Chapter 12 - Estimating the cost of capital

Question 1

In essence, what can we say that the cost of capital includes+

Answer 1

Risk premium

Question 2

What is the cost of capital?

Answer 2

Cost of capital is the return we can get elsewhere in a project with similar risk. More specifically, the cost of capital is the BEST alternative return for similar risk.

Question 3

how does the CAPM relate to cost of capital?

Answer 3

Since CAPM relates beta with expected return, similar risk investments gets the asme expected return. Therefore, “similar risk” means “similar beta”. This is useful because it allows us to use the beta of a firm to evaluate its risk AND thus the expected return.

Question 4

To value a share of a stock, we need to calculate the …

Answer 4

Equity cost of capital

Question 5

What do we need in order to calculate the equity cost of capital for a stock?

Answer 5

We need the beta of the stock.

Question 6

What is total risk?

Answer 6

Volatility of the security

Question 7

What is market risk?

Answer 7

beta

Question 8

what determines cost of capital?

Answer 8

Market risk

Question 9

What inputs do we need to estimate the firms equity cost of capital?

Answer 9

We need the market portfolio, and the market excess return.

Then we need to find the beta (sensitivity) of the investment relative to the market.

Question 10

To apply CAPM, we must…?

Answer 10

Find the expected return of the market portfolio, and the beta of the investment relative to hte market portfolio. This requires us to first consider what the market portfolio is.

Question 11

What is the market portfolio?

Answer 11

Portfolio of all securities. The weights of each security in the market portfolio should equal to the relative market share that its market capitalization is in the entire market.

Thus, the market portfoloi contains more of the larger stocks, and less of the smaller stocks.

Question 12

give the formula of a security’s weight in the market portfolio

Answer 12

Question 13

What do we call a protfolio that is weighted such that its weight is proportional to its market cap size in the market+

Answer 13

Value weighted portfolio.

Question 14

Another term used to describe a value weighted portfolio?

Answer 14

Equal ownership portfolio

Question 15

What do we mean by “equal ownership portfolio”?

Answer 15

We mean a portfolio in which buying the portfolio entails buying the same amount of ownership in each joint. We hold an equal fraction of shares in each security in the portfolio.

Question 16

What is the important outcome of value weighted portfolios?

Answer 16

Value weighted portfolios are so called “passive” portfolios. It means that even when prices and values change, our ownership remain the same. We are good. We dont need to do anything.

Question 17

Something important about DJIA

Answer 17

It is PRICE WEIGHTED.

Question 18

What does it mean that a portfolio is PRICE WEIGHTED?

Answer 18

Holds an equal number of shares of the securities, regardless of the size.

Question 19

Elaborate on market proxy

Answer 19

We call S&P 500 a market proxy because it is not the market portfolio, but it acts like it. No one is claiming that S&P is actually the market, but rather that it is close enough for assumptions to apply.

Question 20

elaborate on why using historical data sucks

Answer 20

1) You need many data points to get accurate results. Old data point may simply not be representative, as they happened 80 years ago.

2) The standard error is still large. 95% confidence interval is excess return mean +- 4.1%

Question 21

What do we refer to when saying the “fundamental apprach” to computing expected returns??

Answer 21

Using the expected cash flows to compute present value of cash flows of all firms.
You’d take the dividend yield and the expected growth in dividends.

r_mkt = div/P0 + g

this model is highly inaccurate for indicviudal firms, but is much more solid for the market as a whole.

Question 22

Say we have found a market proxy, which entails a market risk premium (excess return of the market proxy portfolio). WHat is the next step

Answer 22

Finding the beta.

Question 23

General use of beta is…?

Answer 23

Beign a suitable estimator of risk for an investor. We know that regular volatility sucks because it includes diversifiable risk, which investors will not be compensated for.

However, beta does not include idiosyncratic risk, and is therefore a better measure of the risk exposure of the specific investment.

Question 24

What does beta actually measure?

Answer 24

Sensitivity of the individual invesmtent to the general health of the economy.

Question 25

Say we have a plot of weekly excess return of a security, vs the market excess return (x axis). What can we say about beta?

Answer 25

If we draw the best-fitting line between the scatter plot, the slope of the line is the beta.

It other words, on average, what seems to be the relationship between some excess return in the overall market and the excess return of the specific security.

Question 26

Cough up the linear regression line that relates security’s excess return vs market excess returns

Answer 26

(E[Ri] - rf) = alfa_i + beta_i (E[Rmkt] - rf) + e_i

The error term is zero on average. why? because if it is not, we could improve the fitted line.

Question 27

What is Jensens alpha?

Answer 27

Jensons alpha is hte alpha in the linear regression line.

it represnet the performance of the stock BEYOND what investors requried from it based on its risk level. This means, if investors identify the stock having a certain risk level (beta), and thus outputting a required return, and the stock beat this required return, then it has a positive alpha.

Question 28

Relate jensons alpha to CAPM

Answer 28

So, if investors believe the stock has certain market risk which gives it a beat f say 2, and that this should give the stock a required return of 12%, if the best fitted line through the historical excess return of the security vs the excess return of the market represent an alpha of for instance -3%, then it means that the stock failed to meet its expectations, which means that investors believe it has underperformed in regards to its specific level of risk

Question 29

What exactly is sput out of CAPM?

Answer 29

Required return, equity cost of capital, expected return

Question 30

elaborate on the relationship between CAPM and equity cost of capital

Answer 30

(somewhat messy card, but the core idea here is very important).

because the required return is basically the sum of dividends and capital gain. so the investor will require the dividend yield and capital gain rate to be equal to some percentage, which relates to the uncertainty of the firm. So, as I see it, the firm has a certain riskiness associated with it, typically through industry specifics and other features, and this riskiness produce expectations from investors. Like, investors require a certain return to compensate for the level of risk the firm possess. Thus required return must either come from dividend yield or capital gain rate.
So, from the perspective of the firm, if they want to raise money to fund internal projects, they must ‘show’ that they will produce returns similar to the required return that is determined by their beta.

If the firm want to raise funds, it must produce returns equal to the required return, and the required return is determined by the market risk associated with the firm.

Question 31

What is the debt counterpart to “what returns are expected by equity holders”?

Answer 31

What expected return is required from debt holders/creditors?

Debt holders receive debt interest payment. this is the debt cost of capital. for the firm, the debt cost of capital will represnet what it cost them to loan funds.

Question 32

why do we care about the debt cost of capital?

Answer 32

There are various use cases, like if you are a creditor etc…

However, the most important use case of the debt cost of capital is the fact that we NEED it to compute the “COST OF CAPITAL” of a project. Typically, projcts use a combinations of equity and debt. Therefore, in order to be able to discount the project correctly, and find a correct present value, we need the debt cost of capital.

Question 33

Can we use a bonds YTM to estiamte the debt cost of capital?

Answer 33

Not really. It depends on the grading on the bonds. If the bond is risky, the YTM will overstate the debt cost of capitail.

This approxiomation is only valid if the bond is safe.

Why is this so?
If the bond is risky, the YTM is just promised, and the expected value of the yield is actually lower. Therefore, the YTM is simply not accurate.

Question 34

If we are going to use the YTM to estimate debt cost of capital, how do we do it+

Answer 34

we need to account for the riskiness of the security.
We use the Loss rate L, which is the percetnage we will loose should the firm go shite, and we need the probability of the firm going up in flames.

r_d = expected return for debt holders

r_d = probabilityDefault x ReturnIfDefault + probabilityNotDefault x ReturnIFnotDefault

r_d = p(y-L) + (1-p)y

r_d = py -pL + y - py

r_d = y - pL

So basically, the debt cost of capital (expected value of it) is equal to the yield to maturity less the probability of default multiplied by the shit we get loose from y should the firm default.

This assumes a one year bond.

Question 35

alternative to estimate the firm’s debt cost of capital that does not require the probability of default and the loss rate?

Answer 35

Using debt beta.

Question 36

Elaborate on debt betas

Answer 36

the most important thing to get right immediately, is the fact that bonds are traded much more infrequently than equity as far as FIRMS are considered (not including US treasury). THerefore, it is not reliable to esitmate debt betas the way we estimate equity beta (linear regression and all that).

instead, we estimate hte debt beta by using the grading given to the firm by certain grading authorties.

In general, debt betas tend to be very low.

Question 37

What is the general perspective on debt taken in this chapter?

Answer 37

From the perspective of the investor who are interested in taking the role of creditor to the firm.

Question 38

What is the simplest way/case of finding a project’s cost of capital?

Answer 38

It is definitely simplest if the project is all equity financed.
if we can manage to find another firm that has similar business to our own, we can use their beta. the assumption is that owning their stock is basically the same as owning our assets.

Question 39

What happens if we have a firm that is basically the exact same assets as our own project, but the firm is levered (it has debt)?

Answer 39

This is slightly more tricky than the all equity financed variant.

However, we know that the firm’s cash flows will be used to pay BOTH equity holders and debt holders, we can take a perspective of an “ultimate investor” who holds both debt and equity. The thought here is that we want to consider a position where we are entitled to the entire cash flow of hte firm. WHY? Because when we consider our own project, we are entitled to all cash flow. We need the same capital structure to make the cost of capital be correct.

Question 40

another term for weighted cost of capital

Answer 40

Unlevered cost of capital

Question 41

Another word for weighted cost of capital, that is not unlevered cost of capital

Answer 41

Asset cost of capitalE

Question 42

Elaborate on the asset cost of capital/Unlevered cost of capital/Weighted cost of capital

Answer 42

It represent a claim on the firms underlying assets, and it dont give a fuck about capital structure. The entire point is to free ourselves of capital structure.

it is computed by the relative weighting of the firm in regards to debt and equity, along with the debt cost of capital and equity cost of capital

WACC = (proportion of firm financed by debt)xDebtCostOfCapital + (Proportion of firm financed by equity)xEquityCostOfCapital

Question 43

Elaborate on unlevered beta

Answer 43

exactly the same as WACC, but with betas instead of debt cost of capital and equity cost of capital.

The important part about the unlevered beta is the fact that we can use it in the CAPM to get the required return/expected return of the investment. But we have to understand what we are computing here. The projects cost of capital is correctly computed using the unlevered beta, but this is obviously not the perspective of EQUITY holder. Therefore, it would not be appropriate to use the unlevered beta to compute shit like share price.

Question 44

Elaborate on risk of a firms enterprise value

Answer 44

The main point in using this, is that we want to separate CASH from the process. Cash is a risk free asset. Having cash will neutralize equivalent amounts in debt, as far as RISK is involved.

Recall EV = Market Cap + debt - cash

It is basically the cost of acquiring the assets of the firm.

Question 45

Elaborate on how we use EV in the equatiuons when computing hte cost of capital of a project

Answer 45

Question 46

This chapter (estimating cost of capital) takes a certain perspective in regards to assuming something about the project that we are computing the cost of capital of. What?

Answer 46

That the project is all equity financed.

Question 47

How is CAPM used to price assets

Answer 47

we find the required return, and compare with whatever we have estimated its return to be based on cash flow expectations. If those expectation are higher than whatever CAPM say the required return is, it would generally be classified as a buy