Cost of Capital and its different types of cost of capital

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Cost of Capital
Unit III
Sri Ramakrishna College of Arts & Science,
Coimbatore.
M.VADIVEL
Assistant Professor
Sri Ramakrishna College of Arts & Science, CBE.

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Required Rates on Projects
An important part of capital budgeting is setting the
required rate for the individual project

4
0 1
Example: Consider the following project
+1,100
-1,000

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0 1
+1,100
-1,000
If Required Rate = 9%: NPV = -1,000 + 1,100
(1+ .09 )
= $9.17

6
0 1
+1,100
-1,000
(1+ .09 )
= $9.17
Accept Project since NPV > 0

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0 1
+1,100
-1,000
(1+ .09 )
= $9.17
(1+ .11 )
= –$9.01

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0 1
+1,100
-1,000
(1+ .09 )
= $9.17
(1+ .11 )
= –$9.01
Reject Project since NPV < 0

9
0 1
+1,100
-1,000
(1+ .09 )
= $9.17
(1+ .11 )
= –$9.01
In order to estimate correct required rate, companies
must find their own unique cost of raising capital

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Factors Affecting Cost of Capital
General Economic Conditions--inflation, investment
opportunities
Affect interest rates
The Following Factors affect risk premium
Market Conditions
Operating and Financing Decisions
Affect business risk
Affect financial risk
Amount of Financing
Affect flotation costs and market price of security

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Model Assumptions
Here, we determine the average cost of capital of a
firm by assuming that the firm continues with its
business, financing and dividend policies.
Weighted Average Cost of Capital Model

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Computing Weighted Cost of Capital
Average cost of capital of the firm.
To find WACC
1. Compute the cost of each source of capital
2. Determine percentage of each source of capital
3. Calculate Weighted Average Cost of Capital
Weighted Average Cost of Capital (WACC)

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Computing Cost of Each Source
Required rate of return for creditors
Same cost found in Chapter 7 as “required rate for
debtholders (kd) = YTM”
1. Compute Cost of Debt

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Required rate of return for creditors
Same cost found in Chapter 7 as “required rate for
debtholders (kd)”
P0 = +
I
k
t
d
n
t
n
( )
1
1 

 $M
(1+kd)n
where:
It = Dollar Interest Payment
Po = Market Price of Debt
M = Maturity Value of Debt

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Example
Investors are willing to pay $985 for a bond that pays
$90 a year for 10 years. Fees for issuing the bonds
bring the net price (NP0) down to $938.55. What is the
before tax cost of debt?

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Example
P0 = +
I
k
t
d
n
t
n
( )
1
1 

 $M
(1+kd)n

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Example
938.55 = +
$90
( )
1 12
1
12


 kd
t
$1,000
(1+kd)10
P0 = +
I
k
t
d
n
t
n
( )
1
1 

 $M
(1+kd)n

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Example
The before tax cost of debt is 10%
Interest is tax deductible

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Example
After tax cost of bonds = kd(1 - T)
Marginal Tax Rate = 40%

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Example
After tax cost of bonds = kd(1 - T)
= 10.0%(1– 0.40) = 6 %
Marginal Tax Rate = 40%

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Cost to raise a dollar of preferred stock.
2. Compute Cost Preferred Stock

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From Chapter 8:
Dividend (D)
Market Price (P0)
Required rate kps =

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From Chapter 8:
Dividend (D)
Market Price (P0)
Required rate kps =
However, there are floatation costs of issuing preferred stock:

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Cost of Preferred Stock with floatation costs
Dividend (D)
Net Price (NP0)
From Chapter 8:
Dividend (D)
Market Price (P0)
Required rate kps =
However, there are floatation costs of issuing preferred stock:
kps =

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Example
Your company can issue preferred stock for a price of
$45, but it only receives $42 after floatation costs. The
preferred stock pays a $5 dividend.

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Example
Cost of Preferred Stock
$5.00
$42.00
kps =

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Example
$5.00
$42.00
= 11.90%
kps =

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Example
$5.00
$42.00
= 11.90%
kps =
No adjustment is made for taxes as
dividends are not tax deductible.

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Two kinds of Common Equity
Retained Earnings (internal common equity)
Issuing new shares of common stock
3. Compute Cost of Common Equity

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Cost of Internal Common Equity
Management should retain earnings only if they earn
as much as stockholder’s next best investment
opportunity.

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opportunity.
Cost of Internal Equity = opportunity cost of common
stockholders’ funds.

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opportunity.
Cost of internal equity must equal common
stockholders’ required rate of return.

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opportunity.
Cost of internal equity must equal common
stockholders’ required rate of return.
Three methods to determine
Dividend Growth Model
Capital Asset Pricing Model
Risk Premium Model

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Assume constant growth in dividends (Chap. 8)

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Cost of internal equity--dividend growth model
D1
P0
kcs = + g

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D1
P0
kcs = + g
Example
The market price of a share of common stock is $60. The
dividend just paid is $3, and the expected growth rate is 10%.

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D1
P0
kcs = + g
Example
3(1+0.10)
60
kcs = + .10

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D1
P0
kcs = + g
Example
3(1+0.10)
60
kcs = + .10 = .155 = 15.5%

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D1
P0
kcs = + g
Example
3(1+0.10)
60
kcs = + .10 = .155 = 15.5%
The main limitation in this method is estimating growth accurately.

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Estimate the cost of equity from the CAPM (Chap. 6)

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kcs = krf + b(km – krf)
Cost of internal equity--CAPM

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Example
The estimated Beta of a stock is 1.2. The risk-free rate is 5%
and the expected market return is 13%.

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Example
kcs = 5% + 1.2(13% – 5%)

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Example
kcs = 5% + 1.2(13% – 5%) = 14.6%

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Risk Premium Approach
Adds a risk premium to the bondholder’s required rate of
return.

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return.
kcs = kd + RPc
Cost of internal equity--Risk Premium
Where:
RPc = Common stock
risk premium

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return.
Example
If the risk premium is 5% and kd is 10%
kcs = kd + RPc
Where:
RPc = Common stock
risk premium

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return.
Example
kcs = kd + RPc
kcs = 10% + 5%
Where:
RPc = Common stock
risk premium

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return.
Example
kcs = kd + RPc
kcs = 10% + 5% = 15%
Where:
RPc = Common stock
risk premium

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Cost of New Common Stock
If retained earnings cannot provide all the equity
capital that is needed, firms may issue new shares of
common stock.

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common stock.
Dividend Growth Model--Must adjust for floatation
costs of the new common shares.

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common stock.
Dividend Growth Model--must adjust for floatation
costs of the new common shares.
Cost of new common stock
D1
NP0
kcs = + g

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D1
NP0
knc = + g

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D1
NP0
knc = + g
Example
Using the above example. Common stock price is currently $60.
If additional shares are issued floatation costs will be 12%. D0 =
$3.00 and estimated growth is 10%.

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D1
NP0
knc = + g
Example
NP0 = $60.00 – (.12x 60) = $52.80
Floatation
Costs

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D1
NP0
knc = + g
Example
NP0 = $60.00 – (.12x 60) = $52.80
3(1+0.10)
52.80
kcs = + .10

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D1
NP0
knc = + g
Example
NP0 = $60.00 – (.12x 60) = $52.80
3(1+0.10)
52.80
kcs = + .10 = .1625 = 16.25%

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Capital Structure Weights
Long Term Liabilities and Equity
Weights of each source should reflect expected
financing mix
Assume a stable financial mix–so use Balance Sheet
percentages to calculate the weighted average cost
of capital.

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Balance Sheet Green Apple Company
Current Assets $5,000 Current Liabilities $2,000
Plant & Equipment 7,000 Bonds 4,000
Total Assets $12,000 Preferred Stock 1,000
Common Stock 5,000
Total Liabilities and
Owners Equity $12,000
Assets Liabilities
Firm Raises $10,000 of capital from long term sources

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Common Stock 5,000
Assets Liabilities
Compute Firm’s Capital Structure (% of each source)
Bonds:
4,000
10,000
= 40%
Amount of Bonds
Total Capital Sources

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Common Stock 5,000
Assets Liabilities
Amount of Preferred Stock
Preferred Stock:
1,000
10,000
= 10%

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Common Stock 5,000
Assets Liabilities
Amount of Common Stock
Common Stock:
5,000
10,000
= 50%

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Common Stock 5,000
Assets Liabilities
40%
10%
50%
When money is raised for capital projects, approximately
40% of the money comes from selling bonds, 10%
comes from selling preferred stock and 50% comes from
retaining earnings or selling common stock

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Computing WACC
Green Apple Company estimates the following costs
for each component in its capital structure:
Source of Capital Cost
Bonds kd = 10%
Preferred Stock kps = 11.9%
Common Stock
Retained Earnings kcs = 15%
New Shares knc = 16.25%
Green Apple’s tax rate is 40%

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Computing WACC
If using retained earnings to finance the common
stock portion the capital structure
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock

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Balance Sheet
Plant & Equipment 7,000 Bonds (9%) 4,000
Total Assets $12,000 Preferred Stock (10%) 1,000
Common Stock(13%) 5,000
Tax Rate = 40% Total Liabilities and
Assets Liabilities
40%
10%
50%
Computing WACC - using Retained Earnings

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Balance Sheet
Total Assets $12,000 Preferred Stock (11.9%)1,000
Assets Liabilities
40%
10%
50%
WACC = .40 x 10% (1-.4)

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Balance Sheet
Assets Liabilities
40%
10%
50%
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%

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Balance Sheet
Assets Liabilities
40%
10%
50%
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 15%

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Balance Sheet
Assets Liabilities
40%
10%
50%
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 15% = 11.09%

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Computing WACC
If use newly issued common stock, use knc rather
than kcs for the cost of the equity portion.
knc

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Balance Sheet
Assets Liabilities
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 16.25% = 11.72%
Computing WACC - using New Common Shares
Common Stock(16.25%)5,000

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Weighted Marginal Cost of Capital
A firm’s cost of capital will change as it is raises more
and more capital
Retained earnings will be used up at some level
The cost of other sources may rise beyond a certain
amount of money has been raised

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A firm’s cost of capital will changes as it is raising more
and more capital
amount of money raised
Therefore, beyond a point, the WACC will rise.
Calculate the point at which the cost of capital
increases

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A firm’s cost of capital will changes as it is raising more
and more capital
amount of money raised
Calculate the point at which the cost of capital
increases
Break in cost
of capital curve
Amt of lower cost capital that can
be raised before component cost rises
Weight of this kind of capital
in the capital structure
=

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Break in cost
of capital curve
Retained earnings
available for reinvesting
Percentage of
common financing
=
If Green Apple Company has $100,000 of internally
generated common:

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Break in cost
of capital curve
Retained earnings
Percentage of
common financing
=
generated common:
Break in cost
of capital curve
$100,000
.50
=

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Break in cost
of capital curve
Retained earnings
Percentage of
common financing
=
generated common:
Break in cost
of capital curve
$100,000
.50
= = $200,000

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Break in cost
of capital curve
Retained earnings
Percentage of
common financing
=
generated common:
Break in cost
of capital curve
$100,000
.50
= = $200,000
Once $200,000 is raised from all sources, the
cost of capital will rise because all the lower
cost retained earnings will be used up.

80
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Marginal weighted cost of capital curve:
11.09%
Cost of Capital
using internal
common stock

81
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
11.09%
Break-Point for
common equity

82
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
11.09%
Cost of Capital
using internal
common stock
11.72%
Cost of Capital using
new common equity

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Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
11.09%
11.72%

84
Making Decisions
Choosing Projects Using Weighted Marginal Cost of Capital
Graph IRR’s of potential projects
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Project 1
IRR = 12.4%
Project 2
IRR = 12.1% Project 3
IRR = 11.5%

85
Making Decisions
Graph Weighted Marginal Cost of Capital
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Project 1
IRR = 12.4%
Project 2
IRR = 11.5%

86
Making Decisions
Graph Weighted Marginal Cost of Capital
Choose projects whose IRR is above the weighted
marginal cost of capital
Weighted
Cost
of
Capital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Project 1
IRR = 12.4%
Project 2
IRR = 11.5%
Accept Projects #1 & #2

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