CF Chapter 13: Risk, Cost of Capital, and Valuation

How to determine a firm's cost of equity capital and overall cost of capital

Big picture of Corporate Finance

• Corporate finance theories are mostly about valuation (determining the value of a bond, stock, project, company

• Discounted cash flow valuation

For safe projects, calculate NPV as:

NPV = C₀ + Summation C_t / (1+r_f)^_t

Where

• C_t = project cash flows in period t

• r_f = risk-free rate

For risky projects calculate NPV as

NPV = C₀ + Summation C (bar)_t / (1+r)^t

Where

C (Bar) _t = expected project CF in period t

• r = cost of capital

What is the correct discount rate (r) to calculate NPV?

Cost of capital

Definition: Cost of Capital

Expected return on a financial asset of comparable risk

Two assumptions with NPV

1. The company uses only equity finance (all equity case)

2. The project has the same risk as firm’s existing assets

   1. Cost of capital = Expected return on a firm’s stock

How do we calculate expected return on a firm’s stock?

Capital Asset Pricing Model (CAPM)

Equation for CAPM

r = r_f + B(r_M - r_f )

A firm with excess cash can either ____________ or _____________

can either pay a dividend or make a capital investment

Because stock holders can reinvest the dividend in risky financial assets (______ ___), the expected return (_______ ____) on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk

Because stock holders can reinvest the dividend in risky financial assets (opportunity cost), the expected return (discount rate) on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk

To calculate expected return we need 3 things

1. Risk free rate

2. Market Risk Premium

3. Beta for firm’s stock

Risk free rate

Symbol: R_f

• This reflects the pure time value of money - reward for waiting for your money without any risk

Market Risk Premium

Equation: (r_M - r_f )

• This reflects the reward for the market offers for bearing an average amount of systematic risk

Beta for a firm’s stock

B (beta)

• This reflects the amount of systematic risk a firm has relative to the market average

Assumptions when determining appropriate discount rates for a new plan/project

1. Beta of new project is the same as the beta of the company

2. Firm is entirely equity financed

We accept projects with a ______ NPV, and reject NPVs that are ______

Accept: Positive NPV

Reject: Negative NPV

Equation to determine expected return

E(R_i) = summation P_i R_i (probability economic state will occur x the rate if that state does occur)

How to calculate the expected return of a portfolio

E(R_p) = Summation W_i [E(R_i)]

Using the Security Market Line (SML) to determine whether or not to accept projects

Accept projects whose IRRs exceed the cost of equity capital (above the line) and reject projects whose IRRs fall short of the cost of capital (below the line)

If a stock sits above the SML does that mean that it’s underpriced or overpriced?

it is UNDERPRICED, getting a higher return for the same risk as another stock

• Markets are efficient so investors will begin buying stock B, which will drive the price of the stock up

What is the slope equation for the Security Market Line

Slope = [ E(R_i ) - R_f ] / B

CAPM vs SML

The Capital Asset Pricing Model (CAPM) is a mathematical formula that calculates expected return, while the Security Market Line (SML) is the visual graph of that exact formula.

Core Definitions

• CAPM: A formula that links a security's risk to its expected return.

• SML: A straight line on a chart that plots the CAPM equation

Basic method/equation for measuring company’s beta

B_i = Cov(r_i , r_M) / Var(r_M)

Beta measures…

The responsiveness of a security to movements in the market

What is the beta of a risk free asset?

0

What is the beta of a market portfolio?

1

T/F A Beta cannot change

FALSE

• most analysts argue that betas are generally stable for firms remaining in the same industry

• The is not to say that a firm’s beta cannot change

  • Changes in product line

  • Changes in technology

  • Deregulation

  • Changes in financial leverage

Industry Beta

• Frequently argued that one can better estimate a firm’s beta by involving the whole industry

• If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta

• If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta

• Do not forget about adjustments for financial leverage

Determinants of Beta → two types of business risk

1. Cyclicality of Revenues

2. Operating Leverage

Business Risk: Cyclicality of Revenues

Highly cyclical firms have high betas

• Retailers and automotive firms fluctuate with the business cycle

• Transportation firms and utilities are less dependent on the business cycle

Business Risk: Operating Leverage

Ratio of fixed costs to variable costs

• Firms with higher fixed costs relative to variable costs tend to have higher betas

Read over the information about the two firms. Which firm will tend to have a higher beta?

Firm A - high operating leverage

• If there is a recession → sales will decrease, costs are unchanged, profits go down sharply

Firm B - low operating leverage

• Recession → sales down, scale back on variable costs so costs go down, profits go down moderately

Firm A will tend to have a higher beta

Extended definition Degree of Operating Leverage

Measures how sensitive a firm (or project) is to its fixed costs

Operating leverage __________ as fixed costs rise and variable costs _______

Operating leverage increases as fixed costs rise and variable costs fall

Operating leverage __________ the effect of cyclicality on beta

magnifies

Equation for Degree of Operating Leverage

DOL = Delta EBIT/EBIT x Sales/Delta Sales

Definition: Financial Leverage

The extent to which a firm relies on debt

• Levered firms must make interest payments (fixed costs of finance)

Equation for beta demonstrating relationship between firm’s debt, equity, and assets

B_Asset = D/D+E x B_D + E/D+E x B_E

Beta of _____ is constant, but we must solve for the beta of _____

Beta of debt is constant, but we must solve for the beta of equity

Beta of Equity equation (can also include taxes)

B_E = B_UL [1+D/E]

Version with taxes: B_E = B_UL [1+D/E(1-T_c)]

• Taxes on debt mitigates the impact of debt on beta because of tax savings

If D/E = 0, AKA the firm has no debt, then what is B_E

B_E = B_Asset

If a company has debt, and then pays some of it (but not all of it) off, what is the impact on B_e?

B_e decreases

Ex: Consider Grand Sport Inc., which is currently all-equity financed and has a beta of 0.9. The firm has decided to lever up to a capital structure of 1 part debt and 1 part equity

• Since the firm will remain in the same industry, the asset beta should remain 0.9

• However, assuming a zero beta for its debt, its equity beta would become twice as large

Definition: Cost of debt

Interest rate required on new debt issuance

• Ex: Yield to maturity on outstanding debt

The combination of returns from both equity and debt is called

The weighted average cost of capital (WACC)

Steps to Calculating R_WACC

1. Calculate r_equity using CAPM

2. Calculate D/D+E and E/D+E

3. Put it all together into the r_WACC formula

The correct discount rate for a project should reflect the _______ risk of the project’s cash flows

systematic

The B_equity you estimate for a firm reflects the systematic risk of the company’s _______ assets and _____ financial choices

The B_equity you estimate for a firm reflects the systematic risk of the company’s existing assets and past financial choices

If a project is the same systematic risks of existing assets and will be financed the same way, using estimate ______ ______ to calculate discount rates is valid

B_equity

If a project is higher/lower systematic risk than existing assets or is financed differently, one must…

adjust the betas and the discount rates to reflect this difference

How to go about firm valuation

• The value of the firm is the PV of expected future (distributable) cash flow discounted at the WACC

• To find the equity value, subtract the value of the debt from the firm value

Some example steps to go through when calculating firm value

1. Estimate the cost of equity and cost of debt

   1. Estimate an equity beta to estimate the cost of equity

   2. Can often estimate the cost of debt by observing the YTM of the firm’s debt

2. Second, determine the WACC by weighting these two costs appropriately

How do we determine the cost of equity capital?

CAPM

How can we estimate a firm or project beta?

Firm: Comparing similar industry betas, SML

Project Beta: Using B_asset = B_e = B_UL [ 1+D/E ]

How does leverage affect beta?

Increase in leverage → increase in equity beta

decrease in leverage → decrease in equity beta