FIN 316H Midterm 1 - Final

A Risk-Free Asset and Many Risky Assets

CHECK IMAGE ON SLIDE 31

Correlation (ρ)

Correlation measures the degree to which two things move together linearly. Ranges between -1 and +1.

Russell 2000

By size, the #1000-3000 largest stocks.

Which of the following type of risk is most likely avoided by forming a diversified portfolio? A. Total risk. B. Systematic risk. C. Nonsystematic risk.

C. Nonsystematic risk.

Mean-Standard Deviation Rule

In this class, we will assume that stock returns can be adequately described by their means and standard deviations (or, equivalently, variances). The mean-standard deviation rule is based on two assumptions/facts: 1. Individuals prefer higher returns to lower returns. 2. Individuals prefer less risk to more risk.

Suppose that in the coming year, you expect Nike stock to have a standard deviation of 30% and a beta of 1.2, and Reebok stock to have a standard deviation of 41% and a beta of 0.6. For a diversified investor that wants to add a little bit of Nike or Reebok to her portfolio, which stock is riskier?

Diversification deals with the non-systemic risk, i.e., a diversified investor worries only about the systemic risk, which she cannot eliminate. Nike has a higher systemic risk, so the investor will require a higher return from holding it!

Sometimes steps 1 and 2 are given. For step 3, how do we discount the free cash flows at the firm's WACC to get the total value of the operating assets- the Enterprise Value?

EV = FCF1/(1+WACC)^1 + FCF2/(1+WACC)^2 ... FCFn + TVn/(1+WACC)^N Most of this equation is straightforward- discount the FCFs at the overall firm's cost of capital (WACC). Just don't forget TVn at the end!

Capital Asset Pricing Model (CAPM) Formula

E[Ri] = Rf + Bi x (E[Rmarket]) - Rf) • i is a particular stock or investment • Rf is the risk-free rate • Rmarket is the return on the market (e.g., S&P 500) • E[...] means expectation over the next period

Suppose Ford (F) has a beta of 2.67, while the beta of Safeway (SWY) is 0.72. If the risk-free interest rate is 3% and the market return is 6%, what is the expected return of a portfolio of 70% Ford and 30% Safeway, according to the CAPM? (using CAPM twice, then mean return)

E[Ri] = Rf + Bi x (E[Rmarket]) - Rf) expected return(F) = 11.01% expected return(SWY) = 5.16% μp = 𝑤𝐹 μF + 𝑤SWYμSWY μp = 70%μF + 30% μSWY = 70% × 11.01% + 30% × 5.16% = 9.255% OR USE PORTFOLIO BETA

Suppose McDonalds Inc. has debt with a market value of $15 billion outstanding and a stock price of $95. McD has 982 million shares outstanding, an equity book value of $17 billion, and $1 bil cash. What Equity and NetDebt should we use to calculate WACC for McDonalds?

Equity: 982 shares * $95/share = 93.3 billion NetDebt: $15 bil - $1 bil = $14 billion

Homogeneous Expectations Assumption

Financial economists often imagine a world where all investors possess the same estimates on expected returns, variances, and covariances. Though this can never be literally true, it can be thought of as a useful simplifying assumption in a world where investors have access to similar sources of information.

Solving for r (Yield to Maturity)

For a zero-coupon bond, it much easier: ytm= (FV/PV)^(1/N) -1 PV = PMT/(1+YTM)^1 + ... + if not 0-coupon, use EXCEL

Investors use standardized yield measures to allow for comparison between bonds with varying maturities. For bonds maturing in more than 1 year: For money market instruments of less than 1 year to maturity:

For bonds maturing in more than 1 year: An annualized and compounded yield-to-maturity is used. For money market instruments of less than 1 year to maturity: • These are annualized but not compounded. • We obtain the EAR for them! -Recall that the Effective Annual Rate helps to overcome the problem of varying periodicity, since it is the equivalent interest rate assuming there is just one compounding period per year.

convexity effect

For the same coupon rate and time-to-maturity, the percentage price change is greater when the market discount rate goes down (than when it goes up). -non-linear relationship

maturity effect

For the same coupon rate, a longer-term bond has a greater percentage price change (than a shorter-term bond) when their market discount rates change by the same amount. This effect holds in most cases, but not always! -more price volatility -such exceptions are rare and occur only for bonds priced at a discount w/ low (but not 0) coupons and long maturities

coupon effect

For the same time-to-maturity, a lower-coupon bond has a greater percentage price change (than a higher-coupon bond) when their market discount rates change by the same amount. -lower coupon rater has a greater price change

Determining the Beta of a Project - some info

How do we get the beta of a project? • In the last class, we regressed company stock returns on the market (S&P 500). ➢ Beta measures how much the stock moves relative to how much the market moves. • BUT the firm's stock and the firm itself are not the same thing, and so they may not have the same beta! ➢ Why? Because of LEVERAGE!

maturity

How long until the last payment is made. N: # of evenly spaced periods to maturity

coupon amount ($)

How many dollars is each coupon. (Coupon Rate x Par Value) / (Number of coupon payments per year) PMT is coupon payment per period

What does a spot rate (Zt) really mean?

How much would you pay today (at t=0) to receive $1 at some future time t? - Call that price Pt . • The spot rate, Zt , is then the period interest rate (or percentage return) at which Pt today is compounded to deliver $1 at that future time t: Pt× (1+Zt ) t = $1 ➔ Zt=($1/Pt )^(1/t)-1 - If you know the price Pt , you also know the spot rate Zt , and vice versa. - We use the (actual) prices of the U.S. government bonds to estimate the price Pt and the spot rate Zt !

Recap of Investment Decision. What are the steps?

I. Estimate individual securities' expected returns and standard deviations, as well as their correlations II. Compute the efficient set of risky assets. III. Introduce the risk-free asset. IV. Determine the tangency between the risk-free rate and the efficient set of risky assets. Point m represents the portfolio of risky assets that the investor will hold.

Avant Corporation issues a 1-year zero-coupon bond with face value of $1,000. The 1-year, zero-coupon T-bill has a yield-to-maturity of 4%. What is Avant Corporation's bond's: (No default) 1. Price? 2. Yield-to-maturity?

If all investors agree that there is no chance of default, then, investors will receive $1,000 in 1 year for sure. The bond is then risk-free, as is the zero-coupon T-bill. Hence, it must have the same return to avoid any arbitrage: Price = $1,000/(1 + 0.04)^1 = $961.54 YTM = ($1,000/ $961.54)^(1/1) - 1 = 0.04 = 4%

Avant Corporation issues a 1-year zero-coupon bond with face value of $1,000. The 1-year, zero-coupon T-bill has a yield-to-maturity of 4%. What is Avant Corporation's bond's: (and the recovery rate is 90%) (Certain default) 1. Price? 2. Yield-to-maturity?

If all investors believe that default is certain, then, investors expect for sure 90%*$1,000=$900. The bond is again risk-free, like the T-bill. Hence, it must have the same return to avoid any arbitrage. Price = $900/(1 + 0.04)^1 = $865.38 (lower) YTM = ($1,000/ $865.38)^(1/1) - 1 = 0.156 = 15.6% (higher than before)

Market Equilibrium

Other investors would probably have different estimates of the variables like E[R] or variance. ➢ However, maybe the estimates do not vary by much, since all investors are forming expectations from the same data on past price movements and other publicly available information

Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. The yield-to-maturity of each bond is 5%. 1. What is the price of each bond per $100 face value? 2. Which bond trades at a premium, which trades at a discount, and which trades at par?

P(10% coupon) = (10/0.05) x (1-(1/1.05^30)) + 100/(1.05^30) = $178.86 so it trades at a premium P(15% coupon) = (5/0.05) x (1-(1/1.05^30)) + 100/(1.05^30) = $100 so it trades at par P(3% coupon) = (3/0.05) x (1-(1/1.05^30)) + 100/(1.05^30) = $69.26 so it trades at a discount

IBM issues a 10% annual coupon, 5-year maturity bond, with face value $1000. Annual r = 7%. What's its price?

PV = (100/0.07) x (1-(1/1.07^5)) + 1000/(1.07^5) PV = 1123

Bond price formula given a sequence of spot rates:

PV = PMT/(1+Z1)^1 + PMT/(1+Z2)2 where Z1 , Z2 , and ZN are spot rates for period 1, 2, and N, respectively

Formula for Calculating the Bond Price given the discount rate (r)

PV = PMT/(1+r)^1 + ... + (PMT + FV)/(1+r)^N

Recall what stock price is. Market value of equity = ... What is the formula for stock price?

PV of all the FCF's generated by the firm, minus net debt Stock price = Market value of equity / # shares

Consider a 6-month zero coupon bond with a face value of $1,000 with an Effective Annual Rate of 6%. Compounding takes place monthly. a. What is the bond's price? b. What is the bond's yield-to-maturity? c. What is the bond's APR?

PV x (1+0.06)0.5=$1,000 ➔ PV = $1,000/1.060.5 ➔ PV = $971.28 1 + EAR = (1+APR/m) m ➔ 1 + 0.06 = (1 + APR /12)^12 ➔ APR / 12 = 1.061/12 -1 ➔ APR /12 =0.00487 ➔ APR = 0.0584 or 5.84% Since the bond expires in less than 1 year, we use its EAR (instead of the APR) to refer to its yield! yield-to-maturity = EAR ➔ yield-to-maturity = 6%

coupon rate (%)

Percent (%) of par value paid every year

You paid $50 for a share of stock 1 year ago. Today, you received a dividend of $2, and you sold the stock for $45. What was your realized return?

Percentage Change in Price or Capital Gain = (P1 - P0 ) /P0 = ($45 - $50) / $50 = -$5 /$50 = -10% Dividend Yield or Dividend-to-Price Ratio = Div1 /P0 = $2 /$50 = 4% R1 = -10% + 4% = -6%

Return on Financial Assets (start of stocks part I) 1. Periodic income: 2. Capital gain/loss:

Periodic income: Cash dividends or interest payments. Capital gain/loss: Change in the price of a financial asset

What is the price of a 5-year zero-coupon bond with an annual discount rate of 3.0% and a $100 face value?

Price = $100/(1.03)5 = $86.26

Avant Corp.'s bond exercise - Default Risk Cont'd • Suppose investors demand a risk premium of 1.1% for this bond, so that their expected return is 4% + 1.1% = 5.1%

Price = $950/(1 + 0.051)^1 = $903.90 YTM = ($1,000/ $903.90)^(1/1) - 1 = 0.106 = 10.6% • 10.6% is the promised yield is the most investors will receive. • If Avant defaults, they will receive only $900, and end up having a return of ($900/$903.90)^(1/1) - 1 = -0.004 = -0.4%. • The expected return is indeed 0.50×10.6% + 0.50×(-0.04%) = 5.1% ➔ Avant's cost of debt

par value/face value

Principal amount to be paid at end of bond's life (maturity). The "big final payment. FV of the bond

You paid $50 for a share of stock 1 year ago. Today, you received a dividend of $2, and you sold the stock for $45. What was your realized return? (directly calculate)

R1 = (P1 + Div1 - P0 ) /P0 = ($45 + $2 - $50) /$50 = -6%

how do we notate returns, weights, and expected returns for stocks?

RA : return of stock A RB : return of stock B wA : weight of stock A in portfolio wB : weight of stock B in portfolio μA : expected return of stock A μB : expected return of stock B μp : expected return of portfolio

Given a firm's 𝑟𝐷𝑒𝑏𝑡 (i.e., expected return of bonds, and not YTM!), we can use the CAPM to obtain its 𝛽𝐷𝑒𝑏𝑡:

Rd = 𝑅f + [𝛽𝐷𝑒𝑏𝑡 × Market risk premium] ⇒ 𝛽𝐷𝑒𝑏𝑡 = (𝑟𝐷𝑒𝑏𝑡 − 𝑅f)/Market risk premium so: B(assets) = [Bequity / (Debt/Equity) + 1]

Recall the WACC formula, WACC = Wd x Rd x (1 − τ) + Wp x Rp + We x Re. Where do we get the rates Rd, Re, and τ?

Rd: from Yield-to-maturity on the firm's bonds Re: Use the CAPM to find the required return on a firm's equity. τ: firm tax rate (given)

• The yield to maturity on Gap Inc.'s debt, and hence its pre-tax cost of debt, is 7.13%. • If Gap's tax rate is 40%, what is its effective cost of debt?

Rdebt x (1-τ) = 7.13% * (1-0.4) = 4.28% Since interest payments are tax deductible, debt only costs Gap 4.28%, not 7.13%.

What is a Stock Return?

Realized returns (R): The total return that occurs over a particular time period. (a.k.a. holding period return )

Starbucks' capital structure consists of 80% equity and 20% net debt, and the on Starbucks' equity is 1.0. The risk-free rate is 4% and the market risk premium is 6%. Its tax rate is 35%. 1) What is the required return on Starbucks' equity?

Requity = Rf + (βequity x Market Risk Premium) = 4% + 1.0* 6% = 10%

Example: Cost of Common Equity using the CAPM Problem: If the risk-free rate is 3%, the expected market risk premium is 5%, and the company's stock beta is 1.2, what is the company's cost of equity?

Requity = Rf + 𝛽equity x Market Risk Premium Cost of equity = 0.03 + 1.2 × 0.05 = 0.03 + 0.06 = 0.09, or 9%

2-asset portfolio expected return and variance: What is return of a portfolio consisting of stocks A and B?

Return of a portfolio of stocks A and B: Rp = WaRa + WbRb AND Wa + Wb = 1 so Wb = 1 - Wa

Suppose a company has preferred stock outstanding that has a dividend of $1.25 per share and a price of $20. What is the company's cost of preferred equity?

Rp = $1.25/$20 = 0.0625, or 6.25%

Stock return formula

Rt = [Pt + DIVt -Pt-1] / Pt-1 P=price of the stock or asset DIV=the dividend paid (if any)

variance of US Stocks

SUM[(return1 - mean return)^2 +...] / number of stocks included standard deviation = √(variance)

liquidity risk

Is it easy is to trade the bonds of a country?

Even though we calculated the WACC by using cost of equity and debt to get required return for a project, how is cost of equity and debt really determined? (start of cost of capital part II)

It is really the required return on the project that determines cost of equity and debt.

when a question asks you to find the cost of capital, what is the final answer looking for?

It wants you to get beta project of equity, then get return of the project of equity (using CAPM), and the final answer is the rate you get from using WACC. (weighted average cost of capital)

enterprise value (important topic)

Market value of equity = PV of all the free cash flows generated by the firm, minus net debt = Market Value of Equity + Debt - Cash

Nike has a WACC of 9.75%. It has created a limitededition Mariota shoe line that requires a $10 mil investment today and is projected to return $14 mil in free cash flow in 2 years.

NPV = -$10M + $14M/(1+r)^2 r= WACC = 9.75% NPV = -$10M + $14M/(1+0.0975)^2 = $1.62M > 0, a good project!

A firm is looking to invest in a real estate project that requires an initial investment of $10M today. The project is expected to yield cash flows of $1M for the next 15 years (t=1 to t=15). The beta of similar real estate projects is 1.5. If the expected return on the S&P500 Index is 9% and the risk-free rate is 1%, should the firm take the project?

NPV = -$10M + $1M*(1/r ) * (1-1 /(1 + r) 15 ) so, again we need to find the cost of capital for the project... r = required return = Rf + βproject x (market return - Rf ) = 1% + 1.5 * ( 9% - 1% ) = 13% NPV = -$10M + $1M*(1/r ) x (1-1 /(1 + r)^15 ) = -$10M + $1M*(1/0.13) * (1-1 /(1 + 0.13)^15 ) = -$3.54M < 0, so it is a bad project!

Starbucks' capital structure consists of 80% equity and 20% net debt, and the on Starbucks' equity is 1.0. The risk-free rate is 4% and the market risk premium is 6%. Its tax rate is 35%. 3) Starbucks is considering opening its first CoffeeLand, an amusement park about 50 miles from Seattle. They need to invest $50 million today. Free cash flows generated will be $7 million starting in one year, in perpetuity. Should Starbucks do it?

NPV = -$50M + $7M / r project We could set: r project = WACCcompany ➔ r = 8.65% and obtain: NPV = $30.92M > 0 However, setting r project = WACCcompany assumes that: 1. The project will be financed in the same debt-to-equity ratio as the company's, i.e., the company's capital structure remains the same after the project is financed. 2. The project's financial risk is the same as the company's -problematic assumptions

Question: Is a bigger dividend better?

Not necessarily, though some people mistakenly think so. • If the firm pays a dividend, owners get cash now. Great! • If, instead of paying a dividend, the firm invests the FCF in new positive NPV projects, owners will own a stake in a larger firm that will pay bigger dividends down the road. Also great! As long as a firm only keeps FCF for +NPV projects and dividends it back otherwise, shareholders could not care less which happens*

Interest rate risk: Sensitivity

Ok, bonds are risky because their prices change when interest rates change. When interest rates go up, bond prices go down (and vice versa).

WACC: finding Rdebt. What return do people who have bought a firm's debt require? We assume that what they are actually getting right now is what they require, which is...

Simply the yield to maturity (YTM) ➢ Do NOT use the coupon rate!

zero coupon bonds

Sometimes bonds come without coupons. There is only one cash flow: the repayment of par/face value at maturity. These are even easier to price.

how to spot rates related to YTM?

Spot rates are yields-to-maturity on zero-coupon bonds maturing at the date of each cash flow.

We will use _______________________ to capture the variability of returns.

Standard Deviation It measures the spread from the mean. -σ shows us the variability of returns, if the "randomness" of returns is normal;

What are the steps for Estimating a Beta Using the Pure-Play Method?

Step 1) Select the comparable -companies w/ similar business risk Step 2) estimate the comparable's beta Step 3) Unlever the Comparable's beta -remove financial risk component of the equity beta, leaving the business risk component of the beta Step 4) Lever the beta for the project's financial risk -adjust asset beta for financial risk of the project

What is the Cost of Preferred Stock? What is the formula?

The cost of preferred stock (that is noncallable and nonconvertible) is based on the perpetuity formula: Price(p) = Dividend(p) / Rp ➢ Rp = Dividend(p) / Price(p)

EX: Find the terminal value in year 3

TV3 = FCF4 / WACC - g same thing as TV3 = FCF3(1+g) / WACC - g

terminal value formula

TVn = FCF N+! / WACC - g • N is the number of years of actual, thought out, projections. • Treat the Terminal Value like an extra cash flow in year N. 1. On top is the FCF in the next year, N+1. 2. On bottom is WACC minus the growth rate in future FCFs (g) • This is the same as the growing perpetuity formula. ➢ This is why we had to learn growing perpetuities... • Once you get the TV, you must remember to discount it back from t=N to t=0. Forgetting this step is a common mistake!

what is the Capital Asset Pricing Model? (CAPM)

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk, or the general perils of investing, and expected return for assets, particularly stocks.1 -It is a finance model that establishes a linear relationship between the required return on an investment and risk.

Describe each step of the pure play method: step 2 ("Assumption")

The benchmark is valid, i.e., the beta of the assets of the benchmark (𝛽 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐴𝑠𝑠𝑒𝑡𝑠) coincides with the beta of the assets of the project (𝛽𝑝𝑟𝑜𝑗𝑒𝑐𝑡 𝐴𝑠𝑠𝑒𝑡𝑠). -The objective is to obtain the beta of the project's assets by assuming that it has the same business risk as the benchmark: Assume that: β 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 Assets = β 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 Assets

Suppose that a four-year, 5% annual coupon paying bond is priced at 105 per 100 of par value. The yield-to-maturity is the solution for the rate, YTM, in this equation (using excel is 3.634%). Is the bond traded at par, a premium, or. a discount. Why?

The bond is traded at a premium because its coupon rate is greater than the yield required by investors.

inverse effect

The bond price is inversely related to the market discount rate. When the market discount rate increases, the bond price decreases.

Geometric Mean Return

The geometric mean return accounts for the compounding of returns. Formula: T√[(1+R1)x(1+R2)... -1] EX R=[(1-.5)x(1+.35)(1+.27)-1]^(1/3) cube root because they're 3 stocks

A company issues a bond to finance a new project, with a face value of $100, a 5% semiannual coupon, and maturity in 10 years. Upon issue, the bond sells at $98. What is the after-tax cost of debt if the marginal tax rate is 40%? Assume semiannual compounding frequency. (calculate final #)

The period discount rate is r = YTM/2 ➔ 2.63% = YTM/2 ➔ YTM = 5.26% The after-tax cost of debt is Rd = YTM x (1 - τ) = 5.26% x (1-0.40) = 3.156%

A company issues a bond to finance a new project, with a face value of $100, a 5% semiannual coupon, and maturity in 10 years. Upon issue, the bond sells at $98. What is the after-tax cost of debt if the marginal tax rate is 40%? Assume semiannual compounding frequency. (explain how to do, need EXCEL usually)

The period discount rate is r = YTM/2, the coupon payment is PMT = 0.05 x $100/2 = $2.50. The number of periods is 10*2 = 20 semesters. $98 = $2.5 x (1/r) x [1 - 1 /(1+r)^20] + $100 / (1+r)^20 ➔ r = 2.63%

price of a fixed rate bond (describe and name the 3 types the bonds can be sold at)

The price of a fixed-rate bond (PV) relative to its face value (FV), depends on the relationship of the coupon rate to the market discount rate. -premium -par -discount

Fixed-Rate Bond: Price changes

The price of a fixed-rate bond will change whenever the market discount rate changes. The following effects are important relationships.

What is weighted average cost of capital (WACC)

The weighted average cost of capital (WACC) is the cost of raising additional capital, with the weights representing the proportion (%) of each source of financing that is used

What is a project's (D/E)Target?

Theoretically: one must take the project's contribution to firm debt capacity, i.e., the amount by which the firm's optimal debt level increases by virtue of undertaking the project.

What does the CAPM model tell us?

This equation gives us the r(required return) we will use for discounting future cash flows*

Avant Corporation issues a 1-year zero-coupon bond with face value of $1,000. The 1-year, zero-coupon T-bill has a yield-to-maturity of 4%. What is Avant Corporation's bond's: - 50% chance, the bond will repay its face value in full - 50% chance, the bond will default with 90% recovery 1. Price? 2. Yield-to-maturity?

Thus, they expect to receive: 0.50x1,000 + 0.50x$900 = $950 -The bond is no longer risk-free -Investors will require a higher (expected) return than 4%, as a compensation for the risk they bear from holding the bond!

Describe each step of the pure play method: step 3 ("Relevering the beta")

Use the beta of the assets of the project (𝛽𝑝𝑟𝑜𝑗𝑒𝑐𝑡 𝐴𝑠𝑠𝑒𝑡𝑠) and the beta-formula to solve for the beta of the equity of the project (𝛽𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝐸𝑞𝑢𝑖𝑡𝑦). -The objective is relever the benchmark's beta, by adjusting for the project's financial risk: β 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 Equity = [β 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 𝐴𝑠𝑠𝑒𝑡𝑠 x (1 + (𝐷𝑒𝑏𝑡𝑝𝑟𝑜𝑗𝑒𝑐𝑡/ 𝐸𝑞𝑢𝑖𝑡𝑦𝑝𝑟𝑜𝑗𝑒𝑐𝑡))] ⇔ = β 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 Equity = β 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐸𝑞𝑢𝑖𝑡𝑦 ⋅ [ (1 + (D/E)project) / (1 + (D/E)benchmark) ]

Describe each step of the pure play method: step 1 ("Unlevering the beta")

Use the beta of the equity of the benchmark (𝛽 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐸𝑞𝑢𝑖𝑡𝑦) and the beta formula to solve for the beta of the assets of the benchmark (𝛽𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐴𝑠𝑠𝑒𝑡𝑠). -The objective is to remove the impact of the benchmark's different capital structure from its beta to arrive at the asset beta, which reflects the benchmark's business risk: 𝛽 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 Assets = ]𝛽 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐸𝑞𝑢𝑖𝑡𝑦 / (1 + (Debt benchmark/equity benchmark))]

Starbucks' capital structure consists of 80% equity and 20% net debt, and the on Starbucks' equity is 1.0. The risk-free rate is 4% and the market risk premium is 6%. Its tax rate is 35%. 2) If Starbucks has a weighted average cost of capital (WACC) of 8.65%, what is Starbucks' cost of debt?

Using WACC formula 8.65% = (80% x 10%) + (20% x Rd*(1 - 35%) ➔ 8.65% = 8% + (Rd x 13%) ➔ Rd = 5%

Interpreting yield curve shapes - Declining (inverted) yield curve:

VERY RARE • Means interest rates are expected to be lower in the future than they are today ... • And that probably means bad news expected for economy

Dow Jones Industrial Average (The Dow)

Value of a portfolio holding one share in each of 30 large industrial firms. (First computed in 1896.)

Suppose the Widget Company has a capital structure composed of the following, in billions: Debt $10 and Common Equity $40. If the before-tax cost of debt is 9%, the required rate of return on equity is 15%, and the marginal tax rate is 30%, what is Widget's weighted average cost of capita

WACC = Wd x Rd x (1 − τ) + Wp x Rp + We x Re Wd = $10/$50 = 20%, Wp = 0% (no preferred equity), and We = $40 / $50 = 80% WACC = 0.20 × 0.09 × (1 - 0.30) + 0.80 × 0.15 = 0.0126 + 0.120 = 0.1325, or 13.25%

What is the WACC formula? What do all the other variables mean?

WACC = Wd x Rd x (1 − τ) + Wp x Rp + We x Re Wd=% of debt that the company uses when it raises new funds Rd=before-tax marginal cost of debt τ company's marginal tax rate Wp=% of preferred stock the company uses when it raises new funds Rp=marginal cost of preferred stock We=% of equity that the company uses when it raises new funds Re=marginal cost of equity (see example on cost of capital slide 21)

What is Wd and We?

Wd= net debt / (net debt + equity) = % of financing by debt

What does the answer to the last problem tell us in words?

When the Widget Company raises $1 more of capital, it will raise this capital in the proportions of 20% debt and 80% equity, and its cost will be 13.25%.

picture of possible yield curve shapes

Y axis is spot interest rate Zt and X axis is time to maturity t -declining is a mirror to that going below x-axis

How does FCF projection look on a timeline? EX: 5 years of FCF then terminal value

YR1: FCF1, YR2: FCF2, YR3: FCF3, YR4: FCF4, YR5: FCF5 ... + FCF5 *(1+g)^1 + FCF5 *(1+g)^2 CONDENSED TO FCF1 + FCF2 + FCF3 + FCF4 + FCF5 + TV5 TV5 captures the growth rate of end future cash flows

Relationship between coupon rate and YTM for a coupon bond YTM = coupon rate YTM > coupon rate YTM < coupon rate

YTM = coupon rate: the bond's price will be the same as its par/face value YTM > coupon rate: bond price < par value YTM < coupon rate: bond price > par value

for FCFE, what is the formula?

[Equity payout 2014 x (1+g) / (1+ Re)] + [Equity Payout 2014 x (1+g)^2 / (1+Re)^2] + ...

If the bond price is lower than par value, the bond is said to be traded at ___________ .

a discount. • This happens when the coupon rate is less than the market discount rate. ("deficient" coupon rate)

If the bond price is higher than par value, the bond is said to be traded at ________

a premium. • This happens when the coupon rate is greater than the market discount rate ("excessive" coupon rate)

dividend yield

a stock's expected cash dividend divided by its current price EX: $2 dividends paid 4 times throughout year, beg. year stock price was $22.00. Yield: ($8/$22) = 36.36%

IBM is considering taking a project that requires $1M of investment today. It will yield a cash flow of $1.7M after two years (at t=2). The return on the S&P500 index is 8% and the risk-free rate is 2%. Should IBM take the project: a) If the project is risk-free, i.e., the cash flow is $1.7M for sure? b) If the project is risky, i.e., the expected cash flow is $1.7M, and has a beta of 0.7?

a) If the project is risk-free, then r = Rf = 2% NPV = -$1M + $1.7M / (1 + r)^2 = -$1M + $1.7M / (1 + 0.02)2 = $0.634M > 0 a good project! b) If the project is risky and has a beta of 0.7, then r = required return = Rf + βproject (market return - Rf ) = 2% + 0.7 x ( 8% - 2% ) = 6.2% NPV = -$1M + $1.7M / (1 + r) 2 = -$1M + $1.7M / (1 + 0.062)^2 = $0.507M > 0, good!

The fixed-income market is used to sell ______.

debt securities

If the rating of an issued and traded bond is lowered, its price ____________ .

decreases

credit spread

default probability - risk-free rate

nonsystematic risk can be eliminated by ______________.

diversification

The lower a bond's recovery rate, the lower its _____________ .

expected return

risk premium

expected return - risk free rate

convexity effect: for each bond, the percentage price increases are __________ in absolute value than the percentage price decreases. The relationship between bond prices and the market discount rate is not linear; instead, it is curved.

greater

why is EAR (effective annual rate) important?

higher EAR tells us a higher annualized rate of return

bond price

how much you pay to get the bond today the PV of the bond

As an owner/equity holder, you might get some cash as "dividends", but firms spend some of your $ on ...

investing in new projects for expansion which could be very benificial to you in the future (higher stock price, bigger dividends)

Which of the bonds are investment grade? Which are junk?

investment grade: • AAA • AA • A • BBB junk: • BB • B • CCC • CC • C • D

r

is the required rate of return per period

If the stocks are perfectly positively correlated, the portfolio risk _____________________________________.

is the same as the risk of the individual stocks: σp = σΑ = σΒ means no diversification

If we ignore the CAPM, then 𝛽𝐷𝑒𝑏𝑡 = 0 allows debt to be priced based on ____________________________________________ .

its idiosyncratic (i.e., nonsystematic) risk of default.

All other things being equal, we expect that: 1. If two newly issued bonds have the same term to maturity, the _________________ (with the higher default chance) has a higher coupon rate.

lower-rated bond

systematic risk can't be avoided, it is ___________ .

market built in

Lower-coupon bonds have _____________ than higher-coupon bonds, other things being equal.

more price volatility

total risk =

nonsystematic risk + systematic risk

Equity is market capitalization =

number of shares outstanding × stock price

Expected return of a 1-year risky bond

one year bond expected return = (expected year-end cash flow / initial bond price, P) -1 = [(π(1+Q)xF + (1-π)xλxF)/P] - 1 π F=face value of bond P=price of bond Q=annual coupon rate of the bond π=probability the bond will NOT default at the end of year λ=fraction of bond's value bondholders collect upon default

An investor decides to hold a portfolio with: 1. 80% invested in the S&P 500 U.S. stock index, which has: i. An expected return of 9.93% ii. A standard deviation (risk) of 16.21% 2. 20% invested in the MSCI Emerging Markets index, which has: i. An expected return of 18.20% ii. A standard deviation (risk) of 33.11% What will be the portfolio's expected return and risk given that the covariance between the S&P 500 and the Emerging Markets index is 0.0050?

p1,2 = covar / (𝜎1 x 𝜎2) =15.10% portfolio standard dev (risk) expected return = 11.58%

The Capital Allocation Line (CAL)

plot of risk-return combinations available by varying portfolio allocation between a risk-free asset and a risky portfolio

Suppose the risk-free return is 3% and you believe the market risk premium to be 4%. Intel has a beta of 1.3. According to the CAPM, what is the required return for investing in Intel?

required return𝑖 = 𝑅𝑓 + 𝛽𝑖 x (𝐸[𝑅𝑚] − 𝑅𝑓) required return𝑖 = 3% + 1.3 ∗ (4%) required return𝑖 = 8.2%

Nonsystematic risk, a.k.a. diversifiable or idiosyncratic risk is ...

risk that is company-specific or industry-specific. • E.g., a drug trial failure, major oil discoveries, or an airliner crash. • All these events directly affect their companies and possibly industries, but they have no effect on unrelated assets. • It can be avoided by forming a portfolio with assets that do not have high correlations with one another. We do not care about this risk, because we can avoid it!!!!

The longer the maturity, the more ________________________ .

sensitive to rates

The arithmetic or mean return is the _______________. Describe the formula

simple average of all holding period returns • Assumes that the amount invested at the beginning of each period is the same • However, because the base amount changes each year (since the previous year's earnings is added to the beginning value of the investment), the arithmetic return may be misleading for evaluating a buy-and-hold strategy! Formula: =[R1+R2+R3+...] / T EX R: [-50%+35%+27%]/3 = 4%

Name 2 Violations of the normality assumption

skewness and kurtosis

Term structure of interest rates: The plot of spot interest rates (Zt ) against maturity (t) is called ____________ .

term structure of interest rates or spot curve. - In normal times, it is rising,

The plot of spot interest rates (Zt ) against maturity (t) is called ________________ of interest rates or _______________.

term structure, spot curve.

equity value from the FCFE approach is ...

the SUM of FCFE f / (1+re)^t

In equilibrium, total borrowing and lending must equalize so that the risk-free asset is in zero net supply when we aggregate across all investors. Moreover, in equilibrium, the total market wealth (i.e., the sum of the market capitalizations of all stocks) is equal to ____________________ .

the aggregate wealth of all investors. Example on slide 57

the coupon rate shows

the amount the issuer promises to pay the bondholders in interest each period, while the market discount rate shows the amount investors need to receive in interest each period in order to pay the full par value for the bond.

The yield to maturity on a bond is

the discount rate that will set the present value of the payments equal to the bond price

risk premium (in formula)

the excess return required from an investment in a risky asset over that required from a risk-free investment (E[Rmarket]) - Rf)

EX of the FCFE. the equity value of the company is the discounted value of ...

the future anticipated equity payouts

yield to maturity

the internal rate of return on a bond's cash flows. It is the implied market discount rate.

recovery rate

the percentage of its principal which holders can expect to recover in the case of default.

inflation risk

the prices of products and services in the country changes, and so does investors' purchase power

market discount rate

the rate of return required by investors given the risk of the investment in the bond.

Systematic risk, a.k.a. nondiversifiable or market risk, is ...

the risk that affects the entire market or economy. • E.g., interest rates, inflation, economic cycles, political uncertainty, and widespread natural disasters. • It cannot be avoided, since it is based on factors that are innate within the market. This is the risk that we want to price!!!!

Bond price should be equal to ______________ . (describe it)

the value of all discounted future cash flows.

If the stocks are not perfectly positively correlated (ρAB <1), _______________________ .

they can be combined in a portfolio with less risk than either of the two individually: σp < σΑ= σΒ There is diversification!

inverese effect: All prices go ______ if the rates go down from 20% to 19%. - All prices go __________ if the rates go up from 20% to 21%

up, down

when interest rates go down, the prices of bonds typically go ____ .

up. interest rates are prices for bonds!

If the market price of a bond is known, the "bond pricing formula" can be used to calculate its ________________ . (start of bonds part II)

yield-to-maturity.

The ideal dataset would be ___________________________________________________________________ .

yields-to-maturity on a series of zero-coupon government bonds for a full range of maturities. -This dataset is the government bond spot curve, a.k.a. the zero curve or strip curve (because there are no coupons).

The larger the coupons, the faster, on average, ______________________ .

you're getting your money.

Suppose that in the coming year, you expect Nike stock to have a standard deviation of 30% and a beta of 1.2, and Reebok stock to have a standard deviation of 41% and a beta of 0.6. Which has more systematic (or market) risk?

βNike = 1.2 > 0.6 = βReebok ➔ Nike has more systemic risk

In equation form, where i is the asset (GE here), m is the market (S&P) what is the formula for β.

βi = Pi,m x σi / σm

Portfolio Beta formula

βp = WaβA + Wbβb

Suppose Ford (F) has a beta of 2.67, while the beta of Safeway (SWY) is 0.72. These are the only two assets in your portfolio (bad idea- you should be diversified!). If your portfolio's beta is 1.0, what percent of your portfolio is in Ford?

βp = Wfβf + Wswyβswy 1 = (Wf x 2.67) + ((1-Wf) x 0.72) Wf=14.36%

Suppose Ford (F) has a beta of 2.67, while the beta of Safeway (SWY) is 0.72. If the risk-free interest rate is 3% and the market return is 6%, what is the expected return of a portfolio of 70% Ford and 30% Safeway, according to the CAPM? (using portfolio beta)

βp = Wfβf + Wswyβswy = 70% × 2.67 + 30% × 0.72 = 2.085 = 3% + 2.085 × (6% − 3%) = 9.255%

describe what p=-1, p=0, p=1, and p=0.6 mean?

ρ = -1 always move opposite linearly ρ = 0 uncorrelated; no tendency to move together or opposite each other ρ = 1 always move together linearly ρ = 0.6 usually move the same direction =CORREL(array returns 1, array returns 2)

how do we notate standard deviations and correlations for stocks?

σA : standard deviation of stock A's returns σB : standard deviation of stock B's returns ρA,B : correlation between the returns of stocks A and B

Suppose that in the coming year, you expect Nike stock to have a standard deviation of 30% and a beta of 1.2, and Reebok stock to have a standard deviation of 41% and a beta of 0.6. Which stock has more total risk?

σNike = 30% < 41% = σReebok ➔ Rebook has more total risk

What is a bond?

• A bond is an IOU ("I owe you"), usually issued by governments or corporations • Governments and firms sell these to get money right away for their spending needs. • By buying a bond, you are loaning them money --- paying them its price today

3 rd Evaluation Method: The FCFE Approach

• A firm's shares can also be valued by discounting the stream of anticipated equity payouts at an appropriate cost of equity (rE ). • This method is more direct Free Cash Flow to Equity = Dividends + stock repurchases OR FCFE = FCF - INT(1-tax rate) + net borrowing

The Market Portfolio

• A portfolio with a value-weighted (proportional) share of every risky asset in the world. • Practically, U.S. investors use a proxy for the true market portfolio

bond ratings in order of more likely to default as you go on

• AAA • AA • A • BBB • BB • B • CCC • CC • C • D

1 st Valuation Method: The Efficient Markets Approach (start of equity evaluation)

• According to the Efficient Market Hypothesis: the current market price of a stock is the correct price. ➢ The market has already done the difficult job of stock valuation, and it's done this correctly, incorporating all the relevant information. ➢ Considering the past and public information, there is empirical evidence that you cannot outguess market! -consider before doing stock evaluation

Limitations of the Effective Annual Rate

• Annualizing returns (by deriving the EAR) allows for comparisons among different assets and over different time periods. • But only under the assumption that returns can be repeated precisely; i.e., money can be reinvested repeatedly while earning a similar return. This is not always possible! • Suppose an investor earned a return of 5% during a week, because the market went up during that time • EAR = (1+0.05)^52 - 1 = 11.643 or 1,164.3%. Unlikely possibility it continues

is it proper to assume beta of debt = 0?

• But it might not be proper to assume 𝛽𝐷𝑒𝑏𝑡 = 0 - The higher a firm's leverage, the more likely that its debt depends on less firm-specific factors, e.g., interest rates, industry, and hence the market.

Corporations issue bonds too. What might be the difference between buying a bond from a corporation vs. from the government?

• Corporate bonds have credit risk, i.e., risk of default! - If you buy them, you might not get all their promised payments! - U.S. Treasury bonds are widely regarded to have no default risk. • Corporations with higher credit risk need to pay higher yields to attract buyers to their bonds.

Interpreting yield curve shapes - Rising yield curve:

• Could mean investors think interest rates will rise in the future • Could mean it is riskier to invest longer, so you get more return for buying longer term bonds

Coupon Rate vs. Coupon Amount

• Coupon rate is stated as an annual percent, even if coupons are not paid annually.

Portfolio Beta

• Every asset/bond/company/project has a beta. • A portfolio of stocks (or bonds, or projects, or whatever) is also an asset, and hence portfolios have betas too! • A portfolio's beta is simply the value-weighted average of the component betas.

how to we find beta in real life?

• Go to Yahoo! Finance or similar • And how do they find it? Run a regression like we did. • But how many periods of data should we use? • Tradeoff: - longer time series gives us more data to avoid small sample size issues... - longer time series is bad, however, if the company is not the same as it was in the early days.

U.S. Treasury Bills

• Have only terminal payment (zero coupons) • Short-term securities issued by U.S. government - Typical maturity: less than a year • Bills are discounted: No explicit interest

What What does 𝛽𝐷𝑒𝑏𝑡 = 0 mean?

• If the CAPM is valid, then 𝑟𝐷𝑒𝑏𝑡= 𝑅𝑓 , i.e., the firm borrows at the riskfree rate, independently of its capital structure... • If we ignore the CAPM, then 𝛽𝐷𝑒𝑏𝑡 = 0 allows debt to be priced based on its idiosyncratic (i.e., nonsystematic) risk of default. It means the company's beta does not have market risk

Adding Assets to the Investment Opportunity Set (start of stocks part II)

• If the additional assets are not perfectly correlated with the existing ones, the investment opportunity set expands out to the northwest providing a superior risk-return trade-off. - E.g., the investment opportunity set with international assets dominates the opportunity set that includes only domestic assets. • Thus, we should continue to add assets and asset classes until they do not further improve the risk-return trade-off!

What effects do Taxes and the Cost of capital have?

• Interest on debt is tax deductible; the cost of debt is adjusted to reflect this deductibility. - We multiple the before-tax cost of debt (rd ) by the factor (1 - τ), with t as the marginal tax rate. - Thus, rd × (1 − τ) is the after-tax cost of debt (a.k.a. the effective cost of debt). • Payments to owners are not tax deductible, so the required rate of return on equity (whether preferred or common) is the cost of equity. Ex on slide 26

What are characteristics preferred stock?

• Preferred shares are equities that have preferred rights (relative to common shares) to the cash flows and assets of the company. ➢ The right to receive a specific dividend on a regular basis. ➢ If the preferred share is a cumulative preferred equity, the company must pay the preferred shareholders any previously omitted dividends before it can pay dividends to the common shareholders. ➢ Can't vote ➢ Also, higher claims to assets relative to common shareholders in the event of corporate liquidation.

risk premium

• The "extra" return earned for taking on risk • Treasury bills are considered risk-free. • The risk premium is the return over and above the risk-free rate

The maturity effect: describe an example

• The 20-year bonds have greater percentage price changes than the 10-year bonds for either an increase or a decrease in the market discount rate. • Longer-term bonds have more price volatility than shorter-term bonds, other things being equal.

Market Risk and Beta; what does it mean if beta = 1, =-1, and =1

• The beta of the overall market portfolio is 1. • A beta of 1 implies the asset has the same systematic risk as the overall market • A beta < 1 implies the asset has less systematic risk than the overall market • A beta > 1 implies the asset has more systematic risk than the overall market

describe cost of capital (start of cost of capital - Part I)

• The cost of capital is the cost of using the funds of creditors and owners. • Creating value requires investing in capital projects that provide a return greater than the project's cost of capital. - Also, the firm itself, as a whole, creates value when it provides a return greater than its cost of capital.

cost of capital is ...

• The cost of capital is the rate of return that the suppliers of capital—bondholders and owners—require as compensation for their contributions of capital. - Reflects the opportunity costs of the suppliers of capital.

Market Discount Rates (spot rates)

• The market discount rates for cash flows with different maturities are rarely the same! • Better calculate the price of a bond by using a sequence of market discount rates that correspond to the cash flow dates.

Main Take-Aways from the Multiples Method

• The multiples valuation method is an effective way of comparing the values of several companies, as long as the companies being compared are truly comparable. ➢ Truly comparable firms will have similar operational characteristics (e.g., sales, costs, debt-to-equity ratio). ➢ It does not make sense to compare the stock price of two operationally similar firms if one is financed with a lot of debt and the other firm is financed primarily with equity. CHECK SUMMARY SLIDES AS WELL FOR BETTER UNDERSTANDING!

Market-Capitalization Weighting

• The weight on each security is determined by dividing its market capitalization by the total market capitalization (the sum of the market capitalization) of all the securities in the market. • Market capitalization or value is calculated by multiplying the number of shares outstanding by the market price per share

how do we estimate the weights for projects?

• The weights should reflect how the company will raise additional capital. • Ideally, we would like to know the company's target capital structure, which is the capital structure that is the company's goal, but we cannot observe this goal. Alternatives: 1. Assess the market value of the company's capital structure components. 2. Examine trends in the company's capital structure. 3. Use capital structures of comparable companies (e.g., weighted average of comparables' capital structure). see example on slide 44

Terminal Value: what is g?

• This is the rate at which the FCF will grow into infinity. • Typically, g is assumed to be lower than the nominal rate of economic growth (GDP), or else this firm will eventually grow larger than the economy itself... • Somewhere 2-4% is reasonable. important TV example on slide 56

2nd Valuation Method: The FCF Approach

• This method discounts the future free cash flows (FCF). • This method values the firm's debt and its equity together as the present value of the firm's future FCFs. - The discount rate used is the WACC.

4th Valuation Method: Multiples (a.k.a. Comparative Valuation)

• This valuation technique is based on a comparison of financial ratios for different companies. • Logic: Financial assets that are similar in nature should be priced the same way. Most common multiples: 1. Price = (Price-to-earnings ratio) ➢ Assume that similar firms have similar P/E ratios. 2. Enterprise Value = (EV-to-EBITDA ratio) * EBITDA ➢ Assume that similar firms have similar EV/EBITDA ratios. EX on slide 86 but this isn't a super important topic

Coupon rate and yield-to-maturity are entirely different things! What do we use each for?

• Use coupon rate to calculate how large the bond's intermediate cash flows are. • Use the yield-to-maturity as the discount rate ("r") of those cash flows and calculate the bond's price.

what is terminal value? (TVn)

• We assume that firms live forever, or at least for a long time. • Yet, realistically, we cannot forecast FCF's out that far. • • So, we use a shortcut: ➢ Project out as far as we feel comfortable (e.g., 3-5 years) . ➢ Make an assumption that the firm just grows at the same "economy-wide-ish" rate beyond that. • Terminal Value is the combined discounted value of FCFs from the year we stop explicitly projecting FCFs to infinity.

A proposed investment Z has a correlation with the market of 0.5. Suppose the expected return on the market is 7%, the risk-free rate is 3%, σm = 15%, and σz = 25%. What is this project's required return?

𝛽𝑖 = Pi,m × (𝜎𝑖/𝜎𝑚) = 0.5 × (0.25/0.15) = 0.833 required return𝑖 = 𝑅𝑓 + 𝛽𝑖(𝐸[𝑅𝑚] − 𝑅𝑓) = 3% + 0.83 × (7% − 3%) = 6.3%

how do we calculate portfolio standard deviation?

𝜎𝑝 = √[(Wa^2 x 𝜎a^2) + (Wb^2 x 𝜎b^2) + (2x Wa x Wb x 𝜎a x 𝜎b x pa,b)]

If the bond price is equal to par value, the bond is said to be traded _______ .

at par. • This happens when the coupon rate is equal to the market discount rate.

What is the price today of a 4-year $1,000 par value coupon bond with: • a 6% coupon rate and semi-annual (i.e., twice per year) payments • a market discount rate of 4% per semiannual? ➢ r=0.04 : the period (semiannual) rate ➢ It could have been also quoted as a market APR of 8% for semiannual periods)

$932.67

a bond has a face value of $1,000 and promises to make coupon payments of $30 every 6 months. What is coupon amount

Annually, you get $60. So, the coupon rate is 6%. Coupon Amount = Coupon Rate × Par Value / # of coupon payments per year = 0.06 * 1,000 / 2 = $30 • Your last coupon comes on the maturity date ➔ i.e., on the maturity date (t=N), you get BOTH the coupon + face value.

The common stock of Buildwell Conservation & Construction, Inc., has a beta of 0.90. The treasury bill rate is 4% and the market risk premium is estimated at 8%. BCCI's market value capital structure is: 1. 30% net debt paying a 5% yield 2. 70% equity. BCCI has a 40% corporate tax rate. What is BCCI's cost of equity capital and WACC?

(remember CAPM) Cost of Equity = 4% + 0.90(8%) = 11.2% WACC = (11.2% x 70%) + 5% x (1 - 40%) x 30% = 8.74%

fixed-income market (start of ch 5 bonds)

- A key source of financing for business and governments - A significant investing opportunity for institutions and individuals. - valuation is important for investors, issuers, and financial analysts

It is easier to find the cost of equity and cost of debt, so we do this and infer required return on projects. Explain this concept in more depth.

- E.g., suppose you wish to learn how much a burger place makes. - Calculate how much the manager makes, how much the burger flippers make etc., and from that you estimate how much the burger place makes. - Now, do the manager and flipper salaries drive the restaurant's profit, or does the restaurant's profit drive their salaries? • Takeaway: Projects drive required debt and equity returns! Debt and equity returns do not drive project returns!

What is β ("beta")

- The coefficient on S&P in the regression, i.e. the slope of the line - How much, on average, do GE's returns change when the returns of S&P 500 change

Standard & Poor's Composite Index (The S&P 500)

- Value of a portfolio holding shares in ("give or take") 500 important/big firms. - Holdings are proportional to each company's market capitalization

Find EAR for a weekly return of 0.20% or 20 basis points:

-1 year has 52 weeks, so m=52 -while the periodic rate is r = 0.20% = 0.0020 𝐸𝐴𝑅 = (1 + 0.0020)^52 − 1 = .1095 = 10.95%

Find EAR for an 18-month return of 20%:

-1 year is less than 18 months, so you won't have any incident of compounding within one year (i.e., m<1) The periodic rate is r = 20% = 0.20 -1 year is less than 18 months, so you won't have any incident of compounding within one year (i.e., m<1) In fact, it is 12/18 = 2/3 of 18 months, so m=2/3 𝐸𝐴𝑅 = (1 + 0.2)^(2/3) − 1 = 0.1292 = 12.92%

Name some assumptions of the CAPM

-Investors are risk-averse, utility-maximizing, rational individuals. -Markets are frictionless, including no transaction costs or taxes. -Investors have homogeneous expectations or beliefs. -Investors are price takers.

Security A has weight 30% and standard dev. of 20%. Security B has weight 70% and standard dev. of 12%. If the standard deviation of the portfolio is 14.40%, then correlation between the two securities is equal to:

1

WACC Fallacies: What are 2 enormous mistakes that are common in practice?

1) Applying a firm's WACC to a project unlike what the firm typically does - Suppose you calculate Nike's WACC to be 10%. They decide to get into the restaurant business. You cannot apply this 10% shoe WACC to a restaurant, even if Nike does it! 2) For firms in multiple, diverse, businesses: applying the same WACC to everything -Imagine a firm that sells cars and burgers. When you calculate its WACC, you are getting the WACC for a carburger hybrid.

In every period, a firm's debt is rebalanced, i.e., it gets adjusted to keep it at a constant fraction of its assets. From the liabilities' point of view, a firm is a portfolio that is financed by debt and equity: VAssets = Debt + Equity , so that: 1)... 2)...

1) Wdebt = (debt / debt + equity) and vice versa 2) R(assets) = Wd x Rd + We x Re = (Debt/Debt + Equity) x Rd + (Equity/ Debt + Equity) x Re = WACC + Wd x τ × Rd. 3) same as #2 but with betas

STEPS FOR SOLVING COST OF CAPITAL PROBLEMS (100% on final)

1. (if necessary) compute the benchmark D/E ratio. Find market capitalization = price per share x # of shares. then calculate D/E by dividing debt / market capitalization 2. Plug in and find Beta project of equity 3. Plug in Beta project of equity into CAPM to find return of project of equity 4. plug return of project of equity into WACC to find WACC of the project (this % is the cost of capital for the project) 5. Use r=WACC as the discount rate and calculate the NPV of the project to find if its worth taking risk.

A firm uses its assets to generate free cash flows. • Nike, for example, uses its designers and factories and swooshes to get the $$$. Those FCFs go to two sets of people ...

1. Debtholders (bondholders) get paid their claimed interest first. 2. Equity holders (owners) get the rest!

FCF method for valuing stock. What are the steps to solve?

1. Estimate the free cash flows that the firm will generate with its underlying business in the future. 2. Estimate the firm's WACC. 3. Discount the free cash flows at the firm's WACC to get the total value of the operating assets- the Enterprise Value. 4. Plug this EV into EV equation to get market value of equity. 5. Divide market value of equity by the number of shares outstanding to get your estimate of price per share.

Why do we need this market portfolio again?

1. If our project is AS risky as the market portfolio, then we should only invest in the project if it has a return greater than or equal to the market portfolio. 2. If our project is MORE risky than the market, then we require a return higher than the market to make it worthwhile (but how much higher?). 3. If our project is LESS risky than the market, then we'd be ok investing if the return is lower than the market's (but how much lower?)

Using the WACC in Capital Budgeting and Analysis

1. In capital budgeting, use the WACC, adjusted for project-specific risk, to calculate the net NPV: ➢ E.g., using a company's overall WACC in evaluating a capital project assumes that the project has risk similar to the average project of the company. 2. In financial analysis, use the WACC to find the value of a company by discounting that company's free cash flows.

Steps for Computing the Risk-Free Rate (Rf)

1. In portfolio management, the risk- free rate should be the short- term Treasury rate. 2. In corporate finance, the risk- free rate should match the duration of the cash flows. This rate is available from various sources, e.g.: - Yahoo. - Federal Reserve Economic Data Set

Issues in Estimating a Beta (reason 1)

1. Judgment is applied in estimating a company's beta regarding: a) the estimation period ➢ Longer estimation periods are applied to companies with a long and stable operating history. ➢ Shorter estimation periods are used for companies that have undergone significant structural changes b) the periodicity of the return interval c) the appropriate market index (e.g., S&P500)

Next, the investor must determine how to combine point m, her portfolio of risky assets, with the risk-free asset. What are some options?

1. Might invest some of her funds in the risk-free asset and some in portfolio m. 2. Alternatively, she might borrow at the risk-free rate and contribute some of her own funds as well, investing the sum in portfolio m.

We use the enterprise value (EV) equation in two ways. What are they?

1. Plug in the current market equity value, debt, and cash, and solve for the EV. This tells us what the market thinks the operating assets are worth. (ex on slide 41) 2. Figure out for ourselves what the operating assets are worth (EV), plug in debt and cash, solve for equity. This tells us what we think the equity should be worth! (ex on slide 43) -manipulate and solve for stock price

Why Do Finance Professionals Shun Direct Equity Valuation? (Reason 1)

1. The FCFE method (a.k.a. direct equity valuation) depends on projected equity payouts (dividends plus share repurchases), whereas the FCF method (a.k.a. asset-based valuation) depends on projected free cash flows. i. FCFE's are a function of management decisions about dividends and stock repurchases. ii. FCF's are a function of the firm's operating environment— its sales, costs, capital expenditures, and so on

The yield-to-maturity (YTM) is the rate of return on the bond to an investor provided that 3 conditions are met:

1. The investor holds the bond until maturity. 2. The issuer does not default on coupon or principal payments. 3. The investor is able to reinvest coupon payments at that same yield

summary of interest rate risk. how do changes in interest rates affect bond prices? do interest rate changes affect bonds more with longer maturities or shorter maturities?

1. When interest rates go up, bond prices go down (and vice versa) 2. All else equal, interest rate changes affect more bonds with: i. longer maturity ii. lower coupons

Expected return small cap fund S is 19%, σ is 33%. Bond Fund, B has expected return of 8% and σ=13%.The correlation between the two funds' returns is 0.10. 1. If the investor requires a portfolio return of 12%, what will be the standard deviation of the portfolio that will constructed? 2. If the investor requires a standard deviation of 14%, what will be the expected return of the portfolio that will constructed?

1. Ws = 36.4% 𝜎𝑝 = 15.23% 2. Since the investor aims at a lower risk (σp=14%) than before (15.2%), the investor needs to decrease the weight on S (the riskier asset) and increase the weight on B (the safer asset). μp=11.23%

IMPORTANT NOTE: The expected return of a bond that may default is different from the bond's yield-to-maturity:

1. YTM is the IRR calculated from the bond 's current market price and its promised coupon payments and promised eventual return of principal in the future. 2. Expected return needs to account for: a) Probability of Default b) Recovery Rate: the percentage of its principal which holders can expect to recover in the case of default.

The maturity effect always holds for:

1. Zero-coupon bonds 2. Bonds priced at par value 3. Bonds priced at a premium

A company's credit spread is the difference between:

1. its bonds' yield-to-maturity AND 2. the government bonds' yield-to-maturity

If T-bills returned 1% this year and the S&P 500 returned 12%, then the S&P 500 had a risk premium of __________ this year.

11%

You form a 50/50 portfolio with two stocks, A and B. The standard deviations of A and B are 20% and 10%. What is the portfolio standard deviation if: the correlation is 0.6?

13.6%

Why Do Finance Professionals Shun Direct Equity Valuation? (Reason 2)

2. The FCFE method discounts future equity payouts at the firm's cost of equity rE , whereas the FCF method discounts future FCFs at the firm's weighted average cost of capital (WACC). i. The cost of equity rE is very sensitive to the firm's debt- equity ratio. ii. The WACC is not as sensitive to the firm's debt-equity ratio. • If the firm's leverage fluctuates over time, the FCF method may reflect its fundamentals better than FCFE method.

Issues in Estimating a Beta (reason 2)

2. When estimating the beta of (i) a company that is not publicly traded or (ii) a firm's project, we need to look at the risk of the company or project and use comparables. • When selecting a comparable for the estimation of a project beta, we ideally would like to find a company with a single line of business, and that line of business matches that of the project. - This ideal comparable is a pure play. r- We use the beta of the comparable company to estimate an asset beta (beta reflecting only business risk) and then use it for the subject project or company.

The one-year spot rate (Z1 ) is 2%. The two-year spot rate (Z2 ) is 3%. The three-year spot rate (Z3 ) is 4%. What is the price of a three-year 5% annual coupon paying bond with face value of $100?

5/(1.02^1) + 5/(1.02^2) + 105/(1.04^3) = 4.902 + 4.713 + 93.345 = 102.96

If returns have a normal bell curve shape, then ________ of the time, they will end up within one σ from the mean. If returns have a normal bell curve shape, then _______ of the time, they will end up within two σ from the mean.

68%, 95%

Example: If a bond pays coupons twice a year, and the YTM is 7%, you use what as your 6 month r? What's the formula for "r"?

7/2 = 3.5% as your 6-month r! r = YTM /Number of compounding times in one year

What is the YTM of a 5-year risk-free zero-coupon bond with a face value of $100 that sells for $86.26?

86.26 = 100/(1+ytm)^5 ytm = (100/86.5)^(1/5)-1 = 2.94%

Computing the YTM of the T-bill: Suppose you purchase a 26-week T-bill with face value $10,000 for $9,750. First find the daily interest rate paid by the T-bill:

9750 = 10,000/(1+Rdaily)^182 = 0.0139% - The corresponding EAR of the T-bill is: 1 + 𝐸𝐴𝑅 = (1+0.0139%)^365 ⇒ 𝐸𝐴𝑅 = 5.2086%

A two-year Treasury bond, with a face value of $1,000 and an annual coupon payment of 8%, sells for $982.50. A one-year T bill, with a face value of $100 and no coupons, sells for $90. Given these market prices, find the one- and two-year spot rates. Just describe the process.

983.50 = 80/(1+Z1) + 1080/(1+Z2)^2 90 = 100/(1+Z1). Solve for Z1 then plug into equation above and get Z2. Z1=11.1% and Z2=8.9%

Project D's cash flows have a beta of 1. If the S&P 500 is expected to go up 7%, what rate should we use to discount this project's cash flows? Risk-free rate is 3%

= 3% + 𝟏 × (𝟕% − 3%) = 𝟕%

coupon amount

= 𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ×𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒 # 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑐𝑜𝑢𝑝𝑜𝑛 𝑖𝑠 𝑝𝑎𝑖𝑑 𝑖𝑛 1 𝑦𝑒𝑎r

The bond pays the buyer...

A "small" payments at regular intervals over its life (coupons and interest) AND one "big" payment at the end of its life (principal)

With respect to the pricing of risk in capital market theory, which of the following statements is most accurate? A. All risks are priced. B. Systematic risk is priced. C. Nonsystematic risk is priced.

B. Systematic risk is priced.

Which of the following events is most likely an example of nonsystematic risk? A. A decline in interest rates. B. The resignation of chief executive officer. C. An increase in the value of the U.S. dollar.

B. The resignation of chief executive officer.

Which return calculating method is the best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last 5 years? A. Geometric mean return. B. Arithmetic mean return.

A. Geometric mean return. The geometric mean return accounts for the compounding of returns, whereas... the arithmetic mean return assumes a constant dollar investment (by resetting the amount) at the beginning of each time period.

1) A zero-coupon bond with a face value $1,000 and a 10-year maturity 2) A zero-coupon bond with a face value $1,000 and a 4-year maturity Suppose interest rates suddenly fall from 3% to 2%. a) What happens to the price of these bonds? b) Which bond is affected more?

A: Calculate Bond 1 and Bond 2 price given the different interest rates. Both bonds go UP in price when r falls. B: Bond 1's price- the longer maturity- changed more dramatically. (calculate using % change formula)

1) A 3-year coupon bond with a face value $1,000 and a 8% coupon rate with annual payments 2) A 3-year coupon bond with a face value $1,000 and a 2% coupon rate with annual payments Suppose interest rates suddenly rise. a) What happens to the price of these bonds? b) Which bond would you guess is affected more?

A: Even though both bonds have the same maturity, Bond 2 has a longer "effective" maturity because larger coupons gets your money faster on average • A longer "effective" maturity makes the time value of money matters more! -The smaller the coupons, the higher the sensitivity to interest rates

The yield-to-maturity is always quoted as an _________ .

APR (i.e., in annual terms without compounding)

The Two-Fund Separation Theorem

All investors' optimum portfolios will be made up of some combination of an optimal portfolio of risky assets and a risk free asset investing decision + financing decision = optimal investor portfolio

Bonds' prices change even without interest rate risk. Why?

All thanks to maturity. • Bond prices change as time passes even if the market discount rate remains the same. • As time passes, the bondholder comes closer to receiving the par value at maturity.

The government spot rates are thought to be ____________ .

"risk-free"

What is the 3-year holding period return if the annual returns are 7%, 9%, and -5%?

$1 × (1 + 𝑅) = $1 × (1 + R1)(1 + R2)(1+R3) ⇒ 1 + 𝑅 = $1 × (1 + .07)(1 + .09)(1-.05) ≈ 1.1080 ⇒ 𝑅 = 1.1080 − 1 = 10.80%