Finance 2
Lecture 1
7 February 2023
Valuation (chapter 9)
- Discount the expected value of cash flows at each point in time against an appropriate
discount rate:
o Discount rate is also called the opportunity cost of capital (and/or required rate
of return)
- Dividend discount model: the price of any stock is equal to the present value of the
expected future dividends it will pay.
- Constant dividend growth: the simplest forecast for the firm’s future dividends states
that they will grow at a constant rate, g, forever.
Firm Valuation: Discounted Free Cash Flow Model
- Discounted free cash flow model.
o Determines the value of the firm to all investors, including both equity and
debt holders.
o Enterprise value (=value of the business, excludes cash)
- Free cash flow: cash flow available to pay both debt and equity holders.
- Since we are discounted cash flows to both equity holders and debt holders, the cash
flows should be discounted at the firm’s weighted average cost of capital.
- The enterprise value incorporates the value of the firm from all the cash flows that will
be generated by operations. It does not yet incorporate the cash holdings that the firm
has available.
o To estimate the value of equity, need to add these cash holdings. Moreover,
part of the value will have to be paid to debtholders, so we have to deduct the
value of debt.
o Market value of equity = firm value + cash – debt
- The total payout model also focuses on share repurchases; this is also based on
discounting cash flows.
- Multiples are based on comparable firms.
How to find the discount rate?
- This requires an analysis of how the investors’ required/expected rate of return
depends on risk.
- Investors can reduce risk by holding diversified portfolios.
- Diversifiable risk has no price, the remaining market risk does have a price.
o To price this risk, the appropriate measure relates to the contribution of risk to
the investors’ efficient portfolio.
- Under certain conditions we can derive the CAPM; an equilibrium relationship
between expected/required rate of return and the securities’ contribution to market risk
measured by their beta’s.
o In CAPM only market risk matters
CAPM assumptions
, - When these assumptions hold: the market portfolio is the efficient portfolio → for all
securities, the expected return equals the required return.
o Assumption 1: investors can buy and sell all securities at competitive market
prices (no taxes & no transaction costs) and can borrow and lend at the risk-
free interest rate.
o Assumption 2: investors hold only efficient portfolios of traded securities →
portfolios that yield the maximum expected return for a given level of
volatility.
o Assumption 3: investors have homogeneous expectations regarding the
volatilities, correlations, and expected returns of securities.
Valuation and risk
- Required return (=opportunity cost) on a particular asset/security/activity
o Compensation for patience → risk free rate
o Compensation for risk = units x price of risk
▪ Units of risk = Beta
▪ Business risk: how cyclical are revenues, cost revenues: fixed costs
divided by total costs
▪ Financial risk: how much debt is in the capital structure.
o Price of risk = market risk – risk-free rate (market risk premium)
Empirical Evidence Regarding the CAPM
- Evidence in favor: expected returns are related to betas, as predicted by the CAPM,
rather than to other measures of risk such as the security’s volatility.
- Problems with estimating the CAPM:
o Betas are not observed: if betas change over time, evidence against the CAPM
may be the result of mis-measuring betas.
o Expected returns are not observed: even if beta is a perfect measure of risk,
average returns need to match expected returns. The realized average return
needs to match investors’ expectations.
o The market proxy is not correct: although the S&P 500 is a reasonable proxy
for the U.S. stock market, investors hold many other assets. Any failure of the
CAPM may simply be the result of our failure to find a good measure of the
market portfolio.
The bottom line of the CAPM
- The CAPM remains the predominant model used in practice to determine the equity
cost of capital.
o Although the CAPM is not perfect, it is unlikely that a truly perfect model will
be found in the foreseeable future.
o The imperfections of the CAPM may not be critical in the context of capital
budgeting.
Key to CAPM
- The CAPM provides a method to identify the cost of capital for investments:
o The cost of capital of any investment opportunity equals the expected return of
(widely) available investments in the financial markets with the same beta
Alternative discount rates
- Opportunity cost of debt
- Opportunity cost for equity
, - Weighted average cost of capital.
- Project cost of capital
Ch 12.4 The debt cost of capital
- For the WACC we also need to estimate the (opportunity) cost of debt
o Required return of debtholders (opportunity cost)
- How?
o Combine yield to maturity with probability of default.
o Estimate CAPM for cost of debt (with debt beta)
Yield to maturity.
- Debt yields.
o YTM is the IRR an investor will earn from holding the bond to maturity and
receiving its promised payments.
o If there is little risk the firm will default, YTM is a reasonable estimate of
investors’ expected rate of return.
o If there is significant risk of default, YTM will overstate investors’ expected
return.
CAPM for debt
- Debt betas
o Debt beta measures the sensitivity of the return on debt to the returns of the
market.
▪ If a company has zero probability of default, then the debt is risk free
and the debt beta is 0.
▪ The higher the probability of default the more sensitive the debt return
to the market, the higher the debt beta.
▪ The more exposed an industry is to market risk, the higher the debt
beta.
o Debt betas are difficult to estimate because corporate bonds are traded
infrequently.
Ch12.5 A project’s Cost of capital
- How to determine the cost of capital of a single project? → assume the project is fully
equity financed.
- How to determine the project cost of capital:
o Find an all-equity financed firm in a line of business that is comparable to the
project.
o Use the comparable firm’s beta and cost of capital as estimates.
- What if it is a levered firm?
o Find the cost of capital related to the assets (WACC)
Tutorial 1
8 February 2023
Key concepts
Chapter 9 – valuing stocks
- Stocks → DDM (price = present value dividends) + Total pay-out model (price =
(present value of all dividends + present value repurchase programs) / number of
shares)
- Enterprise value → discounted FCF model
o Present value of free cash flow → EV = Equity + Debt – Cash
Lecture 1
7 February 2023
Valuation (chapter 9)
- Discount the expected value of cash flows at each point in time against an appropriate
discount rate:
o Discount rate is also called the opportunity cost of capital (and/or required rate
of return)
- Dividend discount model: the price of any stock is equal to the present value of the
expected future dividends it will pay.
- Constant dividend growth: the simplest forecast for the firm’s future dividends states
that they will grow at a constant rate, g, forever.
Firm Valuation: Discounted Free Cash Flow Model
- Discounted free cash flow model.
o Determines the value of the firm to all investors, including both equity and
debt holders.
o Enterprise value (=value of the business, excludes cash)
- Free cash flow: cash flow available to pay both debt and equity holders.
- Since we are discounted cash flows to both equity holders and debt holders, the cash
flows should be discounted at the firm’s weighted average cost of capital.
- The enterprise value incorporates the value of the firm from all the cash flows that will
be generated by operations. It does not yet incorporate the cash holdings that the firm
has available.
o To estimate the value of equity, need to add these cash holdings. Moreover,
part of the value will have to be paid to debtholders, so we have to deduct the
value of debt.
o Market value of equity = firm value + cash – debt
- The total payout model also focuses on share repurchases; this is also based on
discounting cash flows.
- Multiples are based on comparable firms.
How to find the discount rate?
- This requires an analysis of how the investors’ required/expected rate of return
depends on risk.
- Investors can reduce risk by holding diversified portfolios.
- Diversifiable risk has no price, the remaining market risk does have a price.
o To price this risk, the appropriate measure relates to the contribution of risk to
the investors’ efficient portfolio.
- Under certain conditions we can derive the CAPM; an equilibrium relationship
between expected/required rate of return and the securities’ contribution to market risk
measured by their beta’s.
o In CAPM only market risk matters
CAPM assumptions
, - When these assumptions hold: the market portfolio is the efficient portfolio → for all
securities, the expected return equals the required return.
o Assumption 1: investors can buy and sell all securities at competitive market
prices (no taxes & no transaction costs) and can borrow and lend at the risk-
free interest rate.
o Assumption 2: investors hold only efficient portfolios of traded securities →
portfolios that yield the maximum expected return for a given level of
volatility.
o Assumption 3: investors have homogeneous expectations regarding the
volatilities, correlations, and expected returns of securities.
Valuation and risk
- Required return (=opportunity cost) on a particular asset/security/activity
o Compensation for patience → risk free rate
o Compensation for risk = units x price of risk
▪ Units of risk = Beta
▪ Business risk: how cyclical are revenues, cost revenues: fixed costs
divided by total costs
▪ Financial risk: how much debt is in the capital structure.
o Price of risk = market risk – risk-free rate (market risk premium)
Empirical Evidence Regarding the CAPM
- Evidence in favor: expected returns are related to betas, as predicted by the CAPM,
rather than to other measures of risk such as the security’s volatility.
- Problems with estimating the CAPM:
o Betas are not observed: if betas change over time, evidence against the CAPM
may be the result of mis-measuring betas.
o Expected returns are not observed: even if beta is a perfect measure of risk,
average returns need to match expected returns. The realized average return
needs to match investors’ expectations.
o The market proxy is not correct: although the S&P 500 is a reasonable proxy
for the U.S. stock market, investors hold many other assets. Any failure of the
CAPM may simply be the result of our failure to find a good measure of the
market portfolio.
The bottom line of the CAPM
- The CAPM remains the predominant model used in practice to determine the equity
cost of capital.
o Although the CAPM is not perfect, it is unlikely that a truly perfect model will
be found in the foreseeable future.
o The imperfections of the CAPM may not be critical in the context of capital
budgeting.
Key to CAPM
- The CAPM provides a method to identify the cost of capital for investments:
o The cost of capital of any investment opportunity equals the expected return of
(widely) available investments in the financial markets with the same beta
Alternative discount rates
- Opportunity cost of debt
- Opportunity cost for equity
, - Weighted average cost of capital.
- Project cost of capital
Ch 12.4 The debt cost of capital
- For the WACC we also need to estimate the (opportunity) cost of debt
o Required return of debtholders (opportunity cost)
- How?
o Combine yield to maturity with probability of default.
o Estimate CAPM for cost of debt (with debt beta)
Yield to maturity.
- Debt yields.
o YTM is the IRR an investor will earn from holding the bond to maturity and
receiving its promised payments.
o If there is little risk the firm will default, YTM is a reasonable estimate of
investors’ expected rate of return.
o If there is significant risk of default, YTM will overstate investors’ expected
return.
CAPM for debt
- Debt betas
o Debt beta measures the sensitivity of the return on debt to the returns of the
market.
▪ If a company has zero probability of default, then the debt is risk free
and the debt beta is 0.
▪ The higher the probability of default the more sensitive the debt return
to the market, the higher the debt beta.
▪ The more exposed an industry is to market risk, the higher the debt
beta.
o Debt betas are difficult to estimate because corporate bonds are traded
infrequently.
Ch12.5 A project’s Cost of capital
- How to determine the cost of capital of a single project? → assume the project is fully
equity financed.
- How to determine the project cost of capital:
o Find an all-equity financed firm in a line of business that is comparable to the
project.
o Use the comparable firm’s beta and cost of capital as estimates.
- What if it is a levered firm?
o Find the cost of capital related to the assets (WACC)
Tutorial 1
8 February 2023
Key concepts
Chapter 9 – valuing stocks
- Stocks → DDM (price = present value dividends) + Total pay-out model (price =
(present value of all dividends + present value repurchase programs) / number of
shares)
- Enterprise value → discounted FCF model
o Present value of free cash flow → EV = Equity + Debt – Cash
