estimating discount rates

7/22/2019 Estimating Discount Rates

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Estimating Discount Rates

Dr. Himanshu Joshi


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Estimating Discount Rates

In DCF Valuations, the discount rates usedshould reflect the riskiness of the cash flows.

Cost of debt has to incorporate a default

premium or spread for the default risk in thedebt.

Cost of equity has to include a risk premium

for equity risk. How do we come up with default and equity

risk premiums?


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What is Risk?

Chinese: Danger

Financial Terms: Risk

Opportunity

Expected Return


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What is Risk?

In Valuation, risk as we see it, refers to thelikelihood that we will receive a return oninvestment that is different from the return

we expected to make. Thus, risk includes not only the bad outcomes,

(returns that are lower than expected) butalso good outcomes (return that are higherthan expected).

Down side Risk and Up side Risk.


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Discounting Rate

For Business or Firm Valuation:

WACC = KdT* WD+ Ke * WE

For Equity Valuation:Ke using CAPM Model

CAPM Model:

Ke = Rf + * (RmRf)

Covariance Market Risk PremiumRisk Free Rate


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Cost of Equity

Cost of Equity is Implied Cost. Cost of equity is what investors in the equity

in a business expect to make on their

investment. Two difficulties in measuring it:

1. Unlike interest rate on debt, the cost is an

implicit cost and cannot be directly observed.2. This expected rate need not be the same forall equity investors in the same company.


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Cost of Equity

The challenge in Valuation is thereforetwofold.

The first task is to make the implicit cost into

explicit cost by reading the mind of theinvestors.

The second and more daunting task is to then

come up with a rate of return that thesediverse investors will accept as the right costof equity in valuing the company.


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Three Estimation Approaches..

1. Risk and Return Models: We derive models thatmeasure the risk in an investment and convertthis risk measure into an expected return, whichin turn becomes cost of equity for that

investment.2. Look at difference in actual returns across stock

over long period of time periods and identify thecharacteristics of companies that best explain

the difference in returns. We then use thisrelationship to forecast expected equity returnsfor individual companies.


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Three Estimation Approaches..

3. The last approach uses observed market

prices on risky assets to back out the rate of

return that investors are willing to accept on

these investments.


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Risk and Return Model Approach

Risk is defined in terms of the distribution ofactual returns around and expected return.

Differentiate between the risk that is specific

to one or few investmentsand the risk thataffects a much wider cross section ofinvestments.

In a market where marginal investor is welldiversified, it is only the market risk that willbe rewarded.


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Diversifiable and Non Diversifiable

Risk.

Firm Specific Market

Project may dobetter or Worse

than expected

Competitionmay be stronger or

weaker than the

expected Entire Sector

may be

affected by

action

ExchangeRate and

Political Risk

InterestRates,

Inflation

and news

about

economy

Affects Few Firms Affects Many firms


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CAPM the Default Model

Expected Return on Asset i = Risk Free Rate +

Beta of asseti*(Risk Premium for Average-Risk

Asset).

CAPM Model:

Ke = Rf + * (RmRf)

Covariance Market Risk PremiumRisk Free Rate


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Components of CAPM: Risk Free Rate

Risk free asset is defined as an asset on which

investor know the return with certainty.

For an investment to be risk free, two conditions

have to be met:

1. There can be no default Risk: Govt. Securities

2. There can be no uncertainty about

Reinvestment Rates: Zero Coupon Bonds with

matching Maturity.


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Risk Free Rates..

A purists view of risk-free rates would thenrequire different risk free rates for cash flows ineach period and different expected returns.

As a practical compromise, however, it is worthnoting that the present value effect of using risk-free rates that vary from year to year tends to besmall for most well behaved term structures.

In these cases, we can use a duration matching

strategy, where the duration of the default freesecurity used as Rf, is matched up with theduration of the cash flows in analysis.


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Duration for level perpetuity

Duration of perpetuity = 1+y/y

At 10% yield, the duration of a perpetuity thatpays $100 once a year forever is

1.10/.10 = 11 years.

But at an 8% yield 1.08/0.08 = 13.5 years.


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2. Risk Premium

What Is the Risk Premium Supposed toMeasure? The risk premium in CAPMmeasures the extra return that would be

demanded by investors for shifting theirmoney from a riskless investment to anaverage risk (market) investment.

It should be function of two variables:

1. Risk Aversion of Investors

2. Riskiness of the average risk Investment.


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Estimating Risk Premiums..

Geometric Average Vs. Simple Average

Geometric Average =[ ValueN ]1/N - 1

Value0


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Estimating Risk Premium

Historical Risk

Premium US

Market

StockTreasury Bills StockTreasury Bonds

Arithmetic Geometric Arithmetic Geometric

1928-2004 7.92% 6.53% 6.02% 4.84%

1964-2004 5.82% 4.34% 4.59% 3.47%

1994-2004 8.60% 5.82% 6.85% 4.51%


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Estimating Risk Premiums..

1. Country Based Risk Premium Approach:

Rating Assigned to countrys debt by a rating

agency.

2. Relative Standard Deviation:

Relative S.D Country X = S.D of Country Xs Eq.

S.D of U.S Equity

Equity Risk Premium for Country X = Risk

Premium in US * Relative SD of Country X.


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Estimating Risk Premium..

3. Default Spread Plus Relative S.D:

Country Risk Premium = Country Default Spread* (Equity/ countryBond)


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3. Beta

There are three approaches available for

estimating beta:

1. Using historical data on market prices and

individual assets.

2. Estimating betas from fundamentals.

3. Using Accounting data.


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Approach 1. Historical Market

Betasbeta.xlsx

Conventional approach for the firms that arepublicly traded for the long time.

The Standard procedure for estimating CAPM

beta is to regress Stock Returns (Ri) againstMarket Returns (Rm):

Ri= a + b Rm

Where a = intercept from the regression. b = slope of the regression = Covariance

(Ri,Rm)/m2
http://localhost/var/www/apps/conversion/tmp/scratch_8/beta.xlsxhttp://localhost/var/www/apps/conversion/tmp/scratch_8/beta.xlsx


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Betasbeta.xlsx

There are three decisions that analyst must

make in setting up the regression just

described:

1. The length of the Estimation Period: The

Trade-Off is simple: A longer estimation

period provides more data, but the firm itself

might have changed in its risk characteristicsover the time period.


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Betasbeta.xlsx

2. The estimation of the Return Interval:Returns on stock and market are available onan annual, monthly, weekly, daily or ever

intra-day basis.Using daily or intraday returns will increasenumber of observations in the regression, butit exposes the estimation process to asignificant biasin beta estimates related tonon-trading.


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Non Trading Bias: Returns in non-trading

periods are zeros (even though the market

may have moved up or down significantly in

these periods). Using these non-tradingperiods returns will reduce the correlation

between stock returns and market returns and

in turn the beta of the stock.)


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Approach 1. Historical Market Betas

RelainceData_beta.xls

3. Choice of Market Index: The right index to

use in analysis should be determined by

holdings of the marginal investor in the

company being analyzed.

If the marginal investor in the company is a

global investor, a more relevant measure of

risk may emerge by using a global index.
http://localhost/var/www/apps/conversion/tmp/scratch_8/RelainceData_beta.xlshttp://localhost/var/www/apps/conversion/tmp/scratch_8/RelainceData_beta.xls


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Determinants of Betas

1. The type of business or businesses the firms

is in. (cyclicality)

2. The degree of operating leverage.

3. The firms financial leverage.


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The Leveraging Effect..Levered

Beta.xlsx

If all of the firms market risk is borne by the

stockholders (i.e., the beta of debt is zero),

and debt creates tax benefit to the firm, then:

L= U[ 1 + (1-t)* D/E]

Where L= levered Beta, U= Unlevered Beta

D/E = Debt- Equity ratio (Market Value Terms),t = tax rate.
http://localhost/var/www/apps/conversion/tmp/scratch_8/Levered%20Beta.xlsxhttp://localhost/var/www/apps/conversion/tmp/scratch_8/Levered%20Beta.xlsxhttp://localhost/var/www/apps/conversion/tmp/scratch_8/Levered%20Beta.xlsxhttp://localhost/var/www/apps/conversion/tmp/scratch_8/Levered%20Beta.xlsx


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Approach 2. Bottom Up Betas..

Breaking Down betas into their business,

Operating Leverage, and financial leverage

components provides us with an alternative way

of estimating betas, where we do not needhistorical returns on an assets to estimate its

beta.

Property: The beta of two asset put together is aweighted average of the individual asset betas,

with the weights based on the market value.


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Bottom Up Beta Estimation..

1. Identify Comparable Firms in industry.2. Beta Estimation using Common Index

3. Unlever Beta

4. Averaging Approach (Simple or Weighted Avg.)5. Adjustment for Cash

(unlevered Beta corrected for Cash =

U/(1-Cash/Firm Value).

6. Calculate Levered Beta for the FirmL= U* (1 + (1-Tc)* D/E)


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Bottom Up Beta for Disney

Bottom Up Beta.xlsx
http://localhost/var/www/apps/conversion/tmp/scratch_8/Bottom%20Up%20Beta.xlsxhttp://localhost/var/www/apps/conversion/tmp/scratch_8/Bottom%20Up%20Beta.xlsx


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Private and Closely Held Business..

Adjust the Beta to Reflect Total Risk rather

than just the market risk.

Total Beta = Market Beta/R2

estimating discount rates

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