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Managerial Finance . FINA 6335 The CAPM and Cost of Capital Lecture 9. Simplifying Assumptions . Individuals can trade securities without regard to fees, taxes, and other frictions. Individuals get any relevant information about the firms they are interested in costlessly.

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managerial finance

Managerial Finance

FINA 6335

The CAPM and Cost of Capital

Lecture 9

simplifying assumptions
Simplifying Assumptions
  • Individuals can trade securities without regard to fees, taxes, and other frictions.
  • Individuals get any relevant information about the firms they are interested in costlessly.
  • Individual investors can borrow or save at the same riskless rate equal the the “riskfree rate”
market equilibrium
Market Equilibrium

All investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate.

CML

return

Optimal Risky Porfolio

rf

market equilibrium4
Market Equilibrium

The CML:

Rp = Rf + (sp /sM)(RM- Rf )

CML

return

Optimal Risky Porfolio

rf

definition of risk when investors hold the market portfolio
Definition of Risk When Investors Hold the Market Portfolio
  • Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security.
  • Beta measures the responsiveness of a security to movements in the market portfolio.
relationship between risk and expected return capm
Relationship between Risk and Expected Return (CAPM)
  • Expected Return on the Market:
  • Expected return on an individual security:

Market Risk Premium

This applies to individual securities held within well-diversified portfolios.

expected return on an individual security

Expected return on a security

Risk-free rate

Beta of the security

Market risk premium

=

+

×

  • Assume bi = 0, then the expected return is RF.
  • Assumebi = 1, then
Expected Return on an Individual Security
  • This formula is called the Capital Asset Pricing Model (CAPM)
summary and conclusions
Summary and Conclusions
  • This chapter sets forth the principles of modern portfolio theory.
  • The expected return and variance on a portfolio of two securities A and B are given by
summary and conclusions13
Summary and Conclusions
  • The efficient set of risky assets can be combined with riskless borrowing and lending. In this case, a rational investor will always choose to hold the portfolio of risky securities represented by the market portfolio.

P

summary and conclusions14
Summary and Conclusions
  • The contribution of a security to the risk of a well-diversified portfolio is proportional to the covariance of the security's return with the market’s return. This contribution is called the beta.
  • The CAPM states that the expected return on a security is positively related to the security’s beta:
estimating b with regression

Characteristic Line

Slope = bi

Estimating b with regression

Security Returns

Return on market %

Ri = ai + biRm + ei

security market line

Security Market Line

Slope = R(m)-R(f)

Security Market Line

Security Returns

Beta

Ri = Rf + bi(Rm – Rf )

practical issues in capm
Practical Issues in CAPM
  • Forecasting Beta
    • The problem is that you assume your estimate of Beta is the true value of Beta
    • “regression toward one”
    • Allow for extremes
    • What Time Horizon
      • 2 years of weekly, or 5 years of monthly
the security market line
The Security Market Line
  • Risk free interest rate?
  • The Market Risk Premium

5.7%

firm valuation
Firm valuation
  • See Chapter 18, Section 1 and 2.
  • We will want to value the firm using the Discounted Cash Flow (DCF) method.
  • Three issues:
    • What do you want to discount?
    • How do you project this over time?
    • How do you discount it?
basic valuation
Basic Valuation
  • What do you want to Discount?
  • How do you project these?
  • How do you discount these?
basic valuation22
Basic Valuation
  • What do you want to Discount?
    • Free Cash Flow
  • How do you project these?
  • How do you discount these?
basic valuation23
Basic Valuation
  • What do you want to Discount?
    • Free Cash Flow
  • How do you project these?
    • From Historical Data
  • How do you discount these?
basic valuation24
Basic Valuation
  • What do you want to Discount?
    • Free Cash Flow
  • How do you project these?
    • From Historical Data
  • How do you discount these?
    • The Cost of Capital or (Weighted Average)
free cash flow
Free Cash Flow
  • Start with EBIT
  • Subtract Taxes
  • Leaves EBIT(1-t) = Unlevered (Operating) Net Income
  • Plus Depreciation
  • Less Capital Expenditures
  • Less Increases in Working Capital
  • Bottom Line: = Free Cash Flow
example
Example:

Current Sales = $60

Cost of Goods Sold 25

Gross Profit 35

Less Operating Expenses 9

Less Depreciation 6

EBIT 20

Less Income Tax Rate (@ 35%) 7

Operating (Unlevered) NI 13

Plus Depreciation 6

Less Capital Expenditures 2

Less Increases in Working Capital 1

Free Cash Flow 16

how do we make estimates
How do we make estimates?
  • 1. Income tax should be the statutory rate.
  • Depreciation: You need to project depreciation into the future. Will increase as Capital Expenditures increase. How do you estimate?
  • Capital Expenditures: Note, to propel growth, you need to invest: How do you determine Cap Ex =???
  • Finally, Changes in Working Capital?
projections of growth
Projections of Growth:
  • Recall: growth depends on 2 variables:

Retention rate = (1 – Payout ratio)

Return on Investments = Operating Income as a percentage of Book Value of Assets

  • Consider Historical Rates as well:
discount rate
Discount Rate
  • Conceptually:

V = Present Value of the firm’s Cash flows, discounted by a number called the “cost of capital”

Basically it is the IRR of the Firm.

Conceptually, you want to discount by a rate that reflects the risk of the firm’s operating Cash Flow.

how do you estimate this
How do you estimate this
  • Weighted Average Cost of Capital

Once you have the stream of operating Cash Flows generated by the firm, the next problem is to determine how to discount it.

The discount rate that makes the Value of the firm equal the firm’s cash flow is what we call the Cost of Capital.

As a practical matter this can be approximated by the Weighted Average Cost of Capital (WACC)

slide31
WACC
  • The WACC is defined as:

rWACC = rE X (E/(E+D)) + rD(1-t) X (D/(E+D))

The weighted average of the (after tax) cost of the component securities issued by the firm, weighted by the proportion of those securities issued by the firm.

rE is the required return to the equity of the firm

rD is the required return to the debt of the firm

D is the (market value) of the debt issued by the firm

E is the market value of the equity.

t is the firms tax rate.

wacc estimation
WACC Estimation
  • Some of these variables are not easily estimated so we make some assumptions:

To estimate D use the Book value of the debt.

To estimate rD use the ratio of Total Interest payments to the total book value of the debt

To estimate rE use the Capital Asset Pricing Model