Download Risk, Return and Capital Budgeting

Risk, Return
and Capital Budgeting
For 9.220, Term 1, 2002/03
02_Lecture15.ppt
Student Version
Outline
1.
2.
3.
4.
5.
Introduction
Project Beta and Firm Beta
Cost of Capital – No tax case
What influences Beta?
Cost of Capital in the Real World
a) Weighted Average Cost of Capital
(WACC)
b) Adjusted WACC
6. Summary and Conclusions
1
Introduction
In doing an NPV, IRR, or PI analysis, we need to have the
relevant discount rate for our project.
Now that we have a better understanding of the relation
between expected return and risk, we can use this to
develop an appropriate discount rate (cost of capital or
opportunity cost of capital) for our analysis.
The implicit comparison we then make when doing capital
budgeting analysis is … should we fund the project or would
we be better off if we place the funds in similar risk financial
securities (that are expected to make the return predicted by
our risk/return model) – the forgone returns from the
financial securities represent our opportunity cost.
We will explore how to determine the firm’s risk and the
project’s risk – and thus the opportunity cost of capital.
A complication we consider is incorporating taxes into the
cost of capital derivation.
Project and Firm Beta
If we know the risk of a project, we can determine the
opportunity cost of capital related to the project.
In most cases it is not possible to directly observe the β of a
project.
If our project is the same risk as our own firm, then we can
jump ahead and use the Weighted Average Cost of Capital
(WACC) for our firm. If not, we must try to find similar risk
comparable companies that have publicly traded equity
outstanding.
Then we can use regression analysis to estimate our
comparable companies’ equity β’s .
Since, even with identical assets, companies’ equity β’s will
differ as the level of debt financing (financial leverage)
differs, we must first make the β’s comparable.
We do this by converting each equity β into an asset or firm β.
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Equity
β and Asset (or firm) β
from comparable companies
Consider holding a portfolio that consists of all the equity
of a firm plus all the debt of a firm. What does this
portfolio own?
Recall the accounting identity…
Now determine the β of this portfolio
βassets = xequity●βequity + xdebt●βdebt
(Since
βdebt is usually very low, for simplicity, it often assumed to be zero.)
Use the data on the next slide to calculate the asset beta
for an oil exploration project – use comparable companies
to estimate the βasset for the project.
Comparable Companies with
SIC=1311
Equity
Beta
D/E
D/(D+E)
E/(D+E)
Asset
Beta
DENBURY
RESOURCES INC
0.89
92.06
47.93%
52.07%
0.46
CANADIAN NATURAL
RESOURCES
0.80
76.81
43.44%
56.56%
0.45
PANAFRICAN
ENERGY
0.45
-
0.00%
100.00%
0.45
TETHYS ENERGY
INC
0.75
65.37
39.53%
60.47%
0.45
CANADIAN 88
ENERGY CORP
0.74
64.29
39.13%
60.87%
0.45
0.73
59.71
34.01%
65.99%
Company Name
Column Average
0.46
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Determining the project’s
βequity from its βassets
Our firm will have its own unique amount of financial
leverage (debt) in its financing mix (capital structure).
Thus, we can use the βassets from the comparable firms for
our project’s overall β. But we need to determine our
project’s βequity so we have the relevant cost of equity
capital related to the project. Use the comparable firms’
βassets and our firm’s specific D/E ratio to do this:
Βequity = βassets●(1 + D/E)
(assumes βdebt =0)
Suppose our firm had a D/E ratio of 1.5, then what is the
βequity for our firm?
βequity =
Cost of equity – return to the CAPM
If we know the βequity, then we can use
the CAPM to determine the E[Requity].
E[Requity] =Rf+βequity●(E[RM]-Rf)
Suppose Rf = .035 and E[RM]=.095
Then E[Requity] =
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Cost of Debt
We know from our D/E ratio of 1.5 that the
target financing for our firm includes a lot
of debt. Thus we have to include the
relevant proportion of debt financing when
determining the overall cost of capital for
our project.
Suppose each of our company’s bonds has
face value of $1,000, a coupon rate of 5%,
20 years until maturity, and a current
market price of $1,219.35.
What is the cost of debt (express as an
effective annual rate)?
Overall Cost of Capital for the
Project
Given the cost of equity financing for the project and the
cost of debt financing for the project, we can calculate the
overall cost of financing for the project as follows:
WACC =
D
E
• E [RD ] +
• E [RE ]
D+E
D+E
This is known as the weighted average cost of capital. The
above equation is calculated ignoring tax effects or
assuming there are no taxes.
Later we will look at WACC for the firm as a whole; note, in
our analysis here we are determining the WACC for the
project because we are using a cost of equity for the
project that is adjusted for the project’s risk – so, as
calculated here, this is not the WACC for the firm!
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A quick check in the no-tax case
With risk-free debt and no taxes, we
can also calculate the project’s WACC
directly from the asset β of the
project and the CAPM.
E[Rproject] =Rf+βproject●(E[RM]-Rf)
=
What affects the asset β?
Cyclicality of Revenues
The more a firm’s revenues move
with market conditions (i.e., are
cyclical), then the more its cash
flows will be correlated with the
market. This correlation causes the
asset β to be positive.
Next consider costs …
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Operating leverage
and the effect on asset β
Operating leverage is the degree of fixed costs in a firm’s
cost structure and is formally defined as follows:
% ∆ in EBIT
% ∆ in Sales
∆EBIT • Sales
=
EBIT ∆Sales
Operating Leverage =
The higher the degree of fixed costs relative to variable
costs, the more EBIT will change as revenues change;
therefore the higher will be a firm’s asset β.
Operating Leverage Example
Company L
Normal High
Market Market
Units Sold
100
210
Total Sales $ $1,000 $2,100
Variable Costs $800 $1,680
Fixed Costs
$150 $150
EBIT
$50
$270
Company H
Normal High
Market Market
100
210
$1,000 $2,100
$200 $420
$750 $750
$50
$930
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From asset β to equity β
We have already seen that the amount of
financial leverage (or proportion of debt
financing) causes there to be a difference
between the firm’s asset β and its equity β.
Given risky cash flows produced by the firm’s
assets, a higher debt level makes the cash flows
left for equity holders even more risky.
Thus higher financial leverage increases the
equity β relative to the asset β.
Reconsider Company H with low and high debt
levels.
Financial Leverage Example
H: Low Debt
H: High Debt
Normal High
Normal High
Market Market Market Market
Units Sold
100
210
100
210
Total Sales $
$1,000
$2,100
$1,000
$2,100
Variable Costs
$200
$420
$200
$420
Fixed Costs
$750
$750
$750
$750
EBIT
Interest
EBT
$50
$10
$40
$930
$10
$920
$50
$200
-$150
$930
$200
$730
Notation: EBT = Earnings Before Tax
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Financial leverage and equity β:
conclusions from the example
Suppose total assets are $8,000 in both cases.
Also suppose that in the low-debt case the debt is $250.
Then equity in the low-debt case must be $7,750.
In this example, the high debt case has 20 times as much
debt in the capital structure (compare the interest charges).
This implies that in the high-debt case, debt must be
$5,000 and therefore equity is only $3,000.
Ignoring taxes, look at the standard deviation of ROE in the
two cases.
Low-debt case: σROE = .08029
High-debt case: σROE = .20742
So high financial leverage (higher D/E) implies more
variable returns to equity holders. Given some correlation
between revenues and the market and a positive asset β,
the higher variation in ROE due to higher financial leverage
implies a higher equity β.
Conclusions on factors that affect β
The three factors that affect an equity
β are as follows
Cyclicality of Revenues
Operating Leverage
Financial Leverage
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WACC and Corporate Taxes
When the real-world consideration of tax is brought into
the analysis, it is more difficult to convert between
asset and equity β’s and thus it is more difficult to use
comparable firms’ data to determine the overall cost of
capital for a specific project.
The reason is that debt interest payments reduce taxes;
thus, holding fixed the risk of the before-tax cash flows,
more debt makes total after-tax cash flows to security
holders greater and of less overall risk.
More debt results in more cash saved from paying tax,
therefore there is more cash in total to be paid to debt
and equity holders. In addition, tax savings are usually
lower risk cash flows. Thus with tax savings added back
into the after-tax cash flows, there is a lower overall
risk of the total after-tax cash flows to debt and equity
holders.
What is the solution with taxes?
We could solve for an after-tax adjusted asset β or we
could derive a new method for converting between
asset and equity β’s in the context of taxes, however,
these tasks are beyond the scope of this course.
Instead, we can look to the after-tax WACC for our
firm as a whole because we can usually observe our
own firm’s securities and their risk characteristics.
With corporate taxes, the only change in the firm’s
cost of capital is that the after-tax cost of debt is
lower. The after tax cost of debt is
This can now be used in the WACC equation.
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WACC revised for taxes
WACC =
D
E
• E[RD ] • (1 − TC ) +
• E [RE ]
D+E
D+E
Redo the WACC with our original data
E[RE]=10.4%
(assume this is the firm’s cost of equity
capital)
E[RD]=3.5%
D/E = 1.5
And now, assume TC=40%
WACC Example 1 – Self Study
Determine the firm’s WACC given the
following data.
Debt financing = 160,000 bonds currently priced
at $1,250 each
Equity financing = 10,000,000 shares currently
priced at $30 per share
Equity β = 1.8 D=
Debt β = 0.2 E=
Rf = 4%
Use CAPM to get E[RD]=
E[RM] = 10% Use CAPM to get E[RE]=
TC = 45%
WACC=
=.10024=10.024%
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WACC Example 2 – Self Study
Determine the firm’s WACC given the
following data.
D/E = 0.6
Current equity price = $50/share. Next constant
annual dividend occurs in one year and is $6.
Bonds are currently priced @ $926.60, coupon rate is
4% (semiannual coupons), face value is $1,000, and
maturity is in 10 years.
TC = 45% Set E = 1, solve for D =
Solve for E[RD]=
Solve for E[RE]=
WACC=
=.0853124=8.53124%
Project risk ≠ Firm Risk
Unfortunately, in the tax case we have limited
ourselves to calculating the WACC from the observed
debt and equity securities (and their returns) of the
firm – not for individual projects.
Thus, if we are to use WACC in the tax case, we must
ensure our project’s systematic risk is identical to our
firm’s overall systematic risk level.
If the project’s market risk is different from the firm’s
market risk, then applying the WACC as the discount
rate will produce an incorrect NPV.
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Project
risk ≠ Firm Risk:
Errors that result if WACC is used as the discount rate
Adjusted WACC
when Project Risk ≠ Firm Risk
We would need to adjust the WACC to reflect the different risk
of the project’s cash flows.
an upward adjustment to WACC to get the discount rate for more
risky projects.
a downward adjustment to WACC to get the discount rate for less
risky projects.
Similarly, a project may have various cash flows with different
risk levels. For example, CCA tax shields are generally thought
to have a lower systematic risk than revenues. Thus we should
have a downward adjustment to WACC to get the discount rate
for CCA tax shields. If some revenues had a higher systematic
risk than the corporation, then we should have an upward
adjustment to the WACC to get the discount rate for these
revenues.
For this course, we will not do the adjustment, but you should
be aware of this important issue and the direction and impact
of such adjustments.
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Summary and Conclusions
In a no-tax world, if we know about a project’s risk, then we
can use the CAPM (or other risk/return models) to determine
the discount rate for the project.
A project or firm’s asset risk, as measured by βassets, is
influenced by the cyclicality of revenues and the degree of
operating leverage. Financial leverage magnifies the asset β
into the equity β.
In the real-world situation that includes taxes, we can use the
firm’s securities to calculate the WACC. Here, the after-tax
cost of debt is used.
The WACC can then be used as the discount rate for the
analysis of projects as long as the projects have the same
market risk as the firm.
If project risk is different, then WACC cannot be used as
shown. WACC must be adjusted up or down to get the correct
discount rates for higher or lower risk projects and for higher
or lower risk cash flows.
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