CHAPTER 10
The Cost of Capital
1
Topics

Cost of Capital Components




Debt
Preferred
Common Equity
WACC



Composite
Risk Adjustments
WACC with Flotation Costs
2
Sources of Long-term Capital
Long-Term
Capital
Long-Term
Debt
rd
Preferred
Stock
rps
Common
Stock rs
Retained
Earnings
rce
New Common
Stock
re
10-3 3
WACC
Weighted Average Cost of Capital
WACC = wdrd(1-T) + wpsrps + wcers
(10.10)
Where:
Weights
wd = % of debt in capital structure
wps = % of preferred stock in capital structure
wce = % of common equity in capital structure
Component
costs
rd = firm’s cost of debt
rps= firm’s cost of preferred stock
rs = firm’s cost of equity
T = firm’s corporate tax rate
4
Capital Components


Capital components = sources of
funding from investors
Accounts payable, accruals, and
deferred taxes ≠ sources of funding
from investors


Not included in calculation of the cost of
capital
Adjustments made when calculating
project cash flows
5
Cost of Debt



Method 1: Ask an investment banker
what the coupon rate would be on
new debt
Method 2: Find the bond rating for the
company and use the yield on other
bonds with a similar rating
Method 3: Find the yield on the
company’s outstanding debt
6
NCC’s Cost of Debt (rd)


A 22-year, 9%
semiannual coupon
bond sells for
$835.42
Bond pays a
semiannual coupon:
rd = 5.5% x 2 = 11%
Calculator Solution
44
,
835.42 S.
45
/
1000
0
%- =
5.50%
7
Component Cost of Debt

Interest is tax deductible, so the after
tax (AT) cost of debt is:



rd AT= rd BT(1 - T)
rd AT
= 11%(1 - 0.40) = 6.6%
Use nominal rate
8
Flotation Costs on New Debt

Flotation costs on debt usually low
Frequently ignored

“Project Financing”



Adjusts project’s cash flows for flotation
costs of debt
Debt has specific claim on the project’s
cash flows
9
Adjusting the Cost of Debt for
Flotation Costs
INT ( 1  T )
M
M( 1  F )  

t
N
[
1

r
(
1

T
)]
[
1

r
(
1

T
)]
t 1
d
d
N
(10 - 2)
Where:
M = Bond’s par value (face value)
F = Flotation cost as a %
N = Number of coupon payments
T = Corporate tax rate
INT = Dollars of interest per period
rd(1-T) = after tax cost of debt adjusted for inflation
10
NCC’s Cost of Debt (rd) with
Flotation Costs




NCC can issue 30-year bonds
Calculator Solution
60
,
 N = 60
990
S.
11% annual coupon rate
33
/
 Coupons paid semiannually
1000
0
 PMT = [(.11 x 1000)/2]*(1-.40)
%- =
 PMT = $33
3.34%
Flotation cost = 1%
Nominal after-tax cost of
 PV = -1000(1-.01) = -990
debt with flotation costs =
Face value = M = 1000
6.68%
11
Preferred Stock

Flotation costs for preferred are
significant


Preferred dividends are not deductible



Use net price
No tax adjustment
Use rps
Nominal rps is used
12
NCC’s Cost of preferred stock:
PP = $100
rps 
$10 Dividend
Dps
Pps ( 1  F )
F = 2.5%
(10 - 3)
Where:
Dps = Preferred dividend
PPS = Preferred stock price
F = Flotation cost %
r ps
$10

 10.3%
$100( 1  .025 )
13
Cost of Common Equity
Two Ways to raise equity financing:
 Directly


Issue new shares of common stock
Indirectly


Reinvesting earnings not paid out as
dividends
Use retained earnings
14
Funding with New Common
Equity

Mature firms rarely issue new
equity
High flotation costs
 Negative signal to the market
 Downward pressure on stock price

15
Cost of Retained Earnings



Earnings can be reinvested or paid out
as dividends
Investors could buy other securities,
earn a return
Thus, there is an opportunity cost if
earnings are reinvested
16
Cost for Reinvested Earnings

Opportunity cost: The return
stockholders could earn on alternative
investments of equal risk


They could buy similar stocks and earn rs,
or company could repurchase its own
stock and earn rs
 rs = the cost of reinvested earnings
= the cost of equity
17
Three ways to determine
the cost of equity, rs:
1. CAPM:
rs
= rRF + (RM - rRF)β
= rRF + (RPM)β
2. DCF:
rs
= D1/P0 + g
3. Own-Bond-Yield-Plus-Risk Premium:
rs
= rd + Bond RP
18
Three ways to determine
the cost of equity, rs:
1. CAPM: rs = rRF + (RM - rRF)β
= rRF + (RPM)β
2. DCF:
rs = D1/P0 + g
3. Own-Bond-Yield-Plus-Risk Premium:
rs = rd + Bond RP
19
CAPM Cost of Equity - Steps
1.
2.
3.
4.
Estimate risk-free rate (rRF)
Estimate market risk premium (RPM)
or expected return on the market (RM)
Estimate beta (β)
Substitute into CAPM
20
Estimating rRF

Common stock = long-term security

T-Bills more volatile than T-Bonds

Most analysts use the rate on a longterm (10 to 30 years) government bond
as an estimate of rRF
21
Estimating RPM or RM

Historical - Ibbotson & Associates




1926-most recent year
6.5% arithmetic mean - if constant risk aversion
4.9 % geometric mean – best future estimate
Ex Ante = Forward-Looking

If market in equilibrium:
ExpectedReturn rˆM 
Value Line
or Reuters
D1
 g  rRF  RPM  RM  RequiredReturn
P0
Historical or analysts’
estimates
22
RPM Estimate – #1
RPM = 11.73%

rM Estimate




Forward-looking RPM:



(Reuters, Spring 2008)
D (1  g )
Dividend yield on S&P500 = 2.61%
rˆM  0
g
P0
Dividend growth rate = 13.20%
rM=[0.0261(1+.132)]+0.132=16.15%
Long-term T-Bond rate = 4.42%
16.15% - 4.42% = 11.73%
Problems:


Past = future?
Growth rates sensitive to period measured
23
RPM Estimate – #2
RPM = 17.79%

rM Estimate




Forward-looking RPM:


(Spring 2008)
Reuters S&P500 dividend yield = 2.61%
Yahoo Earnings growth rate = 19.1%
rM=[0.0261(1+.191)]+0.191=22.21%
22.21% - 4.42% = 17.79%
rˆM 
D0 ( 1  g )
g
P0
Problems:




Earnings growth ≠ dividend growth
1-year growth rate ≠ long-term growth
Analysts’ accuracy
Differing analysts’ opinions
24
Estimating RPM (or RM)

RPM = Equity risk premium


RM



Most analysts use a rate of 5% to 6.5%
for the market risk premium
S&P500 index return =proxy for the
market return
RPM=RM- rRF
Brigham-Daves →RPM = [3.5, 6.5]
25
Estimating Beta - β


Beta estimates vary
Beta estimates are “noisy”


Historical Beta




Wide confidence interval
4-5 years/monthly or 1-2 years/weekly
Adjusted Beta
Fundamental Beta
Multinational issues
26
NCC’s CAPM Cost of Equity
rRF = 8%
RPM = 6%
β= 1.1
rs = rRF + (RM - rRF )β
= 8.0% + (6.0%)1.1
= 14.6%
27
Three ways to determine
the cost of equity, rs:
1. CAPM: rs = rRF + (RM - rRF)β
= rRF + (RPM)β
2. DCF:
rs = D1/P0 + g
3. Own-Bond-Yield-Plus-Risk Premium:
rs = rd + Bond RP
28
DCF Approach: Inputs
Pˆ 0 
D1
rs  g
(10 - 5)
D1
rs  rˆ s
 expectedg
Po
1.
2.
3.
Current stock price (P0)
Current dividend (D0)
Growth rate (g)
29
Estimating the Growth Rate
The historical growth rate


If you believe future = past
The earnings retention model
Analysts’ estimates:



Value Line, Zack’s, Yahoo.Finance
30
Earnings Retention Model

NCC Data:



Retention ratio = 100% - dividend payout


ROE = 14.5%
Dividend payout ratio = 52%
Retention rate = 100% - 52% = 48%
Retention growth rate:


g = ROE x (Retention rate)
g = (14.5%) x 0.48 = 7%
31
Earnings Retention Assumptions
1.
2.
3.
4.
Retention rate is constant
ROE on new investments is constant
No new common stock will be issued
The risk of future projects is very
close to the risk of the overall firm
32
Using Analysts’ Forecasts

Analysts’ estimate earnings growth


= proxy for dividend growth
Sometimes involve non-constant growth


Analysts’ Estimates for NCC:



Develop a proxy constant rate
10.4% annual growth for 5 years
6.5% growth after 5 years
g = 6.9%
Analysts’ estimates usually best source
33
NCC’s DCF Cost of Equity, rs
D1 = $2.40
rs =
=
D1
P0
P0 = $32
+g=
$2.40
D0(1+g)
P0
g = 7%
+g
+ 0.07
$32
= 0.075 + 0.07
= 14.5%
34
Three ways to determine
the cost of equity, rs:
1. CAPM: rs = rRF + (RM - rRF)β
= rRF + (RPM)β
2. DCF:
rs = D1/P0 + g
3. Own-Bond-Yield-Plus-Risk Premium:
rs = rd + Bond RP
35
The Own-Bond-Yield-Plus-Risk-Premium
Method: rd = 11%, RP = 3.7%





rs = rd + RP
rs = 11.0% + 3.7% = 14.7%
This RP  CAPM RPM
Produces ballpark estimate of rs
Useful check
36
Final Estimate of rs
Method
Estimate Used by
CAPM
14.6%
74% - 85%
DCF
14.5%
16%
rd + RP
14.7%
Non-public
Average
14.6%
37
Flotation Costs for Equity
re = Cost of New Equity
D1
re  rˆe 
g
P0 ( 1  F )
NCC: D1 = $2.40
P0 = $32
(10 - 9)
F = 12.5%
$2.40
re  rˆe 
 .07  15.6%
$32( 1  .125 )
38
Topics

Cost of Capital Components




Debt
Preferred
Common Equity
WACC



Composite
Risk Adjusted
WACC with Flotation Costs
39
WACC
Weighted Average Cost of Capital
WACC = wdrd(1-T) + wpsrps + wcers
(10.10)
Where:
Weights
wd = % of debt in capital structure
wps= % of preferred stock in capital structure
wce= % of common equity in capital structure
Component
costs
rd = firm’s cost of debt
rps= firm’s cost of preferred stock
rs= firm’s cost of equity
T = firm’s corporate tax rate
40
WACC Weights


Weights =percentages of the firm that
will be financed by each component
If possible, always use the target
weights for the percentages of the
firm that will be financed with the
various types of capital

NCC: 30% debt, 10% Preferred, 60% Equity
41
NCC’s WACC
Weighted Average Cost of Capital
Component
Debt (before tax)
Preferred Stock
Common equity
w
0.30
0.10
0.60
r
11.0%
10.3%
14.6%
WACC = wDrD (1- T)+ wPsrPs + wcrs
WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%)
WACC = 11.77%
42
Cost of Capital Issues

Before-tax vs. After-tax Capital Costs




Long- and short-term debt affected
Historical Costs vs. Marginal Costs
Target Weights vs. Annual Financing
Choices
Target Weights vs. Book Values
43
Estimating Weights for the
Capital Structure


Estimate the weights using current
market values rather than current
book values
If market value of debt is not known:

Usually reasonable to use the book
values of debt, especially if the debt is
short-term
44
Estimating Weights

Given:
The stock price is $50
 There are 3 million shares of stock
 $25 million of preferred stock
 $75 million of debt

45
Estimating Weights




Vce = $50 x (3 million) = $150 million
Vps = $25 million
Vd = $75 million
Total value = $150 + $25 + $75 = $250
million
46
Estimating Weights
Value
Stock price
Share O/S
$50
$150,000,000
3,000,000
Weight
60%
Preferred Stock
$25,000,000
$25,000,000
10%
Debt
$75,000,000
$75,000,000
30%
$250,000,000
100%
Total Firm
47
WACC
Tax Rate =
Stock price
Share O/S
40%
$50
3,000,000
Value
Weight
Cost of
Capital
$150,000,000
60%
14.60%
8.76%
1.03%
Preferred Stock
$25,000,000
$25,000,000
10%
10.30%
Debt
$75,000,000
$75,000,000
30%
11.00%
$250,000,000
100%
Total Firm
Tax
Effect
60%
WACC
1.98%
11.77%
48
Factors that influence a
company’s WACC

Market conditions






Interest rates
The market risk premium
Tax rates
Firm’s capital structure
Firm’s dividend policy
Firm’s investment policy

Firms with riskier projects generally have
a higher WACC
49
Topics

Cost of Capital Components




Debt
Preferred
Common Equity
WACC



Composite
Risk Adjusted
WACC with Flotation Costs
50
Risk-Adjusted WACC



The composite WACC reflects the risk
of an average project undertaken by
the firm
Different divisions/projects may have
different risks
The division’s or project’s WACC should
be adjusted to reflect the appropriate
risk and capital structure
51
Divisional Risk and the Cost of
Capital
Rate of Return
(%)
Acceptance Region
WACC
WACC H
Acceptance Region
Rejection Region
WACC F
Rejection Region
WACC L
0
Risk L
Risk H
Risk
52
Using WACC for All Projects Example


What would happen if we use the WACC
for all projects regardless of risk?
Assume the WACC = 15%
Project
A
B
C
Required
Return
20%
15%
10%
IRR
17%
18%
12%
Decision
If 15%
Risk Adj
Accept
Reject
Accept
Accept
Reject
Accept
53
The Risk-Adjusted Divisional
Cost of Capital


Estimate the cost of capital that the
division would have if it were a standalone firm
Requires estimating the division’s beta,
cost of debt, and capital structure

CAPM frequently used
54
Pure Play Method for Estimating
Beta for a Division or a Project



Find several publicly traded companies
exclusively in project’s business
Use average of their betas as proxy for
project’s beta
Hard to find such companies
55
Huron Steel Example
Huron Steel Company
Riskfree rate =
Market risk premium =
Division
Steel
Barge
Distrib
Overall
Beta
1.1
1.5
0.5
1.12
COC
13.60%
16.00%
10.00%
13.72%
7%
6%
% Bus
70%
20%
10%
56
Subjective Approach

Consider the project’s risk relative
to the firm overall

If project risk > firm risk


Project discount rate > WACC
If project risk < firm risk

Project discount rate < WACC
57
Subjective Approach Example
Risk Level
Very Low Risk
Discount Rate
WACC – 8%
7%
Low Risk
WACC – 3%
12%
Same Risk as Firm
WACC
15%
High Risk
Very High Risk
WACC + 5%
WACC + 10%
20%
25%
58
Topics

Cost of Capital Components




Debt
Preferred
Common Equity
WACC



Composite
Risk Adjusted
WACC with Flotation Costs
59
Flotation Costs


Flotation costs depend on the risk of
the firm and the type of capital being
raised
Flotation costs:



Highest for common equity
Most firms issue equity infrequently
Flotation costs frequently ignored when
calculating WACC
60
NCC’s WACC
With New Debt
Component
New Debt (after-tax)
Preferred Stock
New Common equity
d
ps
c
w
0.30
0.10
0.60
r
6.68%
10.3%
14.6%
WACC = wdrATd + wpsrps + wcre
WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%)
WACC = 2.004% + 1.03% + 9.36% = 11.794%
61
NCC’s WACC
With New Debt & New Equity
Component
New Debt (after-tax)
Preferred Stock
New Common equity
d
ps
c
w
0.30
0.10
0.60
r
6.68%
10.3%
15.6%
WACC = wdrATd + wpsrps + wcre
WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%)
WACC = 2.004% + 1.03% + 9.36% = 12.394%
62
NCC’s WACC
WACC Description
WACC
No New Issues
11.770%
With New Debt
11.794%
With New Debt & New Equity 12.394%
63
Increasing Marginal Cost of Capital

Externally raised capital  flotation costs


Investors often perceive large capital budgets
as being risky


Increases the cost of capital
Drives up the cost of capital
If external funds will be raised, then the NPV
of all projects should be estimated using this
higher marginal cost of capital
64
Increasing Marginal Cost of Capital
% 16
15
14
WACC2 = 12.394%
13
12
WACC1 = 11.77%
10
9
External
debt & equity
No external funds
8
500
700 Capital Required
61
Four Mistakes to Avoid



Current (YTM) vs. historical (Coupon rate) cost of
debt
Mixing current and historical measures to estimate
the market risk premium
Book weights vs. Market Weights




Use Target weights
Use market value of equity
Book value of debt is a reasonable proxy for market value
Incorrect cost of capital components

Only investor provided funding
66
CHAPTER 10
The Cost of Capital
67