RISK AND RETURN RELATIONSHIPAND

COST OF CAPITAL

Lesson 5

Castellanza,6th October, 2010

Corporate Finance

Corporate Finance

Executive Summary

Risk and return relationship: the financial value

of time

The cost of capital

Capital Asset Pricing Model (CAPM)

Markovitz Portfolio Theory

Corporate Finance

Return

Risk

Time

FINANCIAL DECISIONS

(i.e. capital budgeting/ investment decisions)

Key factors influencing financial decisions

Corporate Finance

1. RETURN

r = rf + Expected Risk PremiumWhere:“rf” = Free Risk Return “Expected Risk Premium” = extra expected return required

by adverse risk investors for taking on risk

2. RISK

- Risk in investment means that future returns are UNPREDICTABLE

- Risk states the possibility that Effective Return can “deviates” from Expected Return (the spread of possible returns is measured by standard deviation)

Key factors influencing financial decisions

Corporate Finance

3. TIME

Financial value of time is connected to:

Risk (it is propotional to the probability that expected

return will be effectively realized)

Flexibility

Temporal distribution of value

Key factors influencing financial decisions

Corporate Finance

DEFINITION:

We define the company cost of capital as “the expected return

on portfolio of all the company’s existing securities”.

That portfolio usually includes DEBT as well as EQUITY.

ASSUMPTIONS:

Every company’s financial fonts have a cost

The returns to investors vary according to the risk the have

borne

RISK = COST OF CAPITAL

The cost of capital

Corporate Finance

The cost of Equity capital (Ke) 1/2

In general terms, in order to estimate “Ke” it is necessary to

consider the OPPORTUNITY COST, defined as “the expected

return on other securities with the same degree of risk”.

It means that:

A potential shareholder will invest in a company’s capital only if

the expected return is at least equal to the return that can be

earned in the capital market on securities of comparable risk.

Ke = rf + Risk Premium

Corporate Finance

When it is possible to estimate the enterprise

market value, the correct ratio to calculate “Ke”

is:

Ke = EPS / P*

Where:

EPS = Earning per Share

P*= Market Value

The cost of Equity capital (Ke) 2/2

Corporate Finance

Kd = i (1-t)

Where:

i = Interest Rate on Debt

(1-t) = Fiscal Effect due to interest tax

deductibility

The cost of Debt (Kd)

Corporate Finance

The WACC is the average rate of return demanded by

investors in the company’s debt and equity

securities:

WACC = [Ke E / (E + D)] + [Kd D / (E + D)]

Where:

E = Equity

D = Debt

Ke > WACC > Kd

The Weighted-Average Cost of Capital (WACC)

Corporate Finance

The Risk/Return relationship 1/4

r = rf + Expected Risk Premium

Where:“rf” = Free Risk Return

“Expected Risk Premium” = extra expected return required by adverse risk investors for taking on risk

From which:Expected Risk Premium = r – rf

Corporate Finance

• HOW TO ESTIMATE RETURN FREE RISK (rf) AND

EXPECTED RISK PREMIUM?

rf = the interest rate free risk is conventionally the return

on Treasury bills: it is fixed and unaffected by what

happens to the market.

Expected Risk Premium = r – rf

= β · (rm – rf)

(Market Risk) (Market Risk Premium)

The Risk/Return relationship 2/4

Corporate Finance

The Risk/Return relationship 3/4

• THE CAPITAL ASSET PRICING MODEL (CAPM)

It states that in a competitive market the expected

risk premium on each investment is proportional to

its Beta.Expected Return on Investment

Security market line

Treasury Bills (β = 0)

Market portfolio (β = 1)

rf

rm

β

…This means that each investment should lie on the sloping security market line connecting Treasury Bills and the Market Portfolio.

0 1

Corporate Finance

• THE CAPM CONCLUSION

An investor can always obtain an Expected Risk

Premium of β (rm –rf) by holding a mixture of the

Market Portfolio and a Risk Free loan

The most efficient way to decrease risk is

DIVERSIFICATION

The Risk/Return relationship 4/4

Corporate Finance

The Markovitz Portfolio Theory

Markovitz Theory is based on the concept that

DIVERSIFICATION REDUCES VARIABILITY (standard

deviation = risk).

The market portfolio is made up of individual stocks, but its

variability doesn’t reflect the average variability of its

components.

Diversification works because prices of different stocks do

not move exactly together.

VARIABILITY = RISK = COST OF CAPITAL

Corporate Finance

Unique Risk and Market Risk 1/3

The risk that potentially can be eliminated by diversification is called

UNIQUE RISK (also called SPECIFIC RISK or UNSYSTEMATIC RISK). It

stems from the fact that many of the perils that surround an individual

company are peculiar to that company and perhaps its immediate

competitors.

It is impossible to totally eliminate risk, because it is impossible to have

stock prices perfectly correlated.

…That is why…

… Diversification reduces risk rapidly at first, than more slowly, untill a point

in which the effect on standard deviation (risk) is null.

Corporate Finance

There is also some risk that it is impossible to avoid, regardless of

how much a company diversify.This risk is generally known as

MARKET RISK (also called SYSTEMATIC RISK).

Market risk stems from the fact that there are other economywide

perils that treaten all businesses.

… That is why…

… Stocks have a tendency to move together, and investors are

exposed to market uncertainities, no matter how many stocks

they hold.

Unique Risk and Market Risk 2/3

Corporate Finance

Unique Risk and Market Risk 3/3

Market Risk

Unique Risk

Number of securities

Portfolio standard deviation

Corporate Finance

How to estimate the Market Risk (β)

From CAPM:

Expected Risk Premium = r – rf

= β · (rm – rf)

MARKET RISK: the Beta of an individual security measures its

SENSITIVITY to market movements.

ß = % re / % rm

Where:

“re” = Expected Return from security

“rm“ = Expected Return on Market

Corporate Finance

The meaning of “Beta”

MARKET RISK: the Beta of an individual security

measures its SENSITIVITY to market movements.

Stocks with β > 1 = tend to amplify the overall

movements of the market;

Stocks with 0< β <1 = tend to move in the same direction

as the market, but not as far.

Corporate Finance

Return on Stock A (%)

Return on Market (%)1.0

1.26

The Return on Stock A changes on average by 1.26% for each additional 1% change in the Market Return. Beta is therefore 1.26

β

- When the market rises an extra 1%, stock A price will rise by 1.26%

- When the market falls an extra 2%, stock A price falls an extra 2X1.26= 2.52%

The meaning of “Beta”

Corporate Finance

The risk of a well-diversified portfolio depends on the Market Risk of the securities included in the portfolio

How do individual securities affect portfolio risk?