15
Cost of Capital
Adapted
from Ross,
Westerfield,
Instructor:
Hung
DuongJordan (10th)
Adapted from Ross Westerfield Jordan (2007) and
Hudgins (2007)
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
 The Cost of Capital: Some Preliminaries
 The Costs of Debt, Equity and Preferred
Stock
 The Weighted Average Cost of Capital
 Flotation Costs and the Weighted
Average Cost of Capital (WACC)
15-1
Required Rates on a Project
 In order to estimate correct required rate, companies
must find their own unique cost of raising capital
110
If R=9.5%, ACCEPT
R
1
0
If R=10.5%, Reject
-100
Accept or reject?
15-2
What is the cost of capital?
 Cost of using money for a particular purpose
 You pay rent for using a car, fee for using cable..
 You may pay higher rent if driving out state, or
higher fee of cable for business
 You pay interest for using capital: higher rate if
investment is riskier
 What are the sources of capital?
 Debt (loans, bonds,..)
 Equity (stocks)
Firm’s Cost of capital = Investors’ Required return
15-3
Why Cost of Capital Is Important
 Riskier the firm higher investors’
required return  Higher Firm’s COC
 the required return on assets depends on the
risk of those assets
 Our COC  how the market views the risk of
our assets. Do you know how risky you are?
 Knowing our cost of capital  the required
return for capital budgeting projects
15-4
How to determine Cost of capital?
 Cost of capital= Weighted Average
of
 + cost of debt
 + cost of common stock
 + cost of preferred stock
15-5
#1: Cost of Debt
What is the cost of debt?
Debt
0
Debt
100@10%
Equity
200
Equity
100
Sales
100
Sales
- Costs
-60
- Costs
EBIT
40
- Interest
EBT
- Tax (40%)
EBIT
-0
40
-16
100
-60
40
- Interest
EBT
-10
30
- Tax (40%)
-12
Net Income
24
Net Income
18
ROE
12%
ROE
18%
Debt magnifies ROE
Before tax: RD=10/100=10%
Tax saving: 16-12=4
After Tax: R*D=(10-4)/100=6%
15-6
R*D=RD (1-T)
#1: Cost of Debt
 The cost of debt is the required return on
our company’s debt
 Bank loan: R*D=[Interest rate] . (1-T)
 Bond: R*D=[YTM] . (1-T)
 (*) indicates After tax
 The cost of debt is NOT the coupon rate
 We usually focus on the cost of long-term
debt or bonds
15-7
Example: Cost of Debt
 Suppose we have a bond issue currently outstanding
that has 25 years left to maturity. The coupon rate is
9% and coupons are paid semiannually. The bond is
currently selling for $908.72 per $1,000 bond. What is
the cost of debt?
1000
45
r
0
1
-908.72
2
…
50
10%*(1-T)=6%
Maturity
N = 50; PMT = 45; FV = 1000; PV = -908.72;
CPT I/Y = 5%; YTM = 5(2) = 10%
What is the after-tax cost of debt
if the tax rate is 40%?
15-8
Cost of Equity
Sales
100
- Costs
EBIT
-60
-10
30
- Tax (40%)
Net Income
Returns to shareholders
40
- Interest
EBT
What is the cost of equity?
D1
Rc 
g
P0
-12
18
- Dividend
-9
Dividend Yield (D1/P0)
∆ Retained
Earning
+9
Growth (capital gain,
Price appreciation,..)
Do we need to adjust tax effect?
"NO"
Interest  tax
not DIV nor RE  tax 15-9
#2: Cost of Equity
 The cost of equity is the return required by
equity investors given the risk of the cash
flows from the firm
 Business risk
 Financial risk
 There are two major methods for
determining the cost of equity
 Dividend growth model
 CAPM
15-10
Dividend Growth Model Example
 Suppose that your company is expected to
pay a dividend of $1.50 per share next year.
There has been a steady growth in
dividends of 5.1% per year and the market
expects that to continue. The current price
is $25. What is the cost of equity?
D1
Rc 
g
P0
1 .50
Rc 
 .051  .111  11 .1 %
25
15-11
Example: Estimating the Dividend
Growth Rate (g)?
 One method for estimating the growth
rate is to use the historical average
 Year
 2002
 2003
 2004
 2005
 2006
Dividend
1.23
1.30
1.36
1.43
1.50
Percent Change
(1.30 – 1.23) / 1.23 = 5.7%
(1.36 – 1.30) / 1.30 = 4.6%
(1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%
15-12
Advantages and Disadvantages of
Dividend Growth Model
 Advantage – easy to understand and use
 Disadvantages
 Only applicable to companies currently paying
dividends
 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
15-13
#3: Cost of Preferred Stock
 Reminders
 Constant Dividends are expected to be
paid every period forever
 RP = D / P 0
(g=0)
15-14
Example: Cost of Preferred Stock
 Your company has preferred stock
that has an annual dividend of $3. If
the current price is $25, what is the
cost of preferred stock?
 RP = 3 / 25 = 12%
15-15
Weighted Average Cost of Capital
WACC
= wE*RE +Cost
wP*RP of
+ wCapital
Weighted
D*RD*(1-TC)
Components of COC
Debt
Pref.
Stock
Common
Stock
*
R d  Rd .(1  T )
Rp 
Dp
Weight
WACC
Wd
WdR*d
Wp
W p Rp
Wc
W c Rc
Pp
D1
Rc 
g
P0
15-16
Capital Structure Weights
Long Term Liabilities and Equity
WACC = wERE + wPRP + wDRD(1-TC)
•
•
•
Weights of each source should reflect expected
financing mix
Market Value Weights are preferred
Balance Sheet percentages are often used if
market values are not available to calculate the
weighted average cost of capital.
15-17
Capital Structure Weights
 Notation
 E = market value of equity = # of outstanding
shares times price (NS*PS) (assume no
preferred stock)
 D = market value of debt = # of outstanding
bonds times bond price (NB*PB)
 V = market value of the firm = D + E
 Weights
 wE = E/V = percent financed with equity
 wD = D/V = percent financed with debt
15-18
Example: Capital Structure Weights
Green Apple Company
Market Values
Bonds
Preferred Stock
Common Stock
4,000
1,000
5,000
40%
10%
50%
10,000
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
retained earnings or selling common stock.
15-19
Example: WACC?
Green Apple Company
Market Values
Source of Capital
Cost
Bonds
Preferred Stock
Common Stock
Rd = 10%
Rps = 11.9%
Rcs = 15.5%
Bonds
Preferred Stock
Common Stock
4,000
1,000
5,000
40%
10%
50%
10,000
Green Apple’s tax rate is 40%
WACC =.4*10%*(1-.4) +0.1*11.9% + 0.5*15.5% =11.34%
15-20
Using WACC for All Projects - Example
What projects will be accepted
if using WACC? RR?
 Assume Blackwater’s WACC = 15%. It is
considering three investment opportunities:
 Project
RR
IRR
A Iraq missions
20%
B Protect Paris Hilton
15%
C Protect ODU students 10%
17%
18%
12%
What rate to be used as discount rate? Why?
15-21
Project Costs of Capital
The required return of a project is determined
by its risk, not by its source of capital
Project Risk
RR
Firm Risk
WACC
Investors
 Using the WACC as our discount rate is only appropriate
for projects that have the same risk as the firm’s current
operations.
 If we are looking at a project that does NOT have the
same risk as the firm, then we need to determine the
appropriate discount rate for that project.
 Divisions also often require separate discount rates. 15-22
Divisional and Project Costs of Capital
 Using the WACC as our discount rate is only
appropriate for projects that have the same risk
as the firm’s current operations.
 If we are looking at a project that does NOT
have the same risk as the firm, then we need to
determine the appropriate discount rate for that
project.
 Divisions also often require separate discount
rates.
15-23
Subjective Approach - Example
 Consider the project’s risk relative to
the firm overall
Risk Level
Discount Rate
Very Low Risk
WACC – 8%
Low Risk
WACC – 3%
Same Risk as Firm
WACC
High Risk
WACC + 5%
Very High Risk
WACC + 10%
15-24
Flotation Costs
 The cost of issuing new securities
 Basic Approach
 Compute the weighted average
flotation cost
 Use the target weights because the firm
will issue securities in these
percentages over the long term
15-25
Flotation Costs - Example
 Your company is considering a project that will cost $1
million. The WACC is 15% and the firm’s target D/E ratio
is .6 The flotation cost for equity is 5% and the flotation
cost for debt is 3%. What is the project’s WACC?
 How many percents of TA are financed by Debt? Equity?
 D/E=0.6  E=1, D=0.6  D+E=1.6
 WD=0.6/1.6=.375 ; WE=1-.375=0.625
 fA = (.375)(3%) + (.625)(5%) = 4.25%
 What is the true cost of the project taking into account
flotation costs?
 X*(1-.0425) =1,000,000  X=1,044,386.42 (CP thực sự)
 PV of future cash flows = 1,040,105
 NPV of Project?
 NPV = 1,040,105 - 1,044,386.42 = -4,281 --> Reject
15-26
15
Cost of Capital
Adapted
from Ross,
Westerfield,
Instructor:
Hung
DuongJordan (10th)
Adapted from Ross Westerfield Jordan (2007) and
Hudgins (2007)
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Financial Leverage
 Degree of Financial Leverage
 Finance a portion of the firm’s assets with debt
 Financial Leverage measures changes in earnings per
share as EBIT changes.
 Degree of Financial Leverage (DFL) at one level of EBIT:
% Change in EPS
DFLEBIT =
% Change in EBIT
Unique Level of EBIT
15-30
Financial Leverage
Interpretation: When EBIT changes 1% (from an existing
level of $500,000) Earnings Per Share will change 1.67%
How much would be DFL if there were no interest?
DFL*=EBIT/EBIT=1 (if I=0)
If EBIT changes by 1%, EPS will also change by 1%
EBIT
DFLEBIT =
EBIT – I
Example:
EBIT = $500,000
Interest Charges = $200,000
500,000
DFLEBIT=500,000 = 500,000 – 200,000
= 1.67 times
15-31
The Effects of Financial Leverage
A Proposed Change in Financial Leverage:
Current
Proposed
Assets
$5,000,000
$5,000,000
Debt
$0
$2,500,000
Equity
$5,000,000
$2,500,000
Debt/Equity
0
1
Share Price
$10
$10
Shares Outstanding 500,000
250,000
Interest Rate
10%
n/a
15-32
The Effects of Financial Leverage
Current Capital Structure:No Debt (Ignore Taxes)
Recession
Expected
Expansion
$300,000
$650,000
$800,000
0
0
0
Net Income $300,000
$650,000
$800,000
EBIT
Interest
ROE
6%
13%
16%
EPS
$.60
$1.30
$1.60
With no debt:
ROE=NI/$5,000,000
EPS = NI/500,000
15-33
The Effects of Financial Leverage
Proposed Capital Structure:Debt/Equity=1
Recession
Expected
Expansion
EBIT
$300,000
$650,000
$800,000
Interest
250,000
250,000
250,000
Net Income $ 50,000
$400,000
$550,000
13% 16%
16% 22%
ROE
6%
EPS
$.60 $.20
With debt:
2%
$1.30 $1.60 $1.60 $2.20
ROE=NI/$2,500,000
EPS = NI/250,000
15-34
Computing Break-even EBIT (ignoring tax)

A.


EPS = EBIT/500,000
B.


With $2,500,000 in debt at 10%:
EPS = (EBIT - $250,000)/250,000
C.


With no debt:
These are equal when:
EPSBE = EBITBE/500,000 = (EBITBE - $250,000)/250,000
D.
With a little algebra:

EBITBE = $500,000

So EPSBE = $1.00/share
15-35
Computing Break-even EBIT
EPS ($)
3
D/E = 1
2.5
2
D/E = 0
1.5
1
0.5
0
– 0.5
–1
EBIT ($ millions, no taxes)
0
0.2
0.4
0.6
0.8
1
15-36