Determinants of Beta
Formally:
1.
Cyclicality of Revenues
– Not the same volatility of revenues
– Biotech vs. Steel
2.
Operating Leverage
– The mix of fixed and variable costs
3.
Financial Leverage
– The mix of debt and equity financing
• All three have an impact on the variability of the Net Income
available to the stockholders
1
1. Cyclicality of Revenues
Does the company make
• Consumer products
–
–
•
βP&G = 0.52
Not very cyclical
Office Products and Supplies
–
–
βOffice Max = 2.68
Very cyclical
2
2. Degree of Operating Leverage
• Mix of Fixed and Variable costs
• DOL increases as fixed costs rise relative to
variable costs
• DOL magnifies the effects of cyclicality on
EBIT
Formula:
DOL =
%D EBIT
%D Sales
3
Degree of Operating Leverage
Three alternatives
• All Variable costs: DOL = 1.00
• Half Fixed, Half Variable: DOL = 1.50
• All Fixed: DOL = 2.00
Units
Price
Var Costs
Fixed Costs
Sales
VC
FC
Total Costs
EBIT
%ΔSales
%ΔEBIT
DOL
All Variable Costs
90
100
$20
$20
$10
$10
$0
$0
$1,800
$900
$0
$900
$900
-10%
-10%
1.00
$2,000
$1,000
$0
$1,000
$1,000
110
$20
$10
$0
Half Fixed Half Variable
90
100
110
$20
$20
$20
$5
$5
$5
$500
$500
$500
$2,200
$1,100
$0
$1,100
$1,100
$1,800
$450
$500
$950
$850
10%
10%
1.00
-10%
-15%
1.50
$2,000
$500
$500
$1,000
$1,000
All Fixed Costs
90
100
110
$20
$20
$20
$0
$0
$0
$1,000 $1,000 $1,000
$2,200
$550
$500
$1,050
$1,150
$1,800
$0
$1,000
$1,000
$800
10%
15%
1.50
-10%
-20%
2.00
$2,000
$0
$1,000
$1,000
$1,000
$2,200
$0
$1,000
$1,000
$1,200
10%
20%
2.00
4
3. Financial Leverage
• Mix of Debt and Equity financing
• Increases as fixed interest payments rise
• Financial Leverage magnifies the effects of
cyclicality on NI (and EPS)
• Financial Leverage is measured by the usual
leverage measures
– See Chapter 3
• Debt/Equity is the most common financial
leverage measure in this context
5
Financial Leverage
Three alternatives
• No Debt: Interest Expense = $0
• Some Debt: Interest Expense = $500
• High Debt: Interest Expense = $800
(These are the “All Variable Cost” example from before)
EBIT
Int Exp
EBT
Taxes
(35%)
NI
%ΔEBIT
%Δ NI
No Debt
$900 $1,000
$0
$0
$900 $1,000
$315
$585
-10%
-10%
$350
$650
$1,100
$0
$1,100
Some Debt
$900 $1,000 $1,100
$500
$500
$500
$400
$500
$600
$385
$715
$140
$260
10%
10%
-10%
-20%
$175
$325
High Debt
$900 $1,000 $1,100
$800
$800
$800
$100
$200
$300
$210
$390
$35
$65
10%
20%
-10%
-50%
$70
$130
$105
$195
10%
50%
6
More about Financial Leverage
• What is the effect on the firm’s Equity Beta from
more debt?
• Recall a Portfolio’s Beta is the weighted average
beta of the components
• So the Company’s Total Beta is the weighted
average beta of the stocks and bonds issued to
finance the company
βPortfolio = E/V βEquity + D/V βDebt
• But the Total Beta is really Asset Beta
βAssets = E/V βEquity + D/V βDebt
7
Beta and Financial Leverage
• We have this relationship:
βAssets = E/V βEquity + D/V βDebt
• But think about βDebt
βDebt = Cov(RDebt,RMkt)/Var(RMkt)
Covariance of debt and the market is close to zero
βDebt ≈ 0
βAssets = E/V βEquity + 0
• Since V = E + D:
βAssets = E/(E + D) βEquity
βEquity = βAssets (E + D)/E
βEquity = βAssets (E/E + D/E)
βEquity = βAssets [1 + D/E]
βEquity = βAssets [1 + (1-T)D/E]
8
Example:
•
CMG is financed only with equity (no debt)
–
This referred to as an “unlevered firm”
•
•
The beta of its stock is 1.02
What is the beta of its assets given that it has no debt?
βEquity = βAssets (1 + D/E) = βAssets (1 + 0/E) = βAssets (1)
βEquity = βAssets = 1.02
• If CMG were to issue enough debt to buy back 20% of its
outstanding stock, what would happen to the beta of the
remaining stock?
D/E = 0.20/0.80 = 0.25
βEquity = βAssets (1 + D/E) = 1.02 (1 + 0.25) = 1.275
• The market risk of the stock increases by 25%
• Solely from a financing decision
9
Recap: Determinants of Equity Beta
1. Cyclical nature of the product
2. Degree of operating Leverage
•
•
DOL = %ΔEBIT/%ΔSales
Is this a business decision or nature of the product?
3. Financial Leverage
•
βEquity = βAssets (1 + D/E)
• We use βEquity to calculate RE
RE = Rf + βEquity[E(RM) – Rf]
• We Use RE to calculate WACC
WACC = WERE + WDRD(1 – TC)
10
Some Beta Terminology
• Corporate Finance: Equity Beta βE and Asset Beta βA
• Investments: Levered Beta βL and Unlevered Beta βU
βE = βL and βA = βU
• Corporate Finance Question:
– Given the Asset Beta (βA cyclicality and DOL), what do financing
decisions do to equity risk (Equity Bata βE) and the cost of equity
capital?
– βA  βE
• Investments Question:
– Given the Levered Beta (the CAPM beta, βL )what does the
company’s risk look like without the leverage (βU)?
– βL  βU
11
Calculating Unlevered Beta
Before (Corporate finance notation)
• Given βA what is βE?
βE = βA [1 + (1-T)D/E]
Now (Investments notation)
• Given βL what is βU?
βL = βU [1 + (1-T)D/E]
βU = βL/[1 + (1-T)D/E]
12
What Happens to Equity Return?
Equity Risk:
βE = βA [1 + (1 - T)D/E]
βL = βU [1 + (1 - T)D/E]
Equity Return:
RE = RA + (RA – RD)(1 – T)D/E
RL = RU + (RU – RD)(1 – T)D/E
(This is MMII with taxes)
13