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Dr. S. Ghose
Cost of Capital
 Cost of Capital - The return the firm’s investors
could expect to earn if they invested in securities
with comparable degrees of risk
 Capital Structure - The firm’s mix of long term
financing and equity financing
Cost of Capital
 The cost of capital represents the overall cost of
financing to the firm
 The cost of capital is normally the relevant
discount rate to use in analyzing an investment
 The overall cost of capital is a weighted average of
the various sources:
 WACC = Weighted Average Cost of Capital
 WACC = After-tax cost x weights
Sources of long-term capital
Long-Term Capital
Long-Term Debt Preferred Stock Common Stock
Retained Earnings New Common Stock
Cost of Capital: Needed for
 Investment (capital budgeting) decisions – neither the
NPV rule nor the IRR rule can be implemented
without knowledge of the appropriate discount rate
 Financing decisions – the optimal/target capital
structure minimizes the cost of capital
 Operating decisions – cost of capital is used by
regulatory agencies in order to determine the “fair”
return in some regulated industries (e.g. electric
utilities)
Cost of Debt
 The cost of debt to the firm is the effective yield to
maturity (or interest rate) paid to its bondholders
 Since interest is tax deductible to the firm, the
actual cost of debt is less than the yield to maturity:
 After-tax cost of debt = yield x (1 - tax rate)
 The cost of debt should also be adjusted for
flotation costs (associated with issuing new bonds)
with stock with debt
EBIT 400,000 400,000
- interest expense 0 (50,000)
EBT 400,000 350,000
- taxes (34%) (136,000) (119,000)
EAT 264,000 231,000
Example: Tax effects of
financing with debt
 Now, suppose the firm pays Rs.50,000 in dividends
to the shareholders
with stock with debt
EBIT 400,000 400,000
- interest expense 0 (50,000)
EBT 400,000 350,000
- taxes (34%) (136,000) (119,000)
EAT 264,000 231,000
- dividends (50,000) 0
Retained earnings 214,000 231,000
Example: Tax effects of
financing with debt
Cost of Debt
After-tax cost Before-tax cost Tax
of Debt of Debt Savings
33,000 = 50,000 - 17,000
OR
33,000 = 50,000 ( 1 - .34)
Or, if we want to look at percentage costs:
-=
Cost of Debt
After-tax Before-tax Marginal
% cost of % cost of x tax
Debt Debt rate
Kd = kd (1 - T)
.066 = .10 (1 - .34)
-= 1
EXAMPLE: Cost of Debt
 ABC Corporation issues a Rs.1,000 par, 20
year bond paying the market rate of 10%.
Coupons are annual. The bond will sell
for par since it pays the market rate, but
flotation costs amount to Rs.50 per bond.
 What is the pre-tax and after-tax cost of
debt?
EXAMPLE: Cost of Debt
Pre-tax cost of debt:
950 = 100(PVIFA 20, Kd) + 1000(PVIF 20, Kd)
using a financial calculator:
Kd = 10.61%
After-tax cost of debt:
Kd = Kd (1 - T)
Kd = .1061 (1 - .34)
Kd = .07 = 7%
So a 10% bond
costs the firm
only 7%
(with flotation costs)
because interest
is tax deductible
Cost of Debentures (Redeemable)
 Kd = {Interest(1-Tax Rate) +
(Redeemable Value – Net Sale Proceeds)/N}
(Redeemable Value + Net Sale Proceeds)/2
Kd = {I (1-t) + (RV – SP)/N}
(RV + SP)/2
Cost of Preference Shares
 Kp = {Preference Dividend (1+Dividend Tax) +
(Redeemable Value – Net Sale Proceeds)/N}
(Redeemable Value + Net Sale Proceeds)/2
Kp = {Dp (1+Dt) + (RV – SP)/N}
(RV + SP)/2
Cost of New Preferred Stock
 Preferred stock:
 has a fixed dividend (similar to debt)
 has no maturity date
 dividends are not tax deductible and are
expected to be perpetual or infinite
 Cost of preferred stock = dividend
price - flotation cost
Cost of Equity:
Retained Earnings
 Why is there a cost for retained earnings?
 Earnings can be reinvested or paid out as dividends
 Investors could buy other securities, and earn a return.
 Thus, there is an opportunity cost if earnings are
retained
Cost of Equity:
Retained Earnings
 Common stock equity is available through
retained earnings (R/E) or by issuing new
common stock:
 Common equity = R/E + New common stock
Cost of Equity:
New Common Stock
 The cost of new common stock is higher
than the cost of retained earnings because
of flotation costs
 selling and distribution costs (such as
sales commissions) for the new
securities
Cost of Equity
The Dividend Growth Model
Approach
 Estimating the cost of equity: the dividend growth model
approach
According to the constant growth (Gordon) model,
D1
P0 =
ke - g
Rearranging D1
ke = P0 + g
Drawbacks of Dividend Growth Model
 Some firms concentrate on growth and do not pay
dividends at all, or only irregularly
 Growth rates may also be hard to estimate
 Also this model doesn’t adjust for market risk
 Not applicable if dividends aren’t growing at a
reasonably constant rate
 Extremely sensitive to the estimated growth rate –
an increase in g of 1% increases the cost of equity by
1%
 Does not explicitly consider risk
Capital Asset Pricing Model (CAPM)
)( fmf RRβRkj 
Cost of
capital Risk-free
return
Average rate of return
on common stocks
(WIG)
Co-variance
of returns against
the portfolio
(departure from the average)
B < 1, security is safer than WIG average
B > 1, security is riskier than WIG average
The Security Market Line (SML)
Required rate
of return
Percent
0.5 1.0 1.5 2.0
SML = Rf +  (Km – Rf)
Beta (risk)
Market risk premium
20.0
18.0
16.0
14.0
12.0
10.0
8.0
5.5
Rf
Finding the Required Return on Common Stock using the
Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) can be used to estimate the
required return on individual stocks. The formula:
( )RKRK fmjfj
 
where
jK = Required return on stock j
fR = Risk-free rate of return (usually current rate on Treasury Bill).
j
 = Beta coefficient for stock j represents risk of the stock
mK = Return in market as measured by some proxy portfolio (index)
Suppose that Baker has the following values:
fR = 5.5%
j
 = 1.0
mK = 12%
.
CAPM/SML approach
 Advantage: Evaluates risk, applicable to firms
that don’t pay dividends
 Disadvantage: Need to estimate
 Beta
 the risk premium (usually based on past data, not
future projections)
 use an appropriate risk free rate of interest
Estimation of Beta
 Theoretically, the calculation of beta is straightforward:
 Problems
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.
 Solutions
 Problems 1 and 2 (above) can be moderated by more sophisticated statistical
techniques.
 Problem 3 can be lessened by adjusting for changes in business and financial risk.
 Look at average beta estimates of comparable firms in the industry.
2
)(
),(
M
iM
M
Mi
σ
σ
RVar
RRCov
β 
Stability of Beta
 Most analysts argue that betas are generally stable for
firms remaining in the same industry
 That’s not to say that a firm’s beta can’t change
 Changes in product line
 Changes in technology
 Deregulation
 Changes in financial leverage
What is the appropriate risk-free rate?
 Use the yield on a long-term bond if you are analyzing cash flows
from a long-term investment
 For short-term investments, it is entirely appropriate to use the
yield on short-term government securities
 Use the nominal risk-free rate if you discount nominal cash flows
and real risk-free rate if you discount real cash flows
Weighted Average Cost of Capital (WACC)
 WACC weights the cost of equity and the
cost of debt by the percentage of each used
in a firm’s capital structure
 WACC=(E/ V) x KE + (D/ V) x KD x (1-TC)
 (E/V)= Equity % of total value
 (D/V)=Debt % of total value
 (1-Tc)=After-tax % or reciprocal of corp tax rate
Tc. The after-tax rate must be considered
because interest on corporate debt is deductible
 WACC should be based on market rates
and valuation, not on book values of debt
or equity
 Book values may not reflect the current
marketplace
 WACC will reflect what a firm needs to
earn on a new investment. But the new
investment should also reflect a risk level
similar to the firm’s Beta used to calculate
the firm’s RE.
 In the case of ABC Co., the relatively low
WACC of 8.81% reflects ABC’s β=.74. A riskier
investment should reflect a higher interest
rate.
The WACC is not constant
It changes in accordance with the
risk of the company and with the
floatation costs of new capital
Marginal cost of capital and investment projects
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
Percent
10 15 19 5039
Amount of capital (Rs.
millions)
11.23%
70 85 95
Marginal
cost of
capital
Kmc
A
B
C
D E
F
G
H
10.77%
10.41%
-
-
-
-
-
-
-
-
-
Optimum Capital Structure
 The optimal (best) situation is associated with the
minimum overall cost of capital:
 Optimum capital structure means the lowest WACC
 Usually occurs with 30-50% debt in a firm’s capital
structure
 WACC is also referred to as the required rate of return
or the discount rate
Optimal Capital Structure
Cost (After-tax) Weights Weighted
Cost
Financial Plan A:
Debt………………………… 6.5% 20% 1.3%
Equity………………………. 12.0 80 9.6
10.9%
Financial Plan B:
Debt………………………… 7.0% 40% 2.8%
Equity………………………. 12.5 60 7.5
10.3%
Financial Plan C:
Debt………………………… 9.0% 60% 5.4%
Equity………………………. 15.0 40 6.0
11.4%
Cost of capital curve

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Cost of capital

  • 2. Cost of Capital  Cost of Capital - The return the firm’s investors could expect to earn if they invested in securities with comparable degrees of risk  Capital Structure - The firm’s mix of long term financing and equity financing
  • 3. Cost of Capital  The cost of capital represents the overall cost of financing to the firm  The cost of capital is normally the relevant discount rate to use in analyzing an investment  The overall cost of capital is a weighted average of the various sources:  WACC = Weighted Average Cost of Capital  WACC = After-tax cost x weights
  • 4. Sources of long-term capital Long-Term Capital Long-Term Debt Preferred Stock Common Stock Retained Earnings New Common Stock
  • 5. Cost of Capital: Needed for  Investment (capital budgeting) decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate  Financing decisions – the optimal/target capital structure minimizes the cost of capital  Operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. electric utilities)
  • 6. Cost of Debt  The cost of debt to the firm is the effective yield to maturity (or interest rate) paid to its bondholders  Since interest is tax deductible to the firm, the actual cost of debt is less than the yield to maturity:  After-tax cost of debt = yield x (1 - tax rate)  The cost of debt should also be adjusted for flotation costs (associated with issuing new bonds)
  • 7. with stock with debt EBIT 400,000 400,000 - interest expense 0 (50,000) EBT 400,000 350,000 - taxes (34%) (136,000) (119,000) EAT 264,000 231,000 Example: Tax effects of financing with debt  Now, suppose the firm pays Rs.50,000 in dividends to the shareholders
  • 8. with stock with debt EBIT 400,000 400,000 - interest expense 0 (50,000) EBT 400,000 350,000 - taxes (34%) (136,000) (119,000) EAT 264,000 231,000 - dividends (50,000) 0 Retained earnings 214,000 231,000 Example: Tax effects of financing with debt
  • 9. Cost of Debt After-tax cost Before-tax cost Tax of Debt of Debt Savings 33,000 = 50,000 - 17,000 OR 33,000 = 50,000 ( 1 - .34) Or, if we want to look at percentage costs: -=
  • 10. Cost of Debt After-tax Before-tax Marginal % cost of % cost of x tax Debt Debt rate Kd = kd (1 - T) .066 = .10 (1 - .34) -= 1
  • 11. EXAMPLE: Cost of Debt  ABC Corporation issues a Rs.1,000 par, 20 year bond paying the market rate of 10%. Coupons are annual. The bond will sell for par since it pays the market rate, but flotation costs amount to Rs.50 per bond.  What is the pre-tax and after-tax cost of debt?
  • 12. EXAMPLE: Cost of Debt Pre-tax cost of debt: 950 = 100(PVIFA 20, Kd) + 1000(PVIF 20, Kd) using a financial calculator: Kd = 10.61% After-tax cost of debt: Kd = Kd (1 - T) Kd = .1061 (1 - .34) Kd = .07 = 7% So a 10% bond costs the firm only 7% (with flotation costs) because interest is tax deductible
  • 13. Cost of Debentures (Redeemable)  Kd = {Interest(1-Tax Rate) + (Redeemable Value – Net Sale Proceeds)/N} (Redeemable Value + Net Sale Proceeds)/2 Kd = {I (1-t) + (RV – SP)/N} (RV + SP)/2
  • 14. Cost of Preference Shares  Kp = {Preference Dividend (1+Dividend Tax) + (Redeemable Value – Net Sale Proceeds)/N} (Redeemable Value + Net Sale Proceeds)/2 Kp = {Dp (1+Dt) + (RV – SP)/N} (RV + SP)/2
  • 15. Cost of New Preferred Stock  Preferred stock:  has a fixed dividend (similar to debt)  has no maturity date  dividends are not tax deductible and are expected to be perpetual or infinite  Cost of preferred stock = dividend price - flotation cost
  • 16. Cost of Equity: Retained Earnings  Why is there a cost for retained earnings?  Earnings can be reinvested or paid out as dividends  Investors could buy other securities, and earn a return.  Thus, there is an opportunity cost if earnings are retained
  • 17. Cost of Equity: Retained Earnings  Common stock equity is available through retained earnings (R/E) or by issuing new common stock:  Common equity = R/E + New common stock
  • 18. Cost of Equity: New Common Stock  The cost of new common stock is higher than the cost of retained earnings because of flotation costs  selling and distribution costs (such as sales commissions) for the new securities
  • 20. The Dividend Growth Model Approach  Estimating the cost of equity: the dividend growth model approach According to the constant growth (Gordon) model, D1 P0 = ke - g Rearranging D1 ke = P0 + g
  • 21. Drawbacks of Dividend Growth Model  Some firms concentrate on growth and do not pay dividends at all, or only irregularly  Growth rates may also be hard to estimate  Also this model doesn’t adjust for market risk  Not applicable if dividends aren’t growing at a reasonably constant rate  Extremely sensitive to the estimated growth rate – an increase in g of 1% increases the cost of equity by 1%  Does not explicitly consider risk
  • 22. Capital Asset Pricing Model (CAPM) )( fmf RRβRkj  Cost of capital Risk-free return Average rate of return on common stocks (WIG) Co-variance of returns against the portfolio (departure from the average) B < 1, security is safer than WIG average B > 1, security is riskier than WIG average
  • 23. The Security Market Line (SML) Required rate of return Percent 0.5 1.0 1.5 2.0 SML = Rf +  (Km – Rf) Beta (risk) Market risk premium 20.0 18.0 16.0 14.0 12.0 10.0 8.0 5.5 Rf
  • 24. Finding the Required Return on Common Stock using the Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) can be used to estimate the required return on individual stocks. The formula: ( )RKRK fmjfj   where jK = Required return on stock j fR = Risk-free rate of return (usually current rate on Treasury Bill). j  = Beta coefficient for stock j represents risk of the stock mK = Return in market as measured by some proxy portfolio (index) Suppose that Baker has the following values: fR = 5.5% j  = 1.0 mK = 12% .
  • 25. CAPM/SML approach  Advantage: Evaluates risk, applicable to firms that don’t pay dividends  Disadvantage: Need to estimate  Beta  the risk premium (usually based on past data, not future projections)  use an appropriate risk free rate of interest
  • 26. Estimation of Beta  Theoretically, the calculation of beta is straightforward:  Problems 1. Betas may vary over time. 2. The sample size may be inadequate. 3. Betas are influenced by changing financial leverage and business risk.  Solutions  Problems 1 and 2 (above) can be moderated by more sophisticated statistical techniques.  Problem 3 can be lessened by adjusting for changes in business and financial risk.  Look at average beta estimates of comparable firms in the industry. 2 )( ),( M iM M Mi σ σ RVar RRCov β 
  • 27. Stability of Beta  Most analysts argue that betas are generally stable for firms remaining in the same industry  That’s not to say that a firm’s beta can’t change  Changes in product line  Changes in technology  Deregulation  Changes in financial leverage
  • 28. What is the appropriate risk-free rate?  Use the yield on a long-term bond if you are analyzing cash flows from a long-term investment  For short-term investments, it is entirely appropriate to use the yield on short-term government securities  Use the nominal risk-free rate if you discount nominal cash flows and real risk-free rate if you discount real cash flows
  • 29. Weighted Average Cost of Capital (WACC)  WACC weights the cost of equity and the cost of debt by the percentage of each used in a firm’s capital structure  WACC=(E/ V) x KE + (D/ V) x KD x (1-TC)  (E/V)= Equity % of total value  (D/V)=Debt % of total value  (1-Tc)=After-tax % or reciprocal of corp tax rate Tc. The after-tax rate must be considered because interest on corporate debt is deductible
  • 30.  WACC should be based on market rates and valuation, not on book values of debt or equity  Book values may not reflect the current marketplace  WACC will reflect what a firm needs to earn on a new investment. But the new investment should also reflect a risk level similar to the firm’s Beta used to calculate the firm’s RE.  In the case of ABC Co., the relatively low WACC of 8.81% reflects ABC’s β=.74. A riskier investment should reflect a higher interest rate.
  • 31. The WACC is not constant It changes in accordance with the risk of the company and with the floatation costs of new capital
  • 32. Marginal cost of capital and investment projects 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 Percent 10 15 19 5039 Amount of capital (Rs. millions) 11.23% 70 85 95 Marginal cost of capital Kmc A B C D E F G H 10.77% 10.41% - - - - - - - - -
  • 33. Optimum Capital Structure  The optimal (best) situation is associated with the minimum overall cost of capital:  Optimum capital structure means the lowest WACC  Usually occurs with 30-50% debt in a firm’s capital structure  WACC is also referred to as the required rate of return or the discount rate
  • 34. Optimal Capital Structure Cost (After-tax) Weights Weighted Cost Financial Plan A: Debt………………………… 6.5% 20% 1.3% Equity………………………. 12.0 80 9.6 10.9% Financial Plan B: Debt………………………… 7.0% 40% 2.8% Equity………………………. 12.5 60 7.5 10.3% Financial Plan C: Debt………………………… 9.0% 60% 5.4% Equity………………………. 15.0 40 6.0 11.4%