Chapter 12 - Estimating cost of capital

Question 1

regarding costo f capital, what is the main challenge?

Answer 1

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.

Question 2

Recall what cost of capital is

Answer 2

Cost of capital is the BEST expected return available in the market that has the same risk as the investment

Question 3

How does CAPM consider “similar risk”?

Answer 3

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.

Question 4

How does SML relate to cost of capital?

Answer 4

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.

Question 5

elaborate on why SML actually relates to a projects cost of capital

Answer 5

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.

Question 6

The process of computing/estimating the cost of capital is straightforward in terms of calculations, but difficult in terms of …?

Answer 6

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.

Question 7

What is a value-weighted portfolio?

Answer 7

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.

Question 8

what is an equal-ownership portfolio?

Answer 8

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.

Question 9

What is a price-weighted portfolio?

Answer 9

Holds equal number of shares of each stock regardless of their size

Question 10

What does it mean that the S&P 500 is a market proxy?

Answer 10

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.

Question 11

Recall market risk premium

Answer 11

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.

Question 12

Quickly define what the risk free rate actually is

Answer 12

THe rate at which investors can borrow and/or save at zero risk.

Generally determiend by US treasery bills.

Question 13

What is worht noting regarding the use of the risk free interest rate in models like CAPM

Answer 13

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.

Question 14

What is the fundamental approach to estimating the market risk premium?

Answer 14

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.

Question 15

Having determined the market proxy, what is the next step?

Answer 15

we need the beta

Question 16

Is it problematic to use historical data to estimate beta?

Answer 16

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).

Question 17

What is the beta-interpretation in regards to actual real life features?

Answer 17

If a stock sell shit that depends on the economic cycle, its beta tend to be large. If not, beta tend to be low.

Question 18

Given a scatterplot of excess returns in both the stock and the market, how do we find the beta?

Answer 18

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

Question 19

Give the linear regression formula and elaborate on its components

Answer 19

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.

Question 20

recall what happens if a bond issuer (corporation) carry significant risk in regards to defaulting on the bond

Answer 20

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.

Question 21

Name a common mistake in terms of debt cost of capital

Answer 21

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.

Question 22

taking probability p of defaulting on a bond into account, how do we find expected value of bond?

Answer 22

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.

Question 23

Can we use CAPM to compute debt cost of capital?

Answer 23

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.

Question 24

why is it difficult to use historical data to find the riskyness of a project?

Answer 24

Projects are not publicly traded securities. There is no history here.

Question 25

What is the most common method for estimating a project’s beta?

Answer 25

Identify comparable firms, typically same industry. Then estimate the cost of capital of the assets of comparable firms, and use this as a proxy for the project’s cost of capital.

Question 26

if we do not consider debt, how do we find cost of capital of a project?

Answer 26

Identify a comparable firm that use all-equity, like we do. Then the idea is that if this firm has the same market risk as our project, then we can use its equity beta to compute the cost of capital, that will serve as a proxy.

This is extremely wild, and is purely based on managing to identify a firm that happens to have the same level of risk as ourselves.

Question 27

if the firm we have selected as comparison to our project (identified same level of risk), what happens if they have debt?

Answer 27

If they have debt, it basically means that their assets will be used to generate cash that will pay off debt holders and equity holders.

Since the firm is leveraged, the returns of the firms equity alone is not a good representation of the underlying assets. The equity will often be much more risky. Therefore, the beta of a levered firms equity is not a good estimate of the beta of its assets and of our project.

Here is what we do:
We create a scenario where we hold the debt and the equity, so that we are basically receiving the entire cash flow that is generated by all of the assets (assets as in equity + debt).
The return of the assets is therefore the same as the return of combined debt and equity of the firm. The beta of the firms assets will match the beta of this combined portfolio.

Question 28

Elaborate on beta and why leveraged firms trouble things

Answer 28

the main point to remember is that beta is still beta. It represent changes to the stock expected returns based on changes in the market portfolio. Beta will capture the relationship between them.

The trouble comes from the fact that we wish to use beta to find cost of capital. The problem is that if the firm that we have selected as similar in risk profile, is leveraged (using debt), then the beta will be a debt-based beta. This means that whatever movements in the expected returns the stock has performed, the leverage has likely influenced this because leverage typically help amplify returns. because we assume that using leverage amplify returns (both positive and negative) using leverage will increase risk because of the financial structure of the firm.

This means that if we want to use a leveraged firms beta to approximate cost of capital, and use this cost of capital as our estimate that we then use to compute the profitability of a project, we must leverage our project the same way the firm has leverageed themselves. BUt, because we want to be equity based (for now) this is off the table.

Therefore, we are exploring ways to make a beta that is more representable for us.

Question 29

elaborate on unlevered cost of capital

Answer 29

We get the unlevered cost of capital by including the debt aspect.

= Fraction of firm financed by equity x equity cost of capital + fraction financed by debt x debt cost of capital

Question 30

How do we find unlevered beta?

Answer 30

beta is computed like a weighted sum, so the unlevered beta is the sum of equity beta and debt beta along with their corresponding weights. Their weights are the total values.

Question 31

Give formula for net debt

Answer 31

net debt = debt - cash and short term investment

Question 32

What happens if we have more cash than debt?

Answer 32

The net debt will be negative. This will make the unlevered cost of capital affected because the part surrounding the debt is negative. In other words, the proportion of the assets that are financed by debt is negative, which gives less risk because having cash is less risky. Cash is a risk free asset.

This can therefore make equity less risky than the underlying activities (from the perspective of WACC and combining equity and debt).

Question 33

recall enterprise value

Answer 33

the cost of buying and OWNING all assets and equity of a company. we have to buy all equity, and all assets. This means paying of debt.
therefore the formula is:
EV = market cap + debt - cash

Question 34

Give formula for WACC

Answer 34

fraction financed through equity multiplied by equity cost of capital + franction fnanced by debt multiplied by debt cost of capital multiplied by (1-tax)

unlevered cost of capital is known as pretax WACC.

Question 35

elaborate on the usage of asset beta

Answer 35

when estimating beta for a project, we need to find the asset beta because when considering projects we are essentially tying up assets (and not equity), and we know that tying up assets will have various costs based on how the assets are financed. If financed through debt, tying up these assets will have a price determined by a specific creditor(s). If the assets are financed by equity, the cost is different from the creditor cost (most likely). What I am trying to say is: When estimating cost of capital for a project, is the reason why we need asset beta because a project is ultimately tying a set of assets, which needs to be financed through either equity or debt.

Question 36

Why does the equity beta include both risks?

Answer 36

Equity beta is created by looking at what the equity-holder historically received vs what he’d get from holding equity in the total market portfolio instead. This perspective makes it equity beta.

Question 37

How can we find debt beta?

Answer 37

We assume the perspective of the creditor, and consider what he would get historically from lending money to the firm vs what he’d get from lending ot the market portfolio.

The issue with this though, is liquidity. We will usually not get reliable results from doing this, but the idea is important.

But in theory we could use the CAPM like we did with the equity beta.
r = rf + beta(Rp - rf), and regress the shit.

Question 38

Elaborate on finding a debt cost of capital.

Answer 38

the goal is to ultimately find cost of capital. We “can” do this, both for equity and debt, through the capital asset pricing model. This is fine for equity. but debt is more challenging because the debt beta is difficult to estimate. However, the goal is not to find the beta or to use Capm, but rather to find an estimate for cost of capital. Therefore, if the corporation is high quality graded, like double or triple A, we know that the yield on their bonds (their debt) is very very close to the expected return (from the perspective of the creditor). Therefore, we can omit the beta-step, and skip to using bond yield as debt cost of capital.

IMPORTANT: if the debt is risky, like BB for instance, we have 2 options:
1) Use the formula “YTM - pL”. ytm is given, p is probability of default (given by bond rating) and L is the expected amount the creditor can expect to loose given a default.

2) Using CAPM and beta. Requires debt beta, which can be difficult to find.

Question 39

What happens if we, as a project considerer, finds a firm with simlar risk profile, but with a debt financing that is much better than what we can ever hope to achieve? Like AAA rating and 100% funded through debt?

Answer 39

It actually does not matter.

The thing that matter is the similar asset risk. We get the estimation of asset cost of capital from this firm.

This asset cost of capital is key. Asset cost of capital represent both equity cost and debt cost of capital. If the firm is 100% debt financed, the asset cost would represent the return we would get from LENDING money to the firm, taking the role as a creditor. If the firm funded 50-50 equity and debt, the asset cost of capital would represent our return from investing 50% in the stock equity, and 50% through lending. Finally, if all equity financed, the asset cost of capital would represent the return we would get from buying pure stock.