WACC vs CAPM Criteria

Description

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:

Please post your initial response by 23:59 EST Day 4 of the Week, and comments on the posts of at least four classmates by 23:59 EST Due Date.

Each Discussion Topic carries 10 points (6 points for own answers and 4 points for responses to classmates’ posts). You must first post your own answers directly to the DT by Day 4 of the Week before accessing other students’ answers. In addition, you should post at least FOUR thoughtful and substantive responses to other classmates’ answers/comments by the due date in order to earn full 10 points for each DT. A mere “Yes, I agree” or “No, I don’t agree” type of responses will not be given any credit.

Additional bonus credit may be given to at least TWO additional substantive responses to classmates’ posts at DIFFERENT DATES as they are valued and enrich our online learning.

Concluding comments on each Discussion Topic will be posted on the Discussion folder after due date.

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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)

̃

0 = 0 = ∑
(1 + )
=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)

( ) = ∑

=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: )

( ) = 2 = ∑ =1[ − ( )]2 (%2 )
( ) = = √ 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 ji covariance between two assets' returns + asset’s own variance 79 Two-Asset Portfolio Case (Assets A & B) 1) Portfolio return ̃ 2) ( ̃ ) = = ̂ + wB ̂ wA Variance of portfolio return p2 2 wA2 A2 + wB2 B2 + 2 wA wB COVAB = = ∑ 4) where wA + wB = 1 Portfolio expected return ̂ 3) ̃ + wB ̃ wA = or [ − ( )]2 (%2 ) =1 Covariance = ∑ [ − ( )][ − ( )] (%2 ) =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) 2 = ∑ [ − ( )]2 (%2 ) =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).
̃ = + ̃ + ̃
2 = 2 2 ( ) + 2 ( )
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.
= ∑
=1 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:
=
,

2
=
,

2

= , ( )

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?
2 = 2 2 ( ) + 2 ( )
Systematic unsystematic
risk
risk
For a fully diversified portfolio, unsystematic risk is close to zero. Therefore,
p2 ≈ ßp2m2
p ≈ ßpm = 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
=
,
2

26.5%

15.1%
= , ( ) = (0.92)
= 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.
= − 0 + ∑ =1

(1+ )
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: 0 (1 − ) =

(1+ )
+

(1+
)2
+ ⋯+

(1+
)
+

(1+ )
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

 Model: 0 (1 − ) =

==> =

0 (1− )
3. Cost of Common Stock: ks or ke
1) Discounted dvidend model (Dividend growth model: DGM)
1
1
1

Model: 0 =

Estimation of growth rate
a. Use the historic average rate of growth
b. Use the regression analysis
Ln(DPS)t =  + ß (YEAR)t + et
̂ = cumulative annual growth rate
c. ̂ = Retention ratio x Return on Equity
−
==> =
0
+ ̂ =
0 (1− )
+ ̂
2) Stock-bond yield spread (Bond-yield-plus risk premium) model

Model: = + ( ̅ − ̅ )
where
kd = firm’s current bond yield (before-tax)
̅ − ̅ = 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: = , ⁄
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

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