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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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)
26-Nov-13
2
Estimating the Hurdle Rate 3
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
Estimating the Hurdle Rate 4
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?
26-Nov-13
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Cost of debt may be approximated by:
Estimating the Hurdle Rate 5
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.
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%)
Estimating the Hurdle Rate 18
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
• 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
Estimating the Hurdle Rate
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
28Estimating the Hurdle Rate
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
29Estimating the Hurdle Rate
-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
26-Nov-13
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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%
Estimating the Hurdle Rate
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%
Estimating the Hurdle Rate
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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
Estimating the Hurdle Rate
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
Estimating the Hurdle Rate
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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
Estimating the Hurdle Rate 35
SML
Beta and its Estimation
26-Nov-13
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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
37Estimating the Hurdle Rate
#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)
Estimating the Hurdle Rate
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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
39Estimating the Hurdle Rate
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.
40Estimating the Hurdle Rate
26-Nov-13
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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
Estimating the Hurdle Rate
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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
Estimating the Hurdle Rate
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)
Estimating the Hurdle Rate
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