Cost of Capital
Lecture Notes
Minggu 10
• Learning Objectives
– Explain the concept and purpose of determining a
firm’s cost of capital.
– Identify the factors that determine a company’s
cost of capital.
– Describe the assumptions made in computing a
firm’s weighted average cost of capital.
– Calculate a corporation’s weighted cost of capital.
– Explain how PepsiCo calculates its cost of capital.
– Compute the cost of capital for an individual
project when the firm’s weighted cost of capital is
not appropriate as the discount rate.
Required Rates on Projects
• An important part of capital budgeting is setting
the required rate for the individual project
Example: Consider the following project
0
1
-1,000
+1,100
If Required Rate = 9%: NPV = -1,000 + 1,100 = $9.17
(1+ .09 )
Accept Project since NPV > 0
Remember:
NPV = PV of Cash Inflows - PV of Cash Outflows
(or Initial Outlay)
Required Rates on Projects
• An important part of capital budgeting is setting
the required rate for the individual project
Example: Consider the following project
0
1
-1,000
+1,100
If Required Rate = 9%: NPV = -1,000 + 1,100 = $9.17
(1+ .09 )
Accept Project since NPV > 0
If Required Rate = 11%: NPV = -1,000 + 1,100 = –$9.01
(1+ .11 )
Reject Project since NPV < 0
Required Rates on Projects
• An important part of capital budgeting is setting
the required rate for the individual project
Example: Consider the following project
0
1
-1,000
+1,100
If Required Rate = 9%: NPV = -1,000 + 1,100 = $9.17
(1+ .09 )
Accept Project since NPV > 0
If Required Rate = 11%:
NPV = -1,000 + 1,100 = –$9.01
(1+ .11 )
In order to estimate correct required rate, companies
must find their own unique cost of raising capital
Factors Determining Cost of
Capital
• General Economic Conditions
– Affect interest rates
• Market Conditions
– Affect risk premiums
• When the economy is doing well, most companies do well. This
reduces the risk that the company will fail.
• When the economy is doing poorly, many companies will also do
poorly. This increases the risk that a company will fail.
• Operating and Financing Decisions
– Affect business risk
– Affect financial risk
• Amount of Financing
– Affect flotation costs and market price of security
Model Assumptions
Weighted Cost of Capital Model
• Constant Business Risk
– The company is not undertaking any new projects
that will substantially change the risk of the
company.
• Constant Financial Risk
– The financing mix of the company will not
substantially change.
• Constant Dividend Policy
– Assume that there are no major changes in
Dividend policy.
Computing Weighted Cost of
Capital
Weighted Cost of Capital Model
• 1. Compute the cost of each source of capital
– Ex: cost of debt, cost of equity, cost of preferred
stock.
• 2. Determine the weight of each source of
capital in the total company’s financing mix.
• 3. Calculate Weighted Average Cost of Capital
(WACC)
Computing Cost of Each
Source
1. Compute Cost of Debt
• Required rate of return for creditors
• Same cost found in Chapter 6 as “required
rate for debtholders (kd)”
n
It
$M
+
P0 = 
n
(1+kd)n
t  1 (1  k d )
where:
It = Dollar Interest Payment
Po = Market Price of Debt
M = Maturity Value of Debt
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
n
P0 =
It
 (1  k
t 1
d
)
n
+
$M
(1+kd)n
+
$1,000
(1+kd)10
12
$90
938.55 = 
10
(
1

k
)
t 1
d
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
n
It
t 1
(1  k d )
P0 = 
12
938.55 =
n
$90

10
(
1

k
)
t 1
d
$M
+
(1+kd)n
$1,000
+
(1+kd)10
10.00
N
10
I%
PV PMT FV
? -938.55 90 1000
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
The before tax cost of debt is 10%
10.00
N
10
I%
PV PMT FV
? -938.55 90 1000
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
The before tax cost of debt is 10%
Interest is tax deductible
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
The before tax cost of debt is 10%
Interest is tax deductible
Marginal Tax Rate = 40%
After tax cost of bonds = kd(1 - T)
Computing Cost of Each
Source
1. Compute Cost of Debt
• 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?
The before tax cost of debt is 10%
Interest is tax deductible
Marginal Tax Rate = 40%
After tax cost of bonds = kd(1 - T)
= 10.0%(1– 0.40) = 6 %
Computing Cost of Each
Source
2. Compute Cost Preferred Stock
– Cost to raise a dollar of preferred stock.
Dividend (D)
Required rate kps =
Market Price (P0)
However, there are floatation costs of issuing preferred stock:
Cost of Preferred Stock with floatation costs
kps = Dividend (D)
Net Price (NP0)
Computing Cost of Each
Source
2. Compute Cost Preferred Stock
• 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.
Cost of Preferred Stock
kps =
$5.00
$42.00
= 11.90%
No adjustment is made for taxes as
dividends are not tax deductible.
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of Internal Common Equity
– Management should retain earnings only if they
earn as much as stockholder’s next best
investment opportunity.
– Cost of Internal Equity = opportunity cost of
common stockholders’ funds.
– 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
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of Internal Common Equity
– Dividend Growth Model
• Assume constant growth in dividends
Cost of internal equity--dividend growth model
kcs
D1
=
P0
+ 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%.
kcs = 3(1+0.10) + .10 = .155 = 15.5%
60
The main limitation in this method is estimating growth accurately.
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of Internal Common Equity
– Capital Asset Pricing Model
• Estimate the cost of equity from the CAPM
Cost of internal equity--CAPM
kcs = rrf + (rm – rrf)
Example
The estimated Beta of a stock is 1.2. The risk-free rate is 5%
and the expected market return is 13%.
= 14.6%
kcs = 5% + 1.2(13% – 5%)
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of Internal Common Equity
– Risk Premium Approach
• Adds a risk premium to the bondholder’s required
rate of return.
Cost of internal equity--Risk Premium
kcs = kd + RPc
Where:
RPc = Common stock
risk premium
Example
If the risk premium is 5% and kd is 10%
kcs = 10% + 5%
= 15%
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• 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.
– Using Dividend Growth Model, must adjust for
floatation costs of the new common shares.
Cost of new common stock
kcs
D1
=
+ g
NP0
NP0 = Current stock price - Cost of issuing securities
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of New Common Stock
Cost of new common stock
knc
D1
=
+ g
NP0
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%.
NP0 = $60.00 – (.12x 60) = $52.80
Floatation
Costs
Computing Cost of Each
Source
3. Compute Cost of Common Equity
• Cost of New Common Stock
Cost of new common stock
knc
D1
=
+ g
NP0
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%.
NP0 = $60.00 – (.12x 60) = $52.80
kcs = 3(1+0.10) + .10 = .1625 = 16.25%
52.80
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.
• In reality, most companies don’t issue debt,
preferred, and equity to finance every project.
They usually just issue one.
• However, most companies DO have a target
capital structure and will stagger the issuance
of securities so as to maintain that target.
Capital Structure Weights
Long Term Liabilities and Equity
Balance Sheet Green Apple Company
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Liabilities
Current Liabilities
$2,000
Bonds
4,000
Preferred Stock
1,000
Common Stock
5,000
Total Liabilities and
Owners Equity
$12,000
Firm Raises $10,000 of capital from long term sources
Capital Structure Weights
Long Term Liabilities and Equity
Balance Sheet Green Apple Company
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Liabilities
Current Liabilities
$2,000
Bonds
4,000
Preferred Stock
1,000
Common Stock
5,000
Total Liabilities and
Owners Equity
$12,000
Compute Firm’s Capital Structure (% of each source)
Amount of Bonds
4,000
= 40%
Bonds:
10,000
Total Capital Sources
Capital Structure Weights
Long Term Liabilities and Equity
Balance Sheet Green Apple Company
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Liabilities
Current Liabilities
$2,000
Bonds
4,000
Preferred Stock
1,000
Common Stock
5,000
Total Liabilities and
Owners Equity
$12,000
Compute Firm’s Capital Structure (% of each source)
Amount of Preferred Stock
1,000
= 10%
Preferred Stock:
10,000
Total Capital Sources
Capital Structure Weights
Long Term Liabilities and Equity
Balance Sheet Green Apple Company
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Liabilities
Current Liabilities
$2,000
Bonds
4,000
Preferred Stock
1,000
Common Stock
5,000
Total Liabilities and
Owners Equity
$12,000
Compute Firm’s Capital Structure (% of each source)
Amount of Common Stock
5,000
= 50%
Common Stock:
10,000
Total Capital Sources
Capital Structure Weights
Long Term Liabilities and Equity
Balance Sheet Green Apple Company
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Liabilities
Current Liabilities
$2,000
Bonds
4,000
Preferred Stock
1,000
Common Stock
5,000
Total Liabilities and
Owners Equity
$12,000
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
Computing WACC
Green Apple Company estimates the following costs
for each component in its capital structure:
Source of Capital
Cost
Bonds
Preferred Stock
Common Stock
Retained Earnings
New Shares
kd = 10%
kps = 11.9%
kcs = 15%
knc = 16.25%
Green Apple’s tax rate is 40%
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
Where:
%Bonds =
Weight of Debt in company
%Preferred = Weight of Preferred in company
%Common = Weight of Common Stock in co.
Computing WACC
- using Retained
Earnings
Balance Sheet
Assets
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Tax Rate = 40%
Liabilities
Current Liabilities
$2,000
Bonds (9%)
4,000
Preferred Stock (10%) 1,000
Common Stock(13%) 5,000
Total Liabilities and
Owners Equity
$12,000
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
40%
10%
50%
Computing WACC
- using Retained
Earnings
Balance Sheet
Assets
Liabilities
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Current Liabilities
$2,000
Bonds (10%)
4,000
Preferred Stock (11.9%) 1,000
Common Stock(15%) 5,000
Total Liabilities and
Owners Equity
$12,000
Tax Rate = 40%
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
WACC = .40 x 10% (1-.4)
40%
10%
50%
Computing WACC
- using Retained
Earnings
Balance Sheet
Assets
Liabilities
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Current Liabilities
$2,000
Bonds (10%)
4,000
Preferred Stock (11.9%) 1,000
Common Stock(15%) 5,000
Total Liabilities and
Owners Equity
$12,000
Tax Rate = 40%
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
40%
10%
50%
Computing WACC
- using Retained
Earnings
Balance Sheet
Assets
Liabilities
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Current Liabilities
$2,000
Bonds (10%)
4,000
Preferred Stock (11.9%) 1,000
Common Stock(15%) 5,000
Total Liabilities and
Owners Equity
$12,000
Tax Rate = 40%
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 15%
40%
10%
50%
Computing WACC
- using Retained
Earnings
Balance Sheet
Assets
Liabilities
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Current Liabilities
$2,000
Bonds (10%)
4,000
Preferred Stock (11.9%) 1,000
Common Stock(15%) 5,000
Total Liabilities and
Owners Equity
$12,000
Tax Rate = 40%
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 15% = 11.09%
40%
10%
50%
Computing WACC
If use newly issued common stock, use knc rather
than kcs for the cost of the equity portion.
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
knc
Computing WACC-using New Common Shares
Balance Sheet
Assets
Liabilities
Current Assets
$5,000
Plant & Equipment
7,000
Total Assets
$12,000
Current Liabilities
$2,000
Bonds (10%)
4,000
Preferred Stock (11.9%) 1,000
Common Stock(16.25%)5,000
Total Liabilities and
Owners Equity
$12,000
Tax Rate = 40%
WACC= k0 = %Bonds x Cost of Bonds x (1-T)
+ %Preferred x Cost of Preferred
+ %Common x Cost of Common Stock
WACC = .40 x 10% (1-.4)
+ .10 x 11.9%
+ .50 x 16.25% = 11.72%
Weighted Marginal Cost of
Capital
• A firm’s cost of capital will changes as it is
raising 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 raised
• Calculate the point at which the cost of capital
increases
Break in cost =
Retained earnings
of capital curve
available for reinvesting
Percentage of
common financing
Weighted Marginal Cost of
Capital
Retained earnings
Break in cost = available for reinvesting
Percentage of
of capital curve
common financing
If Green Apple Company has $100,000 of internally
generated common:
Break in cost = $100,000
.50
of capital curve
= $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.
Weighted Marginal Cost of
Capital
Weighted Cost of Capital
• Marginal weighted cost of capital curve:
12%
11.09%
11%
Cost of Capital
using internal
common stock
10%
9%
0
100,000
200,000
Total Financing
300,000
400,000
Weighted Marginal Cost of
Capital
Weighted Cost of Capital
• Marginal weighted cost of capital curve:
12%
11.09%
11%
10%
Break-Point for
common equity
9%
0
100,000
200,000
Total Financing
300,000
400,000
Weighted Marginal Cost of
Capital
Weighted Cost of Capital
• Marginal weighted cost of capital curve:
11.72%
12%
Cost of Capital using
new common equity
11.09%
11%
Cost of Capital
using internal
common stock
10%
9%
0
100,000
200,000
Total Financing
300,000
400,000
Weighted Marginal Cost of
Capital
Weighted Cost of Capital
• Marginal weighted cost of capital curve:
11.72%
12%
11.09%
11%
10%
9%
0
100,000
200,000
Total Financing
300,000
400,000
Making Decisions
• Choosing Projects Using Weighted Marginal
Cost of Capital
– Graph IRR’s of potential projects
Marginal weighted cost of capital curve:
Weighted Cost of Capital
12%
Project 1
IRR = 12.4%
11%
Project 2
IRR = 12.1%
10%
Project 3
IRR = 11.5%
9%
0
100,000
200,000
Total Financing
300,000
400,000
Making Decisions
• Choosing Projects Using Weighted Marginal
Cost of Capital
– Graph IRR’s of potential projects
– Graph Weighted Marginal Cost of Capital
Weighted Cost of Capital
Marginal weighted cost of capital curve:
12%
11%
Project 1
IRR = 12.4%
10%
Project 2
IRR = 12.1%
Project 3
IRR = 11.5%
9%
0
100,000
200,000
Total Financing
300,000
400,000
Making Decisions
• Choosing Projects Using Weighted Marginal Cost
of Capital
– Graph IRR’s of potential projects
– Graph Weighted Marginal Cost of Capital
– Choose projects whose IRR is above the weighted
marginal cost of capital
Marginal weighted cost of capital curve:
Accept Projects #1 & #2
Weighted Cost of
Capital
12%
11%
Project 1
IRR = 12.4%
10%
Project 2
IRR = 12.1%
Project 3
IRR = 11.5%
9%
0
100,000
200,000
Total Financing
300,000
400,000