Estimating the Hurdle Rate

26-Nov-13

1

Estimating the Hurdle Rate

Estimating the Hurdle Rate 2

Hurdle Rate

• Investment Decision specifies that a firm should invest in assets only if they expect them to earn more than the hurdle rate.

• What should be this Hurdle rate?

o Suppose you borrow all funds required to fund a project, paying 12% pa interest on the funds borrowed.

o The project should earn at least 12% so as to be profitable.

� Cost of Capital represents the minimum return that a firm needs to earn on its projects.

� It is the compensation for time and risk in the use of capital by a project.

• How is it estimated?

� As a firm raises funds from different sources, so the weighted average of the individual costs is the cost of capital (the hurdle rate)

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Cost of Debt

• Discount rate which equates the present value of interest

payments and principal repayments with the net proceeds of the

debt issued or its current market price.

∑n

t n0 t n

t=1 d d

C FP = +

(1+k ) (1+k )

31 2 n n0 1 2 3 n n

d d d d d

CC C C FP = + + +........+ +

(1+k ) (1+k ) (1+k ) (1+k ) (1+k )

where,

P0 = net amount realised on debt issue (or CMP)

Ct = Periodic interest on Debentures

Fn = Face Value/ Redemption price

n = Maturity period

Kd = Cost of debt


Cost of Debt - Illustration

Fn=100/- ; C= 14/- ; n = 5 Years; P0 = 97/-

5

t 5t=1 d d

14 10097= +

(1+k ) (1+k )∑

By trial & error: kd = 14.89%

NTPC issues 14% bonds of Rs.100/- face value, redeemable after 5

years and realises Rs.97/- now. What is the cost of Debt?

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Cost of debt may be approximated by:


Cost of Debt - Approximation

d

(100-97)14+

14.65k = =14.82%(97+100) 98.5

2

≅

n 0

d

0 n

(F -P )C+

nk(P +F )

2

≅

Cost of Debt - Adjustment for Taxes

• Interest on debt is tax-deductible.

Particulars A B Change

EBIT 1000 1000

Interest --- 200

PBT 1000 800 200 ↓

Taxes @ 20% 200 160

PAT 800 640 160 ↓

Post-tax Cost of Debt = Pre-tax Cost of Debt* (1-tax rate)

• Interest payment of 200 in case B, has resulted in reducing the Tax

outflow from 200 to 160, i.e. by 40 which is 200* 20%

(Interest*tax rate)

• PBT has decreased by 200, while PAT decreased only by 160, due

to Interest outgo acting as a “shield” to the profits.

Post-tax kd= 14.89%*(1 - 0.30) = 10.42%Estimating the Hurdle Rate 6

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Cost of Debt - Illustration

Micromax has the following debt instruments outstanding.

Find the average cost of debt.

If the marginal tax rate is 35%, find the post-tax cost of debt.

Instrument Face Value

(Rs Mn)

Market Value

(Rs Mn)

Coupon

Rate

Yield

Non-Convertible Debentures 100 105 12% 10.70%

Bank Loans 200 200 13% 13.00%

Commercial Papers 50 47 - 7.40%

Instrument Market Value

(Rs Mn)

Yield % age Cost

Non-Convertible Debentures 105 10.70% 29.83 3.19%

Bank Loans 200 13.00% 56.82 7.39%

Commercial Papers 47 7.40% 13.35 0.99%

Total Debt 352 100.00 11.57%

Post-tax cost of debt = 11.57%*(1-0.35) = 7.52%


Cost of Preference Capital

• Discount rate which equates the present value of Dividend

payments and redemption value with the net proceeds of the

preference shares(or its current market price)

nt n

0 t nt=1 p p

PD FP = +

(1+k ) (1+k )∑

where,

P0 = net amount realised on issue of Preference share /CMP

PDt = Dividend on Preference Shares

Fn = Redemption Value

n = Maturity period of Preference Shares

kp = Cost of Preference Capital

31 2 n n0 1 2 3 n n

p p p p p

PDPD PD PD FP = + + +........+ +

(1+k ) (1+k ) (1+k ) (1+k ) (1+k )

n 0t

p0 n

(F -P )PD +

nk(P +F )

2

≅An approximation:

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Estimating the Hurdle Rate9

Cost of Preference Capital-Illustration

ABC Ltd. issues Rs.1,000/- face value preference shares carrying 12%

dividend, redeemable at par after 3 years. Net amount realised today

is Rs.960/-. Tax Rate= 40% . What is the cost of Preference Capital?

t0 t

t=1 p

PDP =

(1+k )

∞

∑ tp

0

PDk =

Por

• Irredeemable (Perpetual) Preference Shares

≅p

(1000-960)120+

133.333k = =13.6054%(1000+960) 980

2

∑3

t 3t=1 p p

120 1000960= +

(1+k ) (1+k )

By trial & error: kp = 13.7147% or

Fn = 1000 ; PDt= 120 ; n =3 years; P0 = 960


Cost of Equity

• There is no legal obligation to pay dividends to the shareholders

• Quantum of dividends is also not fixed.

• Cost of Equity shares is an Implicit cost.(not explicit)

• It is an Opportunity Cost. (Returns forgone on the next best

investment opportunity of comparable risk)

• Methods of computing Cost of Equity Capital:

� Dividend Discount Model (DDM)

� Capital Asset Pricing Model (CAPM)

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Cost of Equity Capital: Dividend Discount Model (DDM)

• Discount rate that equates the present value of the stream of

expected future dividends with the current market price/Issue

Price.

31 20 1 2 3

e e e e

DD D DP = + + +..........+

(1+k ) (1+k ) (1+k ) (1+k )

∞∞

t0 t

t=1 e

DP =

(1+k )

∞

∑General Form of DDM

where,

Po = Current Market Price of the Equity Share at time ‘to’

Dt = Expected Dividend per share at time ‘t’

ke = Cost of Equity


DDM - Constant Growth

• If the dividends are expected to grow at a constant rate ‘g’, and ke> g, then,

Assumptions:

• D1 > 0

• Dividends grow at a constant growth rate “g” =ROE*b

• Dividend Payout ratio (1-b) is constant

1 2 3

1 1 1 10 1 2 3 4

e e e e

D D (1+g) D (1+g) D (1+g)P = + + + +..........+

(1+k ) (1+k ) (1+k ) (1+k )∞

10

e

DP =

(k - g)1

e

0

Dk = +g

POr

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DDM - Constant Growth

TrueValue Ltd intends to pay a dividend of Rs. 5/- next year, and

expects the dividends to grow @ 6% each year till perpetuity. The

Company’s market price currently is Rs. 50/-. What of the cost of

Equity shares?

TrueValue Ltd intends to pay a dividend of Rs. 5/- next year, and

expects the dividends to grow @ 6% each year till perpetuity. The

Company’s market price currently is Rs. 50/-. What of the cost of

Equity shares?

D1 = Rs.5/- ; g= 6% forever, P0= Rs.50/-. Find ke.

ke = (5 / 50) + 6%

= 10%+ 6% = 16%.

Mostly used for companies in the mature stage of their life cycle

1e

0

Dk = + g

P


How to estimate Growth Rate?

1. Historical Growth Rates: If earnings and dividends growth

rates have been relatively stable in the past, and investors

expect these trends to continue in the future, then the past

realised growth rates may be used to estimate the expected

future growth rates.

2. Retention Growth Model: Firms pay some part of their net

income as dividends and retain the balance.

Growth rate of a firm will be depended on the net income

retained by it and the rate it earns on the retentions., Thus

g = ROE*Retention ratio, where Retention ratio = 1- Pay-out ratio

3. Analysts’ forecasts: Security analysts provide forecasts on

regular basis, using non-constant growth.

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DDM - Multiple Growth Rate

∑n

t-1 t n n+10 nt n

t=1 e e e n

D (1+g ) P DP = + where P =

(1+k ) (1+k ) k - g

nt-1 t n+1

0 t nt=1 e e e n

D (1+g ) D1P = + ×

(1+k ) (1+k ) k - g

∑

∝

Stage 3Stage 2Stage 1

Years

Gro

wth

ra

te

A firm may pass through

different growth phases and

hence dividends may also grow

at different rates.


DDM - Multiple Growth Rate -Illustration

By trial & error: ke = 12%

The stock price of Advanta Ltd currently is Rs. 125/- The company

paid a dividend of Rs 3.50 in the year just ended. The company

expects that its dividends would grow @ 15% for next 3 years; @

12% for 3 years after that and @ 8% per year, thereafter forever.

What is the cost of Equity capital?

D1 = 4.03; D2 = 4.63; D3 = 5.32; D4 = 5.96; D5 = 6.68; D6 = 7.48; D7 = 8.08

1 2 3 4 5 6 6

e e e e e e e e

4.03 4.63 5.32 5.96 6.68 7.48 8.08 1125 = + + + + + + ×

(1+k ) (1+k ) (1+k ) (1+k ) (1+k ) (1+k ) (k - 8%) (1+k )

P0 = 125 ; D0 = 3.50; g1-3=15% g 4-6=12% g7+=8%

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Cost of Equity Capital: Bond-Yield plus Risk Premium

ke: Bond Yield on Co’s long-term debt + Bond risk premium (3-5%)

Bonds of NCE Ltd has a yield of 11% and the bond risk premium isestimated at 3.8%, then the estimated cost of equity is 14.8% (11% +3.8%)


Cost of Equity Capital: Capital Asset Pricing Model (CAPM)

• Expected rate of return on any security “Ri” is given by:

i fR =R + Equity Risk Premium

where,Ri = Rate of return on security “i”Rf = Risk-free rate of returnRm= Rate of return on Market Portfolioβi = beta of security “i”Rm - Rf = Market Risk Premium

Rf =10%; Rm=15%; βA= 0.5; βB =1.0; βC = 1.5; Find Ri

� RA =10% + 0.5(15%-10%) = 12.5%

� RB =10% + 1.0(15%-10%) = 15.0%

� RC =10% + 1.5(15%-10%) = 17.5%

i f i m fR =R + (R - R )β

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External and Internal Equity

• Equity � External equity (additional /Outside) and Internal

equity(Retained Earnings)

• In both cases, the shareholders are providing the funds to the

firm, hence they would expect same returns on both.

• But, Internal Equity is cheaper than External Equity due to:

– New equity is issued at less than the Current Market Price;

– Issue of new Equity involves Floatation Costs.

• As External Equity is expensive than Internal Equity, an

adjustment has to be made.1

re

0

DInternal Equity k = +g

P1

e

0

DExternal Equity k = +g

ICMP = Rs 100/- ; I0 = Rs 95/- ; D1 = Rs 5/- ; g = 6%

re

5k = +6%=11%

100e

5k = +6%=5.26%+6%=11.26%

95


Weighted Average Cost of Capital

• After having calculated the cost of individual components of the

capital structure, we need to calculate the Weighted Average

Cost of Capital (WACC).

• Weights MAY be either:

(a) Market Value of the various forms of financing, which the company

intends to employ�Consistent with the objective of maximization of

shareholder’s wealth

(b) Book Value of the Capital Structure.

• WACC should be estimated on post-tax basis.

0 e d

E DWACC(k )=k +k (1-t)

(D+E) (D+E)

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Marginal Cost of Capital

• WACC is calculated based on the various sources of capital

already employed by the firm.

• Such WACC provides a historical perspective – can at best be

used to compare with some predetermined cost of capital.

• However, the most important use of the concept of Cost of

Capital is to evaluate Investment decisions.

• Therefore, more relevant cost to be worked out – should be cost

of raising new funds to finance new projects and not the

historical costs which have been incurred in the past.

• Therefore, weighted average cost of capital should be calculate

for the incremental or marginal capital � Weighted Marginal

Cost of Capital (WMCC).

Risk & Return

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Stock Returns

• Stock Returns = (845 - 625) /625 = 35.20%

• Total Stock Returns = (845-625+25) /625= 39.20%

23

• Stock returns are considered instead of stock prices.

• Stock Returns = (Pt- Pt-1) /Pt-1

• Log Returns = ln(Pt/Pt-1)

• Total Stock Returns = (Pt- Pt-1+Dt) /Pt-1


The price of Reliance share is Rs. 845/- today and was Rs 625/- one

year ago. It paid a dividend of Rs. 25/- per share. What is the return

over the one-year period?

Stock returns over the years

24

-40%

-20%

0%

20%

40%

60%

80%

19

91

-92

19

92

-93

19

93

-94

19

94

-95

19

95

-96

19

96

-97

19

97

-98

19

98

-99

19

99

-00

20

00

-01

20

01

-02

20

02

-03

20

03

-04

20

04

-05

20

05

-06

20

06

-07

20

07

-08

20

08

-09

20

09

-10

20

10

-11

20

11

-12

Stock returns are high but are volatile also.


Instrument Nominal Real Average Risk Premium(over 1-year GOI)

1- year G-Sec yield9.29 1.71 0.00

Corporate Bonds

(AAA rated)13.50 6.35 4.21

Equity Shares22.89 15.98 13.61

Average Rates of Return (1978 -2011) % per year

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Stock Returns

Expected Stock Returns = (0.30*16%) + (0.50*11%) + (0.20*6%)

= 11.50%

25

• Expected Stock returns : E(Ri) = ∑pi*Ri


State of Economy Probability of

Occurrence

Rate of Return

(%)

Boom 0.30 16

Normal 0.50 11

Recession 0.20 6

• Portfolio returns is the weighted average of the individual stock returns.

where,

x1, x2: %age of funds invested in stock 1,2.

r1, r2 : %age return of stock 1,2.

Portfolio Returns

26

1 1 2 2Portfolio Returns = x r + x r


Expected returns on security A is 16 % and on security B is14 per cent and an investor wants to create a portfolio oftwo asset with equal weightage. What would be theexpected portfolio returns?

E(Portfolio AB) =(0.5 x 14%) + (0.5 x 16%) = 15%

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Risk• Risk is the possibility of adverse outcome.

• In finance, risk is defined as the likelihood of outcome being different from expected outcome.

• Actual outcome may be better or worse than expected.

1. Company Specific: Risks which are unique to a company.

�Law suits, strikes, Successful /Unsuccessful projects etc.

� Impact of such factors can be minimized, hence are called Diversifiable risks.

2. Market Risks are caused by factors which systematically affect all or most firms.

�War, Inflation, Change in Govt. Policies. Interest Rates etc.

�Such risks cannot be eliminated, hence called Non-diversifiable risk

�Originates from the system, hence called Systematic Risk.• Statistical measure of risk is Standard Deviation (or Variance )

27Estimating the Hurdle Rate

Portfolio Risk


YearStock A Stock B

Portfolio AB

(50%) (50%)

2008 40% -10% 15%

2009 -10% 40% 15%

2010 35% -5% 15%

2011 -5% 35% 15%

2012 15% 15% 15%

Average 15% 15% 15%

Standard Deviation 22.64% 22.64% 0.00%

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Portfolio Risk


-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

Stock A

-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

Stock B

-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

Portfolio AB

-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

-20%

-10%

0%

10%

20%

30%

40%

50%

2008 2009 2010 2011 2012

When stocks are

When stocks are

Portfolio Risk

30

Sto

ck 1

Sto

ck 2

2 2

1 1x σ

2 2

2 2x σ

1 2 1 2x x σ

1 2 12 1 2x x ρ σ σ=

1 2 1 2x x σ

1 2 12 1 2x x ρ σ σ=

Stock 1 Stock 2

2 2 2 2

1 1 2 2 1 2 12 1 2Portfolio Variance = x σ + x σ + 2(x x ρ σ σ )

where,

x1, x2 : %age of funds invested in stock 1,2.

σ1, σ2 : standard deviation return of stock 1,2

ρ12 : coefficient of correlation between stock 1 & 2.Estimating the Hurdle Rate

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Risk (Standard Deviation) selected stocks

31

Stock Standard Deviation

Hindustan Unilever 28.60%

Hero Honda 28.80%

Infosys 29.20%

NTPC 30.00%

Bharati Airtel 33.50%

ONGC 37.30%

L&T 46.90%

Tata Motors 54.80%

Sterlite Industries 59.60%

Tata Steel 62.30%


Portfolio Risks & Returns

32

Hero Honda Tata Steel

Stock Returns 16% 24%

Stock Standard Deviation 29% 62%

Weights 50% 50%

Portfolio Returns: 20.00%

Portfolio Standard Deviation:

Case 1: ρ = + 1 45.50%

Case 2: ρ = 0 34.22%

Case 3: ρ = - 1 16.50%


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10%

15%

20%

25%

30%

1 4 7 10 13 16 19 22 25

No. of Securities

Reducing Risk

33

Sta

nd

ard

De

via

tio

n

Market Risk


By combining stocks, the Company specific risks get eliminated (hence Diversifiable

Risks), while the Market risk still remains (hence Non-diversifiable Risks).

Company Specific Risks

Risk (Standard Deviation & Beta) selected stocks

34

Stock Standard Deviation Beta (ββββ)

Hindustan Unilever 28.60% 0.41

Hero Honda 28.80% 0.57

Infosys 29.20% 0.55

NTPC 30.00% 0.72

Bharati Airtel 33.50% 0.76

ONGC 37.30% 0.95

L&T 46.90% 1.38

Tata Motors 54.80% 1.48

Sterlite Industries 59.60% 1.66

Tata Steel 62.30% 1.77

Stocks with high standard deviation also have high beta


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Risk-Return relationship of various securities

Risk (%)

Re

turn

s (%

)

Equity Shares

Preference Shares

Corporate Bonds

Government Bonds

Risk-free securities


SML

Beta and its Estimation

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Estimating Beta

• Beta of a security measures the Market (Non-

diversifiable or Systematic) risk.

• Methods of estimating beta:

�Regression method

�Bottom-up Beta

�Accounting Beta


#1 Regression Method

38

Year RaRm

1 12 10

2 14 12

3 16 13

4 12 8

5 -5 3

6 21 14

7 20 14

8 16 8

9 9 4

10 -2 -1

11 13 10

12 15 16

13 19 12

14 15 10

15 20 17

-10

-5

0

5

10

15

20

25

-5 0 5 10 15 20Sto

ck R

etu

rn (

Ra)

Market Return (Rm)


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Estimating Beta – Regression Method

Coefficients

Standard

Error t Stat P-value

Lower

95%

Upper

95%

Intercept -0.075 2.317 -0.032 0.975 -5.080 4.930

Rm 1.307 0.209 6.264 0.000 0.857 1.758

Regression Statistics

R Square 0.751

Adjusted R Square 0.732

Observations 15

a mR = -0.075+1.307 R

75% of the risk is

due to Market


Regression Statistic

• Coefficient of Determination (R2) :

�Goodness of Fit- indicates the %age of risk attributed to

Market risk.

�R2 = 0.751 or 75% of change in stock returns are due to

changes in market returns,

� (1-R2) or 25% is caused by firm specific reasons.

• Standard Error (se):

� Indicates the error in estimate between estimated Beta and

“true” beta

� Se =0.209: true beta lies between 1.037 ± 1(0.209) with 67%

confidence.


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Direct Method

41

Year RaRm Ra-AvgRa Rm-AvgRm (Ra – avg Ra)x

(Rm-AvgRm)

(Rm-AvgRm)2

1 12 10 -1 0 0 0

2 14 12 1 2 2 4

3 16 13 3 3 9 9

4 12 8 -1 -2 2 4

5 -5 3 -18 -7 126 49

6 21 14 8 4 32 16

7 20 14 7 4 28 16

8 16 8 3 -2 -6 4

9 9 4 -4 -6 24 36

10 -2 -1 -15 -11 165 121

11 13 10 0 0 0 0

12 15 16 2 6 12 36

13 19 12 6 2 12 4

14 15 10 2 0 0 0

15 20 17 7 7 49 49Estimating the Hurdle Rate

Beta estimation

42

∑n

a a m m

(a,m)

1

(R - Avg R )(R - Avg R ) 455Covariance = = = 32.50

(n-1) 14

∑2n

m m(m )

1

(R - Avg R ) 348Variance = = =24.86

(n-1) 14

(a,m)

a

(m)

Covariance 32.50β (Beta)= = = 1.3075

Variance 24.86


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Comparing Returns• By regressing stock returns on Market returns, we get

• Further, using CAPM, we have

� In terms of excess returns:

(Regress excess returns on security on excess returns on market)

� In terms of raw returns:

(Regress raw returns on security on raw returns on market)

• In both regressions, slope of the regression is the beta of the

security.

• Intercept is measure of stock performance relative to the market:

� In excess returns regression:

� if intercept is 0, the stock performed as per market.

� if intercept is +ve (-ve), stock performed better (worse) than the market.

43

j f j m fR =R +β (R - R )

j j mR =α+β R

j f j j mR =R (1-β )+β R


j f j m fR - R = β (R - R )

Comparing Returns� In raw returns regression: the intercept has to be compared with

predicted intercept .

� If , stock performed better than expected

� If , stock performed worse than expected

� Measure of stock performance α in case of excess returns

regression and in case of raw returns regression is

called Jensen’s Alpha.

44

fα > R (1-β)

fα < R (1-β)

fα - R (1-β)


fR (1-β)

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Issues in estimating Beta�Length of estimation period:

• Longer period provides more data points but firms might change in its risk profile over longer period.

• Most estimates of beta use 5 year data

�Return Interval:

• Daily /Intra day interval increases data points but increases non-trading bias

• Monthly/Weekly interval reduces non-trading bias.

�Choice of Market Index:

• Most estimates use stock market index

• Should be a broad based index


Risk-free rate of return (Rf)• Return on a riskless asset is the risk-free rate.

• Risk-less asset should be:

�Default free security i.e. should be issued by Government.

�No uncertainty of reinvestment i.e. there are no cash flows

prior to the end of horizon period. – Zero Coupon securities.

• Tenure of G-Securities:

�Depends upon the cash Flows being analyzed.

� If CFs are 5yr CFs, we need 5 yr rate.

• Risk-free rate is the rate of return on Zero-coupon Govt.

Securities that matches the time horizon of the cash flows being

analyzed.


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Factors affecting Beta

1. Type of Business:

– More sensitive the business is to market conditions,

higher would be the Beta of the security.

– Cyclical firms – higher beta

– Food processing/tobacco firms are less sensitive to

market conditions.

– If product purchase is discretionary, such firms would

have higher beta (P&G/HUL vs. Designer Wear)



%age change in OperatingProfitDOL=

%age change in Sales

ΔEBIT*100

EBITDOL=ΔSales

*100Sales

48

2. Degree of Operating Leverage:Firms with high DOL will also have high variability in operating

profits, hence higher Beta.


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25


3.Degree of Financial Leverage:

� As Financial Leverage increases, Beta also increases.

49

%age change in EPSDFL=

%age change in Operating Profit

ΔEPS*100

EPSDFL=ΔEBIT

*100EBIT


Levered and Unlevered Beta

50

• Assets of a levered firm are financed by debt & equity.

• Asset beta should be weighted average of equity beta & debt beta.

• For an all-equity financed firm (Unlevered), the asset beta and

equity beta would be same.

Asset or Unlevered Equity Debt

E D=β +β

D+E D+E

β


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26


51

• For a levered firm, if we assume that beta of Debt is zero, then

asset beta would be:

� As leverage increases, equity beta also increases.

• If we consider the tax deductibility of debt, equity beta of a

levered firm, would be:

(developed by Hamada,1972)

Equity Asset or Unlevered

Dβ =β 1+(1-t)

E

Asset or Unlevered Equity

Eβ =β

D+E

Equity Asset

Dβ =β 1+

E


# 2 Bottom-up Beta• What if historical stock prices are not available?

• Steps:

1. Identify the businesses in which the firm operates(pure-play

firms)

2. Estimate the unlevered betas of these pure-play publicly

traded firms in each businesses.

3. Take the weighted average of the unlevered betas, using

proportion of firm value in each business as the weights.

4. Use current value of debt & equity of the firm, to compute

the levered beta.


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27

Bottom-up Beta

53

Find the beta of Co. X with Equity of Rs 517 million and Debt of

Rs. 113 million. Betas of comparable firms are as follows:

(tax rate = 35%)


Company Beta Equity Debt

A 0.60 250 150

B 1.25 16 26

C 0.95 612 152

D 0.75 187 158

E 0.55 32 9

Bottom-up Beta

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( )

0.82= = 0.63405

1+(1-0.35) 0.4512

Average Levered Beta = 0.82

Average D/E = 495/1097 = 0.4512

Unlevered Beta =

Equityβ

D1+(1-t)

E

U

D= β 1+(1-t)

E

113= 0.63405 1+(1-0.35) =0.72413

517


Company Beta Equity Debt

A 0.60 250 150

B 1.25 16 26

C 0.95 612 152

D 0.75 187 158

E 0.55 32 9

Average 0.82 1,097 495

Levered beta of Co. X

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55

Company Y has an Equity Beta of 0.80 when the firm had D/E of 0.2:1

(t=30%). The company intends to increase the D/E to 1:1. What would

be the beta at D/E of 1:1. (Assume Debt has tax advantage).

Given: at D/E of 0.2:1 and t = 30%

To estimate:

�Unlevered Beta:

� Equity (Levered) Beta at D/E of 1:1

Equityβ = 0.80

U

0.80β = =0.7018

0.201+(1-0.30)

1

E

1β =0.7018 1+(1-0.30) =1.1931

1

Equityβ at D/E of 1:1


# 3 Accounting Beta• Instead of regressing stock returns on index returns, if we use the

accounting earnings -> accounting beta.

• Pitfalls:

– Accounting earnings are relatively smoothen.

(betas are likely to be closer to one)

– Likely to be influenced by accounting policies – depreciation

method, allocation of expenses etc.


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Beta of select companies

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Company Beta R2

ABB 0.89 0.53

ACC 0.70 0.38

BHEL 1.02 0.59

ITC 0.53 0.36

Reliance Infrastructure 1.79 0.74

SBI 1.10 0.64

Suzlon 1.55 0.49

Unitech 1.68 0.42

Tata Steel 1.44 0.62


Portfolio Beta


• Beta of a portfolio of securities is the weighted average of its

individual securities’ betas.

• β Portfolio = β1*w1 + β2*w2 + β3*w3+ …….+ βn*wn

Company Beta Weights Beta * W

ABB 0.89 0.30 0.267

ACC 0.70 0.15 0.105

BHEL 1.02 0.45 0.459

ITC 0.53 0.10 0.053

Portfolio Beta 0.884

Estimating the Hurdle Rate

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