Risk (beta), Return & Capital Budgeting
Chpt. 12: problems 2,6,9,13,15
I. Applications of CAPM
1) risk premium
estimate from historical data (Ibbotson)
2) risk free rate
Tbill vs. Tbond, consistent with risk premium
3) Calculating beta: Regression analysis
β i=σ i,m /σ m2
Chpt 12 - 1
Basic Methodology:
The basic approach is to run a regression of returns on the stock on returns
on the market,
Rit = ai + biRmt + e it
where
Rit = returns on stock i in interval t (t=1,…,T)
Rmt = returns on market index in interval t
ai = intercept from regression (alpha)
bi = estimate of beta
e it = error term in the regression
Calculating returns:
stock return = (Pt – Pt-1 + Div)/Pt-1
(returns must be split adjusted)
market return = (Indext – Indext-1)/Indext-1+ Dividend yield
Key output from the regression:
Slope (beta): This is an estimate of the beta of the firm which can then be
used in the CAPM.
Variance of the stock (σ j2): This is the total return variance of the stock
over the time period for which you have historical returns (If you use daily
(weekly, monthly) returns this will be a daily (weekly, monthly) variance
and can be annualized by multiplying by 365 (52,12).
Variance of the market index (σ m2): This is the total return variance of the
market index that you use in the regression.
Systematic variance (=β 2σ m2): This is the portion of the total variance of the
stock returns that is due to market movements (and hence cannot be
diversified).
Unsystematic variance (= σ j2 - β 2σ m2): This is the portion of the total
variance of the stock returns that is firm-specific and can be diversified
away.
R2 ( = β 2σ m2/σ j2): This is the proportion of the total variance of the stock
that is due to market movements. A high (low) R squared indicates that a
small (large) proportion of the firm’s total risk is due to firm-specific risk.
Practical aspects of estimating beta.
Chpt 12 - 2
Example: Home Depot
S&P*
RSPLS
RS&P
[RSPLS-average(RSPLS)] 2
2.2357
306.05
6.017
387.86
9.1704
417.8
8.5011
458.93
9.2739
462.71
8.8047
584.41
12.5584
687.33
17.2644
947.28
26.1656
1017.01
45.5687
1282.71
48.5625
1520.77
*split & dividend adjusted
169.13%
52.41%
-7.30%
9.09%
-5.06%
42.63%
37.47%
51.56%
74.15%
6.57%
26.73%
7.72%
9.84%
0.82%
26.30%
17.61%
37.82%
7.36%
26.13%
18.56%
1.589275
0.008727
0.253661
0.115435
0.231607
0.000019
0.003129
0.007211
0.096651
0.133199
0.007817
0.010344
0.006473
0.029125
0.007076
0.000008
0.039723
0.011085
0.006783
0.000045
43.07%
17.89%
Variance
0.271
0.013
s.d.
0.521
0.115
Date
Home Depot*
Sep-90
Sep-91
Sep-92
Sep-93
Sep-94
Sep-95
Sep-96
Sep-97
Sep-98
Sep-99
Sep-00
Ave return
[RS&P-average(RS&P)] 2 [RSPLS-average(RSPLS)]
*[RS&P-average(RS&P)]
0.111458
-0.009501
0.040520
0.057983
-0.040483
0.000012
-0.011148
-0.008941
0.025604
-0.002443
Covariance
0.018
Correlation
0.303
Beta
1.376
Chpt 12 - 3
II. DETERMINANTS OF BETA:
1) Operating leverage
Price – variable cost = contribution margin
Operating lev
= % change in EBIT for a given % change in sales
= change in EBIT/EBIT x sales/change in sales
Increases in fixed costs
Decreases in variable costs
2) Financial leverage
Equity (levered) beta vs. asset (unlevered) beta
With no taxes, beta of a portfolio of debt & equity = beta of assets, or
βA =
D
E
βD +
βE
D+E
D+E
If Debt is not too risky, assume β D = 0 , so
βA =
E
βE
D+E
or
 D
β E = β A 1+ 
E

In most cases, it is more useful to include corporate taxes (hint: use this
for the Boeing case!). If so, then
D

β E = β A 1 + (1 − T ) 
E

where T is the corporate tax rate.
The beta of a project should match the risk of the assets.
Chpt 12 - 4
Example: McDonnell Douglas equity betas at different levels of leverage.
Current equity (levered) beta 0.59
D/E .875%
current tax rate 34%
market premium = 8.5%
current T-Bill rate = 5.24%
Unlevered beta = current beta/(1 + (1-tax rate)(D/E)
= .59/(1+(1-.34)(.875) = .374
Levered beta at different levels of debt can be estimated:
Levered beta = unlevered beta*(1+(1-tax rate)(D/E)
D/(D+E)
D/E
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.00
0.11
0.25
0.43
0.67
1.00
1.50
2.33
4.00
9.00
Levered
beta
0.37
0.40
0.44
0.48
0.54
0.62
0.74
0.95
1.36
2.60
Cost of
equity (%)
8.42
8.65
8.94
9.32
9.82
10.52
11.57
13.31
16.81
27.30
The unlevered beta (asset beta) for a multi-divisional firm is the weighted
average of the unlevered betas for the divisions, where the weights are the
relative market values.
Chpt 12 - 5
Estimating betas using betas of comparable companies:
Example: Continental Airlines, 1992 restructuring
American
Airlines
Delta Air Lines
United Airlines
USAir Group
Average
D/(D+E) 1
0.598
D/E
1.49
Equity beta
1.45
0.380
0.430
0.740
0.537
0.61
0.75
2.85
1.16
1.10
1.25
1.65
1.36
Unlevered beta of comparable companies =
asset beta for Continental =
1.36/(1+(1-.34)(1.16)) =
0.77
Note: Industry betas: text (p. 315) calculates industry betas as the average
of equity betas, and does not account for differences in leverage.
Chpt 12 - 6
Examples: Estimating beta
Novell, which had a market value of equity of $2 billion and a beta of 1.50,
announced that it was acquiring WordPerfect, which had a market value of
equity of $1 billion, and a beta of 1.30. Neither firm had any debt in its
financial structure at the time of the acquisition, and the corporate tax rate
was 40%.
a. Estimate the beta for Novell after the acquisition, assuming that the
entire acquisition was financed with equity.
b. Assume that Novell had to borrow the $1 billion to acquire WordPerfect.
Estimate the beta after the acquisition.
Southwestern Bell, a phone company, is considering expanding its
operations into the media business. The beta for the company at the end of
1995 was 0.90, and the debt/equity ratio was 1. The media business is
expected to be 30% of the overall firm value in 1999, and the average beta
of comparable media firms is 1.20; the average debt/equity ratio for these
firms is 50%. The marginal corporate tax rate is 36%.
a. Estimate the beta for Southwestern Bell in 1999, assuming that it
maintains its current debt/equity ratio.
b. Estimate the beta for Southwestern Bell in 1999, assuming that it decides
to finance its media operations with a debt/equity ratio of 50%.
Chpt 12 - 7
III. COST OF CAPITAL
The key is that the rate will depend on the riskiness of the cash flows from
assets.
The cost of capital is an opportunity cost -- it depends on where the money
goes, not where it comes from.
i. Estimating the cost of equity:
a. The dividend growth model approach
RS = D1/P0 + g
We can observe P0 and D0. D1 = D0(1+g). We need to estimate g,
either using historical data or an analyst's forecast.
b. The SML approach
RS = Rf + ß S x [RM - Rf]
ii. The cost of debt: Cost of debt, RB, is the interest rate on new borrowing.
Historic debt cost is irrelevant.
a. Yield on currently outstanding debt.
b. Yields on newly-issued similarly-rated bonds.
Chpt 12 - 8
iii. The cost of preferred stock
Valuing preferred stock as a perpetuity, the cost is
RP = D/P0
(i.e. the dividend yield)
Weighted average cost of capital (WACC)
Let
S = market value of the equity (# shares x price/sh )
B = market value of the debt (price x # bonds)
(may use book value for short term debt)
Then
V=S+B
1 = S/V + B/V = 100%
The firm's capital structure weights are S/V and B/V.
The weighted average cost of capital is calculated as:
RWACC = (S/V) x RS + (B/V) x RB x (1 - TC)
where RB x (1 - TC) = after tax cost of debt
Chpt 12 - 9
Example, WACC:
Hills Stores has 1 millions shares of common stock outstanding with a
market price of $12 per share. The firm's outstanding bonds have ten years
to maturity, a face value of $5 million, a coupon rate of 10%, and sell for
$985 per $1000 in face value. The risk-free rate is 5.5%, and the expected
return on the market is 14%. Hills stock has a beta of 1.2, and Hills is in the
34% tax bracket.
Example, WACC & capital budgeting:
A project can save $6 million cash at the end of the first year and these
savings will grow 4% per year indefinitely. The debt/equity ratio = 5, cost of
equity = .20, and aftertax cost of debt = .12. The new project has the same
risk as the overall firm.
Under what circumstances should the firm accept the project?
Chpt 12 - 10