the lowest variance the stock with the lowest variance
the stock with the lowest beta
Which stock is safest for an undiversified investor who puts all her funds in one of these stocks? the stock with the lowest total volitility the stock with the highest total volatility
the stock with the lowest total volitility, aka lowest SD
Macro events only are reflected in the performance of the market portfolio because: only macro events are tracked by economists. the market portfolio contains only risk-free securities. the firm-specific events would be too numerous to quantify. the unique risks have been diversified away.
the unique risks have been diversified away.
CAPM
theory of the relationship between risk and return which states that the expected risk premium on any security = b*market risk premium rf+b*(rm-rf)
The idea that investors in a common stock may expect a lower total return if they purchase a stock with limited price volatility rather than one with high price volatility suggests that: real rates of return will be lower during periods of price stability. stocks should be avoided when inflation is low. there is a relationship between risk and return. investors are irrational.
there is a relationship between risk and return.
tf: investors demand higher expected rates of return from stock with returns that are highly exposed to macroeconomic changes
true
tf: investors demand higher expected rates of return on stock with higher volatility
true
tf:investors demand higher expected rates of return from stock with returns that are very sensitive to fluctuations in the stock marker
true
CAPM e(r)<e(r)
underpriced
diversification decreases variability from ---risk but not ----risk
unique risk, market risk
To calculate the present value of a business, the firm's free cash flows should be discounted at the firm's: aftertax cost of debt. cost of equity. pre-tax cost of debt. weighted-average cost of capital.
weighted-average cost of capital.
What is the beta of a 3-stock portfolio including 25% of stock A with a beta of 0.90, 40% of stock B with a beta of 1.05, and 35% of stock C with a beta of 1.73?
βPortfolio = 0.25 × 0.9 + 0.4 × 1.05 + 0.35 × 1.73 = 1.25
