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As a recent MBA graduate, you are involved in the project analysis of your company that has three divisions in different business sectors. Your company’s current practice for project analysis is to apply its weighted average cost of capital (WACC) of 12% as a single hurdle rate to all projects across all three divisions.
(a) Criticize your company’s current practice of project evaluation; (b) Discuss the long-term consequences of following this practice including with respect to the riskiness of projects to be accepted and rejected; and (c) What alternative PRACTICAL criteria and approach(es) to measure them would you suggest to your boss for project evaluation? (Hints: Refer to my lecture video and class notes in Session IV.)
Instructions:
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Session IV:
Risk Analysis in Capital Budgeting
1.
2.
3.
4.
Modern Portfolio Theory
Concepts of the Capital Asset Pricing Model
Application of the Capital Asset Pricing Model
Measuring Weighted Average Cost of Capital
(WACC)
𝑛
̃𝑡
𝐶𝐹
𝑉0 = 𝑃𝑉0 = ∑
(1 + 𝑘)𝑡
𝑡=1
General Valuation Model
76
MODERN PORTFOLIO THEORY:
RISK-RETURN RELATIONSHIP
Learning Objectives:
Describe how to measure return and risk for a single asset and a portfolio
Explain the difference between diversifiable risk and market risk
Explain the concept of beta and how to measure the beta of a single asset and a
portfolio of assets
Describe what the CAPM is and illustrate how it can be used to estimate a stock’s
required rate of return given its beta
Explain the difference in project analysis between WACC criteria and CAPMbased criteria
——————————————————————————————————ki = kf + Risk Premiumi
where i = a risky asset
How to Measure Risk Premium of i?
1.
Risk-Return for a Single Asset
1)
Expected Return: E(k)
𝑛
𝐸 (𝑘 ) = ∑
𝑘𝑖 𝑝𝑖
𝑖=1
where
2)
ki
pi
n
=
=
=
the ith possible outcome
the probability of ith outcome
# of possible outcomes (states)
Var variance (2) or standard deviation (SD: )
𝑛
𝑉𝑎𝑟(𝑘 ) = 𝜎 2 = ∑𝑖=1[𝑘𝑖 − 𝐸 (𝑘 )]2 𝑝𝑖 (%2 )
𝑆𝐷 (𝑘 ) = 𝜎 = √𝜎 2 (%)
3)
Coefficient of variation: CV
CV
=
/ E(k)
shows risk per unit of expected return.
useful to compare assets with different expected return
77
σ = σ , but A is riskier because A has the same amount of risk (measured by σ)
A
B
for smaller returns => CVA > CVB => B is preferred to A.
σ
USR
< σ , but also k
HT
USR
< k . HT is riskier but also has a higher expected return.
HT
How to determine which is less risky and thus preferred? Compare CV
78
USR
vs. CV
HT
2.
Risk-Return for a Portfolio of Assets
1)
Portfolio return: kp
kp
=
where
2)
wi ki
wi = proportion of portfolio invested in asset I ( wi = 1)
N = # of assets in the portfolio
Portfolio expected return: E(kp)
E(kp) =
3)
N
i=1
N
wi E(ki)
i=1
n
where E(ki) = ki pi
i=1
Variance of portfolio return: p2
p2
p2
=
N
i=1
=
N
wi2 p2
i=1
[ kpi – E(kp) ]2 pi
or
N N
wi wj COVij
i=1 j=1
ji
covariance between
two assets' returns
+
asset’s
own variance
79
Two-Asset Portfolio Case (Assets A & B)
1)
Portfolio return
𝑘̃𝑝
2)
𝐸(𝑘̃𝑝 ) =
=
̂𝐴 + wB 𝑘̂𝐵
wA 𝑘
Variance of portfolio return
p2
2
wA2 A2 + wB2 B2 + 2 wA wB COVAB
=
𝜎𝑝 = ∑
4)
where wA + wB = 1
Portfolio expected return
𝑘̂𝑝
3)
̃𝐴 + wB 𝑘̃𝐵
wA 𝑘
=
𝑛
or
[𝑘𝑝𝑖 − 𝐸(𝑘𝑝 )]2 𝑝𝑖 (%2 )
𝑖=1
Covariance
𝑛
𝐶𝑂𝑉𝐴𝐵 = ∑
[𝑘𝐴𝑖 − 𝐸 (𝑘𝐴 )][𝑘𝐵𝑖 − 𝐸 (𝑘𝐵 )] 𝑝𝑖 (%2 )
𝑖=1
Example) Measuring expected returns and risk:
(Numbers in blue and bold are given for the problem)
State of Economy Probability
Bad
0.10
Average
0.60
Good
0.30
Single Asset Case
E(k)
2
CV
Two-Asset Portfolio Case
wi (given)
E(kp)
p2
p
kA
5%
10%
15%
kB
-5%
15%
30%
0.11
0.0009
0.03
0.27
0.175
0.01013
0.1006
0.57
0.25
0.75
0.15875 or 15.875%
0.00687657 or 68.7657%2
0.082925 or 8.2925%
80
Computation
i)
E(kp) = (0.25) * 11% + (0.75) * 17.5% = 15.875%
ii)
𝜎𝑝 2 = ∑
𝑛
[𝑘𝑝𝑖 − 𝐸(𝑘𝑝 )]2 𝑝𝑖 (%2 )
𝑖=1
State of
Probability
Economy
Bad
.1
kpi
kpi – E(kp)
(kpi – E(kp))2 * Pi
-2.5%
33.7641%2
Average
.6
13.75%
Good
.3
26.25%
-2.5 – 15.875=
-18.375%
13.75- 15.875 =
-2.125%
26.25-15.875 =
10.375%
2.7094%2
32.2922%2
p2 = 68.7657(%2)
p = 8.2925%
where
kpi
= wA * kAi + wB * kBi
e.g.) For bad state, kpi = (.25) x 5% + (.75) x (-5%) = -2.5%
3.
Covariance and Correlation Coefficient
Covariance: measures the degree to which two assets' returns move together.
=
AB A B
-1 < AB (correlation coefficient) < +1
COVAB
where
kA(%)
kA
kA
20
20
20
10
10
10
kB(%)
10
20
= +1.0
kB
10
= -1.0
81
20
kB
10
= 0.0
20
Accordingly, the variance of a portfolio can be measured as:
p2
=
wA2 A2 + wB2 B2 + 2 wA wB COVAB
p2
=
wA2 A2 + wB2 B2 + 2 wA wB AB A B
Example) Measuring portfolio risk using correlation coefficient
AT&T
0.6
28%
Weight invested in each stock
Standard deviation ()
Correlation coefficient ()
0.4
AT&T
.6 (28%)2
=282(%2)
.6 .4 .4 28% 42%
=113(%2)
2
AT&T
Google
Google
0.4
42%
Google
.6 .4 .4 28% 42%
=113(%2)
.42 (42%)2
=282(%2)
Portfolio variance (p2= 282(%2) + 282(%2) + (2 113(%2)) = 790 (%2)
Porofolio standard deviation (p2= 790(%2) = 28.1% or 0.281
The riskiness of a portfolio depends upon
i)
weight of each asset
ii)
asset's own variance (risk)
iii)
AB
-1 AB 1
Question: With what value of correlation coefficient would a portfolio's risk or
variance be minimized?
82
Example) Effects of Different Correlation Coefficient
I.
Portfolio of Two Perfectly Negatively Correlated Stocks( = -1.0)
a. Rate of Return
kW (%)
kM (%)
kP (%)
Stock W
Stock M
15
15
0
2005 0
-10
-10
Portfolio WM
15
2005
0
2005
b. Probability Distribution of Returns
Probability
Density
Probability
Density
Stock W
0
15
Stock M
0
15
0
Percent
= kW (%)
Year
2013
2014
2015
2016
2017
Average return
Standard deviation
Probability
Density
Portfolio WM
15
Percent
= kM (%)
Stock W(kW)
40%
-10
35
-5
15
15%
22.6%
= kP (%)
Stock M(kM)
-10%
40
-5
35
15
15%
22.6%
83
Percent
Portfolio WM(kP)
15%
15
15
15
15
15%
0.0%
II.
Portfolio of Two Perfectly Positively Correlated Stocks( = +1.0)
a. Rate of Return
kM (%)
kM’ (%)
kP (%)
Stock M
Stock M’
15
15
0
0
2005
-10
-10
Portfolio MM’
15
0
2005
2005
-10
b. Probability Distribution of Returns
Probability
Density
0
Probability
Density
15
= kM (%)
Percent
Year
2013
2014
2015
2016
2017
Average return
Standard deviation
0
Probability
Density
15
Percent
0
= kM’ (%)
Stock M (kM)
-10%
40
-5
35
15
15%
22.6%
Stock M’ (kM’)
-10%
40
-5
35
15
15%
22.6%
84
15
= kP (%)
Percent
Portfolio MM’ (kP)
-10%
40
-5
35
15
15%
22.6%
III. Portfolio of Two Partially Correlated Stocks( = +0.65)
a. Rate of Return
kW (%)
Stock W
kM (%) Stock Y
15
kP (%)
15
0
2005
Portfolio WY
15
0
2005
0
2005
-15
b. Probability Distribution of Returns
Probability Density
Portfolio WY
Stocks W and Y
0
Year
2013
2014
2015
2016
2017
Average return
Standard deviation
15
= KP
Stock W (kW)
40%
-10
35
-5
15
15%
22.6%
Percent
Stock Y (kY)
28%
20
41
-17
3
15%
22.6%
85
Portfolio WY (kP)
34%
5
38
-11
9
15%
20.6%
4.
Components of Portfolio’s Total Risk
Total risk =
unsystematic risk +
diversifiable risk
unique risk
systematic risk
non-diver. risk
market risk
p2
Unsystematic risk
Systematic risk
# of securities in portfolio
Investors can always diversify away all risk except the covariance of an asset
with the market - systematic risk. Therefore, investors will not pay a premium to
avoid diversifiable, unsystematic risk, or will not require a premium to accept
this risk.
The only relevant risk for an asset is non-diversifiable, systematic risk.
How to measure this risk -----> BETA
5.
Concepts of Beta
(1) “Beta” measures the sensitivity of a security’s return to general market
movements (or to the return on market portfolio).
𝑘̃𝑖 = 𝛼 + 𝛽𝑖 𝑘̃𝑚 + 𝜀̃𝑖
𝜎𝑖 2 = 𝛽 𝑖 2 𝜎 2 (𝑘𝑚 ) + 𝜎 2 (𝑘𝑖 )
systematic
risk
unsystematic
risk
(2) Beta is the slope of a Characteristic line (CL) which relates individual
asset’s returns to market returns.
Characteristic Line: ki = + ßi km
86
Example) Computation of Beta Using Rise over Run Method
Year
2019
2020
2021
kH
10%
-20%
25%
kA
10%
-10%
20%
kL
10%
0%
15%
km
10%
-10%
20%
ki
i =
Beta for L = -10% /(-20%) = .5
Beta for H = -30%/(-20%) = 1.5
km
ki (or ki – kf)
High-beta stock: =1.5
3%
Average-beta stock: =1
2%
Low-beta stock: =.5
1%
km (or km – kf)
1%
2%
3%
(3) Portfolio Beta: The BETA of any portfolio is the weighted average of
all component assets’ betas.
𝛽𝑝 = ∑𝑁
𝑖=1 𝑤𝑖 𝛽𝑖 where N = number of securities in the portfolio
Question: What is the BETA of a portfolio investing ½ in Treasury-bill
and ½ in S&P 500 stock index?
87
CONCEPTS OF THE CAPITAL ASSET PRICING MODEL
Question:
For a given level of BETA, what rate of return will investors
require on a stock in order to compensate for their risk?
kA
=
kf
+
Risk premium on asset A
Capital Asset Pricing Model (CAPM): Security Market Line (SML)
E(ki)
E(km)
SML
E(ki) = kf + risk premium
Risk premium
on ith stock
E(ki) = kf + [E(km) – kf] ßi
where slope =
kf
Risk-free rate
CAPM (SML):
E(ki) or ki
=
ßm (= 1)
= market risk
premium
ßi
ßm=1
[E(km) – kf]
kf
+
[E(km) – kf] ßi
Notes:
1.
Slope of SML = (km – kf) = market risk premium
2.
Beta of risk-free asset (ßf)= 0; Beta of market portfolio ßm = 1
3.
Beta is statistically measured as:
𝛽𝑖 =
𝐶𝑂𝑉𝑖,𝑚
𝜎𝑚
2
=
𝜌𝑖,𝑚 𝜎𝑖 𝜎𝑚
𝜎𝑚
2
𝜎
= 𝜌𝑖,𝑚 ( 𝑖 )
𝜎𝑚
Hence, a stock’s BETA depends upon
i)
its correlation with market return as a whole
ii)
its own variability
iii) market variability
Example)
XYZ Company Stock Beta = 0.4; kf = 9%; km = 13%.
What should the required return for XYZ Company stock be?
=> kXYZ = 9% + (13% – 9%) * 0.4 = 10.6%
88
Example) Computing beta and understanding concept of the CAPM
The market portfolio has a standard deviation of 20%, and the covariance between the
returns on the market and those on stock Z is 800 (%2).
(a) What is the beta of stock Z?
800(%2)
COVz,m
ßz =
m2
=
= 2.0
(20%)
2
(b) What is the standard deviation of a fully diversified portfolio of such stocks?
𝜎𝑖 2 = 𝛽 𝑖 2 𝜎 2 (𝑘𝑚 ) + 𝜎 2 (𝑘𝑖 )
Systematic unsystematic
risk
risk
For a fully diversified portfolio, unsystematic risk is close to zero. Therefore,
p2 ≈ ßp2m2
p ≈ ßpm = 2 x (20%) = 40%
(c) If the market portfolio gave an extra return of 5%, how much extra return can you
expect from stock Z?
Market risk premium = E(km) – kf = 5%
Hence, risk premium for stock z
= ßz x Market risk premium
= 2.0 x 5% = 10%
89
Example) Estimating Beta from Historical, Realized Stock Returns
Year
2015
2016
2017
2018
2019
HT (ki)
38.6%
-24.7
12.3
8.2
40.1
Market (km)
23.8%
-7.2
6.6
20.5
30.6
Average
STD
Correlation Coeff.
14.9%
26.5%
14.9%
15.1%
(1)
0.92
Using a time-series regression line:
kHTt = HT + ßHTkmt + HTt
where
Dependent variable (kHTt): HT stock returns
Independent variable (kmt): Market returns (S&P 500)
Regression estimates:
kHT = – 8.90 + 1.6 km
(2)
Using statistics
𝛽𝑖 =
𝐶𝑂𝑉𝐻𝑇,𝑚
𝜎𝑚 2
𝜎
26.5%
𝜎𝑚
15.1%
= 𝜌𝐻𝑇,𝑚 ( 𝐻𝑇 ) = (0.92)𝑥
= 1.6
Other Methods
Published beta such as Value Line beta or from other brokerage company
Pure play method
Accounting beta method
90
Words of Caution When Using the CAPM
The CAPM is an ex ante model, but we use expost-data to measure it.
No adjustment for future expectations
SML can shift over time due to changes in the risk-free rate of return
BETAs can change over time
Anomalies (inefficiencies) observed empirically
i)
Small capitalization stocks
ii)
Low P/E stocks
iii)
Seasonal effects
Reading – Does the CAPM Work?
(by D. Mullins, Harvard Business Review, 1982)
91
Changes in the Security Market Line
Required and Expected
Rates of Return(%)
35
30
25
Increased Risk Aversion
20
Increased Inflation
15
10
Original Situation
5
0.00
0.50
1.00
Beta
92
1.50
2.0
APPLICATIONS OF THE CAPM TO CAPITAL BUDGETING
In equilibrium, all securities and assets should lie on the SML. Thus, E(ki) from the
CAPM represents the minimum required rate of return or Risk-Adjusted Discount
Rate (RADR) for the asset given its level of risk.
Example)
Stock A’s beta = 0.4; kf = 9%; rm = 13%;
E(kA) = kA = 9% + (13% – 9%) x 0.4 = 10.6% 0, accept the project.
𝑁𝑃𝑉 = −𝐶0 + ∑𝑛𝑡=1
𝐶𝐹𝑡
(1+𝑘)𝑡
where k (RADR) is measured from the CAPM.
ii) To be compared with the project’s estimated (projected) return or IRR.
If estimated return or IRR > E(ki) or RADR => Accept.
Required (Expected)
Rate of Return (%): E(ki)
SML
E(kB)
Market Price Risk (MPR)
Criteria or CAPM (SML) Criteria
A
E(kA)
B
kf
ßA
ßB
ßi
For asset A:
Estimated return > Required rate of return (RADR)
=> underpriced => a good buy (or Accept)
For asset B:
Estimated return < Required rate of return (RADR)
=> overpriced => not a good buy (or Reject)
In disequilibrium, the asset is either overpriced (return too low) or underpriced
(return too high). Investors will bid up (down) underpriced (overpriced) assets.
93
Application of the CAPM to Capital Budgeting (or Project Evaluation)
Step 1:
Estimate the project’s beta
Step 2:
Use the CAPM to measure the project’s risk-adjusted discount rate
(RADR) or the project’s required rate of return or cost of capital.
Step 3:
Compare the project’s RADR with its expected return (or IRR).
If expected return > RADR => ACCPET the project. (Lies above SML)
If expected return < RADR => REJECT the project. (Lies below SML)
Example 1) Security evaluation using CAPM
Step 1: Estimate betas
Security
High Tech (HT)
US Rubber (USR)
Collections (Coll)
Expected Return
12.4%
9.8%
1.0%
Beta
1.32
0.88
-0.87
• Assume that kf = 5.5% and MRP = 5.0%.
Step 2: Calculating RADRs (or Required Rates of Return)
kHT = 5.5% + (5.0%) x 1.32 = 12.10%
kUSR = 5.5% + (5.0%) x 0.88 = 9.90%
kColl = 5.5% + (5.0%) x (-0.87) = 1.15%
Step 3: Compare Expected Return with RADR of Each Security
Expected
Return
RADR or
Required
Return
HT
12.4%
12.1%
>
Undervalued
(or Accept)
USR
9.8
=>
good buy
bad buy
Company Cost of Capital (WACC or Hurdle Rate) vs. Project’s COC
E(ki)
SML
A
C
B
D
Company Cost of Capital
(WACC)
kf
ßC ßWACC ßA
ßD
ßB
ßi
Questions: Should Project B be accepted? / Should Project C be rejected?
If a company’s WACC is being used as a criterion in investment decision, it would
accept/reject a project regardless of the project’s risk (BETA) as long as the project
offers a higher return than the company’s WACC.
This may lead to rejecting many good low-risk projects (such as C) and to accepting
many poor high-risk projects (such as B). Because each project may have a risk
different from the company’s overall asset, the company’s WACC cannot be employed
as an across-the-board cutoff rate.
In sum, the company’s WACC is the correct cutoff rate for projects that have the
same risk as the company’s existing business, but it is not for projects that are safer or
riskier than the company’s average risk.
Divisional Cost of Capital
across-the-board expansion: use the company’s stock beta
expansion into other industry: use the beta of a similar firm in other industry
Also holds true for subsidiaries of a holding company use the BETA of a
similar, independent company operating in the same industry.
Example : Old AT&T
– New project in telephone industry: can use its own beta of 0.50
– New project in PC industry: should use a higher beta of 1.49
97
Example) Company Beta vs. Project Beta
A company is deciding whether to issue stock to raise money for an investment
project which has the same risk as the market and an expected return of 20%. If the
risk-free rate is 10% and the expected return on the market is 15%, the company
should go ahead
(a) Unless the company’s beta is greater than 2.0.
(b) Unless the company’s beta is less than 2.0.
(c) Whatever the company’s beta.
Which answer is correct? Say briefly why.
——————–Answer is _____.
βA = 1.0; E(kA) = 20%; kf = 10%; E(km) = 15%.
According to the CAPM,
kA = kf + (E(km) – kf) x βA = 10% + (15% – 10%) x 1.0 = 15%.
The project’s expected return is 20%, which is greater than its required rate of
return of 15%. Hence, the company should accept the project regardless of the
company’s beta. In this analysis, the company’s beta is irrelevant since the
investment project has a different risk (beta is equal to 1) than the company’s
average risk.
98
Practical Approach to Determining Cost of Capital
for a Project in a Division / Product Line
1.
Determine the company-wide cost of capital (weighted average cost of capital)
WACC = wd kd (1-T) + wps kps + ws ks
Where
kd = cost of debt
kps = cost of preferred stock
ks = cost of common stock
2.
Classify the company divisions / product lines into three to five groups of risk
level, and then adjust the company’s WACC accordingly to reflect the risk
level of each division / product line:
Add or Subtract
Division’s Risk Level
Risk Premium
High risk
+2%
Average risk
+0%
Low risk
-2%
3.
Similarly, classify each division’s projects into three to five groups of risk
level, then adjust the division’s cost of capital accordingly to reflect the risk
level of each project.
Add or Subtract
Project’s Risk Level
Risk Premium
High risk
+2%
Average risk
+0%
Low risk
-2%
Divisional
Cost of capital
H
Average
H
Low
L
A
L
Company’s
WACC
High
Higg
hh
A
H
Project’s
Cost of Capital
99
A
L
MEASURING WEIGHTED AVERAGE COST OF CAPITAL
Learning Objectives:
Describe the components of a firm’s weighted average cost of capital
Estimate the costs of different capital components-debt, preferred stock, retained
earnings, and common stock
Explain the difference between internal cost of common stock (retained earnings)
and external cost of common stock (newly-issued common stock)
Combine the different component costs to determine the firm’s WACC
——————————————————————————————————
Purpose
1)
Investment decision
2)
Financing decision
Two Key Issues
1)
After-tax cost basis
2)
Market value basis
Components of Weighted Average Cost of Capital (WACC)
Firms’ Sources of Capital
Capital
Debt
Notes
Payable
Preferred
Stock
LongTerm Debt
Common
Equity
New
Retained
Common
Earnings
Stock
WACC = wd * kd (1-T) + wps * kps + ws * ks (or ke)
where
kd
=
cost of debt
kps
=
cost of preferred stock
ks
=
cost of internal common stock (retained earnings)
ke
=
cost of newly-issued (external) common stock
100
1. Cost of Debt: kd
Model: 𝑃0𝐵 (1 − 𝑓) =
𝐼
(1+𝑘𝑑 )
+
𝐼
(1+𝑘𝑑
)2
+ ⋯+
𝐼
(1+𝑘𝑑
)𝑛
+
𝑀
(1+𝑘𝑑 )𝑛
where f = flotation cost percentage (%) ≈ 0 for issuing debt
Then, the after-tax cost of debt = kd (1 – Tc) where Tc = corporate tax rate
Notes: Cost of current liabilities
Accruals (accrued taxes and wages) and Accounts payables (and other
spontaneous current liabilities) do not carry explicit interest charges to the firm.
Cost of notes payable can be proxied by the prime rate.
2. Cost of Preferred Stock: kps
𝑝𝑠
Model: 𝑃0 (1 − 𝑓) =
𝐷
𝑘𝑝𝑠
==> 𝑘𝑝𝑠 =
𝐷
𝑝𝑠
𝑃0 (1−𝑓)
3. Cost of Common Stock: ks or ke
1) Discounted dvidend model (Dividend growth model: DGM)
𝐷1
𝐷1
𝐷1
Model: 𝑃0𝑠 =
Estimation of growth rate
a. Use the historic average rate of growth
b. Use the regression analysis
Ln(DPS)t = + ß (YEAR)t + et
𝛽̂ = cumulative annual growth rate
c. 𝑔̂ = Retention ratio x Return on Equity
𝑘𝑠 −𝑔
==> 𝑘𝑠 =
𝑃0
+ 𝑔̂ 𝑜𝑟 𝑘𝑒 =
𝑃0 (1−𝑓)
+ 𝑔̂
2) Stock-bond yield spread (Bond-yield-plus risk premium) model
Model: 𝑘𝑠 = 𝑘𝑑 + (𝑘̅𝑠 − 𝑘̅𝑑 )
where
kd = firm’s current bond yield (before-tax)
𝑘̅𝑠 − 𝑘̅𝑑 = firm’s historical average risk premium of common stock
over debt.
3) Capital asset pricing model
Model: kS = kf + risk premium of a firm’s stock = kf + ßs (km – kf)
101
Estimation of beta
2
a. statistics: 𝛽𝑠 = 𝐶𝑂𝑉𝑠,𝑚 ⁄𝜎𝑚
b. regression analysis
c. Value Line beta
d. pure play method (proxy)
=============================================================
Selected Realized Returns, 1926-2012
Historical U.S. Real Asset Class Returns & Equity Risk Premia:
U.S. Equity Risk Premium Histogram (vs. U.S. T-ills)
102
Example) Measuring WACC – Fisher Company
Cost of Debt: kd
Fisher Company is in the 34% marginal tax bracket. Its investment bankers estimate
that the firm would have to set a coupon rate of 12 percent on its new par bonds.
After-tax cost of debt = kd (1 – T) = 12% (0.66) = 7.9%
Cost of Preferred Stock: kps
The firm could sell preferred stock with a $10 annual dividend for $100, but would
incur $3 in flotation costs on each share sold.
$10
kps
=
Dp / P0
=
=
10.3%
$100 – $3
Cost of Retained Earnings: ks
Fisher Company’s common stock is expected to pay a dividend over the next year of
$5.00, and it sells for $50.00. The firm has an expected constant growth rate of 5
percent, its beta is 1.6, the risk free rate is 7 percent, and the market risk premium is 5
percent. Over the years, the company has paid an average risk premium of 3% for its
stock over bonds.
(a)
DCF Approach:
D1
ks =
$5
+g =
P0
(b)
+ 5% = 15.0%
$50
CAPM Approach:
ks = kf + (km – kf) x BETA = 7% + (5%)1.6 = 15.0%
(c)
Bond Yield Plus Risk Premium Approach:
ks = Bond rate + risk premium = 12% + 3% = 15.0%.
103
Cost of Newly Issued Common Stock:ke
Fisher Company expects flotation costs of 6 percent on new common stock sales.
D1
ke
=
$5
+g
=
P0 (1 – F)
+ 5% = 15.6%
$50 (1-0.06)
Flotation premium = 15.6% – 15.0% = 0.6%.
=======================================================================
Target Capital Structure:
i)
Using Cost of Retained Earnings (ks):
WACC
ii)
30% LT Debt
10% Preferred
60% Common equity
=
=
=
.3(12%) (0.66) + 0.1(10.3%) + 0.6(15%)
2.38% + 1.03% + 9.0%
12.41%
Using Cost of Newly Issued Common Stock (ke)
WACC
=
=
=
.3(12%) (0.66) + 0.1(10.3%) + 0.6(15.6%)
2.38% + 1.03% + 9.36%
12.77%
104
