Chapter 12 - Estimating cost of capital Flashcards
regarding costo f capital, what is the main challenge?
We want to find the risk premium. There is risk involved with every project, and as investors we want to be compensated for every risk that comes beyond the risk-free investment. THe challenge is to find this risk premium so that we can estimate the cost of capital.
Recall what cost of capital is
Cost of capital is the BEST expected return available in the market that has the same risk as the investment
How does CAPM consider “similar risk”?
Capital Asset Pricing Model considers the market portfolio, which consists of only the market risk (as all diversificiable risk is eliminated). It then relates an investment in terms of how sensitive it is to the market risk. For instance, a beta of 0.6 indicates that the investment is less risky than the market portfolio, as it will only change 60% of what the market portfolio does.
Therefore, CAPM considers two investments to be of similar risk if they have the same beta.
Therefore, according to CAPM, the cost of capital equals the expected return of an investment with the same beta.
How does SML relate to cost of capital?
SML - The security market line - IS the capital asset pricing model in a graphical sense. we assign parameter values to the model equaiton, and plot it to get teh security market line result.
SML, the security market line, represent the equation:
E(Ri) = rf + beta (E(Rp) - rf)
This is a function of beta, since rf is known, and the expected value of the portfolio return is also known.
The SML place all investments along the line, so it is actually only dependent on the beta.
So, the security market line GIVES us the cost of capital.
elaborate on why SML actually relates to a projects cost of capital
The project as a risk level associated with it. In order to figure out if the project is beneficial (positive NPV) we need to discount it using a cost of capital. Since the cost of capital is the best alternative usage of the money in an investment that offer the same risk level, we can use the SML to estimate the cost of capital.
SML is about stocks. The projecti s not necessarily about stocks. However, the cost of capital can still be measured by stock market because law of one price etc.
We consider the SML, and find out what we would get in expected returns if we use a risk level that corresponds to the project. The expected return from the stock market represent an alternative investment for us. If this one makes more cash than the project, why the fuck would we invest in the project?
The reason why SML is so great, is that it relates a certain beta with a certain expected return.
The process of computing/estimating the cost of capital is straightforward in terms of calculations, but difficult in terms of …?
Inputs.
We need primarily two things:
1) the excess returns of the market portfolio beyond the risk free rate. We also need to construct the market portfolio.
2) Estimate the stocks beta - sensitivity to the market portfolio.
What is a value-weighted portfolio?
A value-weighted portfolio is one that gives weights that corresponds with the value of the stock. so for the market portfolio, each stock gets a weight corresponding to its relative market cap when compared with the total market cap of all stocks.
what is an equal-ownership portfolio?
Equal ownership means that we own the same fraction in each stock.
This means that unless the number of shares outstanding change, we dont have to trade to maintain the equal ownership portfolio.
Therefore, it is also called passive portfolio.
A value weighted portfolio is also an equal-ownership portfolio.
What is a price-weighted portfolio?
Holds equal number of shares of each stock regardless of their size
What does it mean that the S&P 500 is a market proxy?
IT measn that it is not actually representing the market, but rather an estimation.
No one use CAPM with the belief that S&P is the market, but rather as a proxy.
Recall market risk premium
Excess return required to hold market:
E(Rmkt) - riskFreeRate
market risk premium serves as a benchmark for what investors demand for holding the market risk.
Quickly define what the risk free rate actually is
THe rate at which investors can borrow and/or save at zero risk.
Generally determiend by US treasery bills.
What is worht noting regarding the use of the risk free interest rate in models like CAPM
The rate at which people can borrow sometimes is significatly different from the risk free rate. Because of this, some choose to use high grade corporate yield as a measure instead.
What is the fundamental approach to estimating the market risk premium?
This is a method one can use that is different from the classical backwards-looking option of historical returns.
It makes use of the constant growth dividend model.
rate = div/P0 + g = dividend yield + Expected growth rate
While being inaccurate for individual stocks, when used on the market it can be accurate.
The benefit of this approach is that we dont need to compute the capital gain rate. Capital gian rate is notoriously difficult to measure using past data.
Having determined the market proxy, what is the next step?
we need the beta
Is it problematic to use historical data to estimate beta?
Ideally, yes. We actually want to know the future beta, because we are interested in future results.
However, using past data actually turns out to work quite well for sensitivity of a stock to the market (proxy).
What is the beta-interpretation in regards to actual real life features?
If a stock sell shit that depends on the economic cycle, its beta tend to be large. If not, beta tend to be low.
Given a scatterplot of excess returns in both the stock and the market, how do we find the beta?
The beta would then be the slope of the best-fitting line that considers all the points in the scatter.
In other words: linear regression
Give the linear regression formula and elaborate on its components
Ri - rf = alfa_i + beta_i (R_mkt - rf) + e
Excess return equals alfa plus sensitivty to market times the excess market return plus residual term (error term).
The error term represent the deviation between a point in the scatter, and the line (linear regression line). This residual/error temr is basically the diversificiable risk, and is 0 on average.
We can take the expected value of the function:
E(Ri - rf) = E(alfa) + E(beta (R_mkt-rf)) + E(e)
E(Ri) - rf = E(alfa) + beta(E(Rmkt - rf))
E(Ri) - rf = E(alfa) + beta (E(Rmkt) - rf)
E(Ri) - rf = E(alfa) + beta E(R_mkt) - beta rf
E(Ri) = rf + beta (E(R_mkt) - rf ) + alfa
What is alfa?
Alfa is the intercept of the original regression line. Alfa represent the historical performance of the security relative to the expected return predicted by the SML security market line.
Therefore, alfa can be interepreted as a risk-adjusted measure of the stocks historical performance.
According to CAPM, alfa should not be significalntly differnet from 0.
recall what happens if a bond issuer (corporation) carry significant risk in regards to defaulting on the bond
The yield to maturity, whcih is the IRR that equates price and present value of holdign the bond to maturity, will be OVERSTATED compared to the investors expected returns.
In other words, investors will locate the riskiness, and expect less return than what the yield to maturity happen to be.
Name a common mistake in terms of debt cost of capital
using bond yield/debt yield. This is a mistake because it is often much higher than the expected returns. Therefore, using bond yield or debt yield as debt cost of capital only works if the debt is very safe.
taking probability p of defaulting on a bond into account, how do we find expected value of bond?
r = (1-p)y + p(y-L) = y - py + py - pL = y - pL
the reason why it is like this, is because if default, we (as creditors) dont loose everything necessarily. L represent an amount per dollar that we expect to loose if the bond if defaulted. y is promised.
Can we use CAPM to compute debt cost of capital?
Yes, but it is difficult because of how little many debt securities are traded. We develop methods in later chapters. For now, we are given tables of different grades debts (bonds) and we can use the CAPM equaiton like always.
but we actually only need the debt beta. Given the debt beta, we know the risk level of the “investment” which is a lending operation in this case. The CAPM will relate this risk level with a required return that the investor must recieve (the lender) in order to be willing to do it.
For highly graded firms, AA, AAA etc, the debt beta is typically extremely low because the firm’s abiltiy to repay the debt is close to guaranteed regardless of market scenario. Therefore, one can expect only a slighlty higher yield than for risk free rate.
For firms that are not so highly graded, the beta will be larger, and relate to a higher level of risk and therefore a higher level of expected return.
The point is that CAPM relate risk with expected return/cost of capital. Therefore it can be used with debt as well.
why is it difficult to use historical data to find the riskyness of a project?
Projects are not publicly traded securities. There is no history here.