Week 2: Cost of Capital

Question 1

Cost of Capital + components

Answer 1

–>The cost of capital reflects the riskiness of cash flows.
–>It is the return required by investors for investing in the firm.

Every cost of capital consists of two parts:
1. Risk-free rate: Compensates investors for providing capital rather than consuming it today
(“time value of money”).
2. Risk premium: Compensates investors for providing capital for a risky investment rather than
for a risk-free investment

Cost of capital should be higher for riskier investments and lower for safer investments. (Costs of capital higher if FCFs are riskier)

Question 2

WACC and its components

Answer 2

The most widely used approach to estimating the cost of capital of the firm involves estimating the cost of equity and the cost of debt, and taking a weighted average of the costs.

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Question 3

Cost of Equity and approaches to calculate.

Answer 3

− The cost of equity reflects the riskiness of the cash flows to shareholders.
− It is the return required by shareholders for investing in the equity of the firm.

The two most important approaches to estimate:
− Capital asset pricing model (CAPM)
− Multi-factor models

Question 4

Modern Portfolio Theory

Answer 4

Y axis: expected return
X axis: variance- total risk

*rf point- investment in only risk free assets
*SML (security market line)
Investments in risk-free assets AND stocks–>combination
*Efficiency frontier:
As good as it gets if we can invest in stocks”
Happens when we diversify the risk away.
*Market portfolio (point)

Basically every investor will hold stocks and Rf assets. So, everyone holds market portfolio. We only have systematic risk–> risk added by the stocks we hold. —> CAPM

Question 5

CAPM

Answer 5

Relationship between expected return and systematic risk.
–>SML

The expected return of a stock can be derived as:
rf + beta * risk premium

Expected return of the stock of firm X = Cost of equity of firm X

Question 6

Theory VS Practice for CAPM

Answer 6

− In theory:
all investors are perfectly diversified globally, i.e., they hold the same global market portfolio.
− In reality:
investors are not perfectly diversified globally, i.e., the do not hold the same global market portfolio.

Risk has to be measured from the perspective of the marginal investor- investor most likely to trade a stock. (likely to be an institutional investor (e.g., mutual fund))
Thus apply CAPM from institutional investor view.

Question 7

Home bias

Answer 7

Institutional investors tend to invest higher % in local assets than international.

Question 8

Risk-free rate

Answer 8

Expected return occurs with certainty.

In developed countries, government bonds are usually considered to be risk-free. Therefore, government bonds are used as risk-free asset.

− Short-term risk-free asset: When duration of cash flows is short
− Long-term risk-free asset: When duration of cash flows is long

duration= year span when repayment is made from CFs of the investment.

Question 9

Long-term government bond risk free rate differences across countries- reasons

Answer 9

–> inflation
–> policy of government debt

Question 10

Equity risk premium + ways to derive

Answer 10

The equity risk premium is the additional return expected by a market participant for investing into
equity rather than investing into the risk-free asset.
Can be derived in three ways:
− Historical equity risk premium
− Survey equity risk premium
− Implied equity risk premium

Question 11

Historic equity risk premium: 3 factors

Answer 11

*Length of the estimation period:
− Shorter estimation period: Equity risk premium might change over time
− Longer estimation period: More precise estimation (“over the cycle”)
*Choice of the risk-free asset:
− Short-term risk-free asset: When duration of cash flows is short
ex. treasury bills
− Long-term risk-free asset: When duration of cash flows is long
ex. treasury bonds
*Arithmetic vs. geometric average:
− Arithmetic average: When duration of cash flows is short
− Geometric average: When duration of cash flows is long
ex. If economy has changed a lot recently —> choose short estimate
If not —> choose long

Question 12

Implied equity risk premium

Answer 12

The value of the ENTIRE stock market can be defined as the present value of future dividends paid by
all firms in that market.

E; div; and growth rate are observable. Only thing we need to solve is “Re”
<not on formula sheet! but on slides formula>
This is essentially the dividend discount model (DDM) applied to the entire stock market rather than to an individual stock.

Question 13

Which equity risk premiums do analysts usually use?

Answer 13

With a small difference:
->historical equity risk premium
->implied equity risk premium
Smaller part:
->I do not estimate an equity risk premium (e.g., survey equity risk premium)

Question 14

Betas and derivation of betas

Answer 14

The beta measures how a stock moves when the overall stock market moves. As such, the beta is a
useful measure of the contribution of a stock to the risk of the market portfolio. Thus, the beta is
referred to as a stock’s systematic risk, non-diversifiable risk, or market risk.

The beta can be derived in (at least) two ways:
− Historical betas
− Betas based on peer firms (bottom-up betas)

Question 15

Historical betas

Answer 15

–>The estimated 𝛽 tells us how stock X moves relative to the market portfolio.

The usual way to determine the historical beta of a company is to regress the company’s stock returns on the market returns in an OLS (ordinary least squares) regression

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Question 16

Factors important to estimate beta

Answer 16

*Length of the estimation period:
− Shorter estimation period: Beta might change over time
− Longer estimation period: More precise estimation
*Return interval:
− Shorter return intervals (e.g., daily): More observations
− Longer return intervals (e.g., monthly): Less non-trading observations (with zero return)
*Market portfolio:
− Global stock market index (e.g., MSCI World Index): If investors are perfectly diversified
worldwide (theory)
− National stock market indices (e.g., U.S.: S&P500) If investors have a geographic focus (practice)

Question 17

Issues with Beta estimations

Answer 17

Issue: Using daily return observations when estimating the historical beta of a small firm might lead to biased estimates.

Why?
Because for small firms there can be days where the stock is not traded. So these 0’s are included in the sample and creates BIAS in the beta estimation.
“Using these non-trading-period returns in the regression will reduce the correlation between stock returns and market returns and the beta of the stock.”
So it is better for small firm beta’s to use monthly or weekly beta estimations.

Question 18

Cyclical vs non-cyclical industry betas

Answer 18

Cyclical industries have high betas–> economy doing well so high beta companies do well.
Non-cyclical–> low beta

Question 19

Bottom up betas

Answer 19

In some situations, we cannot estimate historical betas (e.g., private firms). –>
bottom up betas: based on peer firms.
steps:
1) Identification of comparable firms that are publicly traded.
2) Estimation of historical betas of comparable firms.
3) “Unlever” historical betas of comparable firms to derive unlevered betas (operating asset betas).

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4) Unlevered beta of the firm =(Weighted) average of unlevered betas of comparable firms.
5) “Relever” the beta of the firm to obtain the levered beta of the firm.
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Question 20

Multi-factor models

Answer 20

− Empirical evidence suggests that the CAPM with its market factor is not very good at explaining differences in stock returns.

*Fama and French (1992, 1993):
−>Firm size: small firms earn higher returns than large firms (size premium).
−>Book-to-market ratio: value firms earn higher returns than growth firms (value premium).

Fama and French (2015):
−>Operating profitability: high profitability firms earn higher returns than low profitability firms.
−>Investment: low investment firms earn higher returns than high investment firms.

!!However, no widely-accepted explanation has evolved for why these factors should be priced risk
factors!!

Question 21

Which model do analysts use?

Answer 21

Mostly CAPM, even though it has strong downfalls.
Also determine cost of equity based on own judgement.

Question 22

Cost of debt

Answer 22

*Reflects the riskiness of the cash flows to debt-holders.
*It is the return required by debt-holders for investing in the debt of the firm.
*The main risk debtholders are confronted with is the default risk (or repayment risk).
−>Default risk: The risk that a borrower will not be able to make the required payments on the debt obligation.
<Borrowers with higher default risk should have higher cost of debt, while borrowers with lower default risk should have lower cost of debt.>

cost of debt= rf + company’s default spread

Question 23

Default spread

Answer 23

3 ways to derive default spread:
− Traded bonds
− Credit ratings
− Synthetic ratings (“our own credit rating”)

The credit rating is the most widely used measure of a firm‘s default risk. It is usually assigned by an independent rating agency (e.g., Standard & Poor‘s, Moody‘s, Fitch).

Question 24

Weights for cost of equity and cost of debt: market or book value?

Answer 24

The weights used in the cost of capital computation should be based on market values (not on book values).
So, we need the market value of equity and the market value of debt before we value the firm.
→Circularity issue!

Question 25

Ways to overcome circularity

Answer 25

1) Target capital structure of the firm
2) Current capital structure of the firm: Market value of equity ≈ Market capitalization;
Market value of debt ≈ Book value of debt (in case of investment grade rating)
3) Industry average

Question 26

What should be counted as debt?

Answer 26

− All interest-bearing liabilities (e.g., bonds, loans)
− All lease commitments
− Non-interest bearing liabilities should not be counted (e.g., unfunded pension obligations)