Required Returns and Cost of Capital

Lecture 13
Required
Required Returns
Returns and
and
Cost
Cost of
of Capital
Capital
Overall Cost of
Capital of the Firm
Cost of Capital is the required

rate of return on the various
types of financing. The overall
cost of capital is a weighted
average of the individual
required rates of return (costs).
Market Value of
Long-Term Financing
Type of Financing Mkt Val Weight

Long-Term Debt Rs 35M 35%
Preferred Stock Rs 15M 15%
Common Stock Equity Rs 50M 50%
Rs 100M 100%
Cost of Debt
Cost of Debt is the required rate
of return on investment of the
lenders of a company.
n
Ij + Pj
P0 = S (1 + kd)j
j =1
ki = kd ( 1 - T )
Determination of
the Cost of Debt
Assume that ABC has Rs1,000 par
value zero-coupon bonds outstanding.
ABC bonds are currently trading at
Rs385.54 with 10 years to maturity.
ABC’s tax bracket is 40%.
Rs0 + Rs1,000
Rs385.54 =
(1 + kd)10
Determination of
the Cost of Debt
(1 + kd)10 = Rs1,000 / Rs385.54
= 2.5938
(1 + kd) = (2.5938) (1/10) =
1.1
kd = .1 or 10%
ki = 10% ( 1 - .40 )
ki = 6%
Cost of Preferred Stock
Cost of Preferred Stock is the

required rate of return on
investment of the preferred
shareholders of the company.
kP = D P / P 0
Determination of the
Cost of Preferred Stock
Assume that ABC has preferred stock
outstanding with par value of Rs100,
dividend per share of Rs6.30, and a
current market value of Rs70 per
share.
kP = Rs6.30 / Rs70
kP = 9%
Cost of Equity
Approaches
 Dividend Discount Model
 Capital-Asset Pricing
Model
 Before-Tax Cost of Debt
plus Risk Premium
Dividend Discount Model
The cost of equity capital, ke, is

the discount rate that equates the
present value of all expected
future dividends with the current
market price of the stock.
D1 D2 D¥
P0 = + +...+
(1+ke)1 (1+ke)2 (1+ke) ¥
Constant Growth Model
The constant dividend growth

assumption reduces the model to:
ke = ( D1 / P0 ) + g
Assumes that dividends will grow

at the constant rate “g” forever.
Cost of Equity Capital
Assume that ABC has common stock
outstanding with a current market value of
Rs64.80 per share, current dividend of Rs3
per share, and a dividend growth rate of 8%
forever.
ke = ( D 1 / P0 ) + g
ke = (Rs3(1.08) / Rs64.80) + .08
ke = .05 + .08 = .13 or 13%
Constant Growth
Model Example
Stock CG has an expected growth rate of
8%. Each share of stock just received an
annual Rs3.24 dividend per share. The
appropriate discount rate is 15%. What
is the value of the common stock?
D1 = Rs3.24 ( 1 + .08 ) = Rs3.50
VCG = D1 / ( ke - g ) = Rs3.50 / ( .15 - .08 )

= Rs50
Zero Growth
Model Example
Stock ZG has an expected growth rate of
0%. Each share of stock just received an
annual Rs3.24 dividend per share. The
appropriate discount rate is 15%. What
is the value of the common stock?
D1 = Rs3.24 ( 1 + 0 ) = Rs3.24
VZG = D1 / ( ke - 0 ) = Rs3.24 / ( .15 - 0 )

= Rs21.60
Growth Phases Model
The growth phases assumption

leads to the following formula
(assume 3 growth phases):
a D0(1+g1)t b Da(1+g2)t-a
P0 = S (1+ke)t
+ S (1+ke)t
+
t=1 t=a+1
¥ Db(1+g3)t-b
S
t=b+1 (1+ke)t
Growth Phases
Model Example
Stock GP has an expected growth
rate of 16% for the first 3 years and
8% thereafter. Each share of stock
just received an annual Rs3.24
dividend per share. The appropriate
discount rate is 15%. What is the
value of the common stock under
this scenario?
Growth Phases
Model Example
0 1 2 3 4 5 6

D1 D2 D3 D4 D5 D6
Growth of 16% for 3 years Growth of 8% to infinity!
Stock GP has two phases of growth. The first, 16%,

starts at time t=0 for 3 years and is followed by 8%
thereafter starting at time t=3. We should view the time
line as two separate time lines in the valuation.
Growth Phases
Model Example
0 1 2 3 Growth Phase
#1 plus the infinitely
long Phase #2
D1 D2 D3
0 1 2 3 4 5 6

D4 D5 D6
Note that we can value Phase #2 using the
Constant Growth Model
Growth Phases
Model Example
V3 = D 4
We can use this model because
dividends grow at a constant 8%
k-g rate beginning at the end of Year 3.
0 1 2 3 4 5 6

D4 D5 D6
Note that we can now replace all dividends from Year
4 to infinity with the value at time t=3, V3! Simpler!!
Growth Phases
Model Example
0 1 2 3 New Time
Line
D1 D2 D3
0 1 2 3 D4
Where V3 =
V3 k-g
Now we only need to find the first four dividends
to calculate the necessary cash flows.
Growth Phases
Model Example
Determine the annual dividends.
D0 = Rs3.24 (this has been paid already)
D1 = D0(1+g1)1 = Rs3.24(1.16)1 =Rs3.76
D2 = D0(1+g1)2 = Rs3.24(1.16)2 =Rs4.36
D3 = D0(1+g1)3 = Rs3.24(1.16)3 =Rs5.06
D4 = D3(1+g2)1 = Rs5.06(1.08)1 =Rs5.46
Growth Phases
Model Example
0 1 2 3 Actual
Values
3.76 4.36 5.06
0 1 2 3 5.46
Where Rs78 =
.15-.08
78
Now we need to find the present value
of the cash flows.
Growth Phases
Model Example
We determine the PV of cash flows.
PV(D1) = D1(PVIF15%, 1) = Rs3.76 (.870) = Rs3.27
PV(D2) = D2(PVIF15%, 2) = Rs4.36 (.756) = Rs3.30
PV(D3) = D3(PVIF15%, 3) = Rs5.06 (.658) = Rs3.33
P3 = Rs5.46 / (.15 - .08) = Rs78 [CG Model]
PV(P3) = P3(PVIF15%, 3) = Rs78 (.658) = Rs51.32

Growth Phases
Model Example
Finally, we calculate the intrinsic value by
summing all the cash flow present values.
V = Rs3.27 + Rs3.30 + Rs3.33 + Rs51.32
V = Rs61.22
3 D (1+.16)t 1 D4
V=S
0
+
t=1 (1 + .15)t (1+.15)n (.15-.08)
Capital Asset
Pricing Model
The cost of equity capital, ke, is
equated to the required rate of
return in market equilibrium. The
risk-return relationship is described
by the Security Market Line (SML).
ke = Rj = Rf + (Rm - Rf)bj
Cost of Equity (CAPM)
Assume that ABC has a company beta
of 1.25. Research by Analyst suggests
that the risk-free rate is 4% and the
expected return on the market is 11.2%
ke = Rf + (Rm - Rf)bj
= 4% + (11.2% - 4%)1.25
ke = 4% + 9% = 13%
Before-Tax Cost of Debt
Plus Risk Premium
The cost of equity capital, ke, is the
sum of the before-tax cost of debt
and a risk premium in expected
return for common stock over debt.
ke = kd + Risk Premium*
* Risk premium is not the same as CAPM risk

premium
Cost of Equity (kd + R.P.)
Assume that ABC typically adds a 3%
premium to the before-tax cost of debt.
ke = kd + Risk Premium
= 10% + 3%
ke = 13%
Comparison of the
Cost of Equity Methods
Constant Growth Model 13%

Capital Asset Pricing Model 13%
Cost of Debt + Risk Premium 13%
Generally, the three methods
will not agree.
Weighted Average Cost
of Capital (WACC)
n
Cost of Capital = S
kx(Wx)
x=1
WACC = .35(6%) + .15(9%) +

.50(13%)
WACC = .021 + .0135 + .065
= .0995 or 9.95%
Theories of Capital
Structure
 Signaling Theory
 Trade Off Theory
 Pecking Order Theory
 Preferred Habitat Theory
Signaling Theory
 Debt signaling is a theory that
correlates a stock's future
performance with any
announcements made regarding its
debt. Announcements typically made
about a company taking debt are
seen as positive news.
Trade-Off Theory
 The trade-off theory of capital
structure is the idea that a company
chooses how much debt finance and
how much equity finance to use by
balancing the costs and benefits.
Pecking Order Theory
 Financing comes from three sources, internal funds, debt
and new equity. Companies prioritize their sources of
financing, first preferring internal financing, and then
debt, lastly raising equity as a "last resort".
 Equity is a less preferred means to raise capital because

when managers (who are assumed to know better about
true condition of the firm than investors) issue new
equity, investors believe that managers think that the firm
is overvalued and managers are taking advantage of this
over-valuation. As a result, investors will place a lower
value to the new equity issuance.
Preferred Habitat Theory
 Habit
 Complacency
 Status Quo Bias
 Fear of the Unknown

Required Returns and Cost of Capital

Uploaded by

Copyright:

Available Formats

Required Returns and Cost of Capital

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Required Returns and Cost of Capital

Uploaded by

Copyright:

Available Formats

Lecture 13

Cost of Capital is the required

Type of Financing Mkt Val Weight

Cost of Preferred Stock is the

The cost of equity capital, ke, is

The constant dividend growth

Assumes that dividends will grow

VCG = D1 / ( ke - g ) = Rs3.50 / ( .15 - .08 )

VZG = D1 / ( ke - 0 ) = Rs3.24 / ( .15 - 0 )

The growth phases assumption

Growth of 16% for 3 years Growth of 8% to infinity!

Stock GP has two phases of growth. The first, 16%,

PV(D2) = D2(PVIF15%, 2) = Rs4.36 (.756) = Rs3.30

PV(D3) = D3(PVIF15%, 3) = Rs5.06 (.658) = Rs3.33

P3 = Rs5.46 / (.15 - .08) = Rs78 [CG Model]

PV(P3) = P3(PVIF15%, 3) = Rs78 (.658) = Rs51.32

* Risk premium is not the same as CAPM risk

Constant Growth Model 13%

WACC = .35(6%) + .15(9%) +

 Equity is a less preferred means to raise capital because

You might also like