Capital budgeting and valuation
with leverage
Chapter 18
outline
Focus on constant debt to equity ratio
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Present WACC valuation method
WACC/APV link
Project based WACC
Levering up and WACC
Capital budgeting procedure
• Remember the steps we follow
– Estimate the incremental cash flows generated by the
project
– Discount the free cash flow based on the project’s
cost of capital to determine the NPV
• How to estimate the appropriate cost of capital?
• How does the financing decision affect the free
cash flows and the project’s cost of capital?
Some simplifying assumptions
• To lay out the method of valuation we require
three simplifying assumptions
– The project has average risk (same as the firm’s)
– The firm’s debt-to-equity ratio is fixed over time
– Corporate taxes are the only imperfection
• We will simplify some assumptions later on
The WACC method
To calculate project value
• Calculate project’s (unlevered) FCFs
– see chapter 7
• Discount using WACC
rwacc = E/(E+D) rE + D/(E+D) rD(1-τc)
VL = PV(FCF’s, rwacc)
Deriving the WACC method
Deriving the WACC method
Using WACC an Example
• Example page 577
• Avco, Inc. is a manufacturer of custom packaging
products and is considering a new line of packaging
(RFX) that includes an embedded radio-frequency
identification tag. This improved technology will
become absolute after 4 years. In the meanwhile it
is expected to increase sales by $60 million per year.
Manufacturing costs and operating expenses are
expected to be $25 million and $9 million
respectively per year.
Using WACC an Example
• Example continued
• Developing the product will require upfront R&D
and marketing expenses of $6.67 million together
with an investment of $24 million in equipment.
The equipment will be obsolete in four years and
will depreciate via straight-line method over that
period. Avco bills its customers in advance, and it
expects no net working capital requirements for
the project. Avco’s tax rate is 40%.
First step: predicting FCF’s
• This implies the following steam of expected
future cash flows
Calculating WACC
• The market risk of RFX is expected to be
similar to that for the company’s other lines of
business.
• We will use WACC to discount the cash flows
generated from the project
• We need information on the Avco’s capital
structure
• This can be found in the firm’s balance sheet
The data we need
NPV calculation
Using the APV method when D/E ratio is fixed
• See chapter 15 for the case of fixed $D
• Alternative method of valuation
APV:
VL = APV = VU + PV(int. tax shield)
• First, calculate the unlevered value VU by discounting FCF’s
using rU. With constant D/E ratio we can estimate rU by:
rU = (D/(E+D))rD + (E/(D+E))rE
• Second, calculate the value of the interest tax shield. With
constant D/E ratio we discount the tax shield with rate rU
Deriving the unlevered cost of capital
Deriving the unlevered cost of capital
The unlevered value of the project
• The RFX project has initial investment of $28
million and 4 annual FCF’s of $18 million
• We discount FCF’s using Avco’s unlevered cost
of capital (with target leverage ratio)
The WACC/APV link
Financing the project with fixed D/E
ratio
• The value of leveraged project (in $millions):
time
0
1
2
3
4
VLt
61.24
47.42
32.64
16.86
0
• To maintain the ratio D/E=1
time
0
1
2
3
4
Debt
30.62
23.71
16.32
8.43
0
Equity
30.62
23.71
16.32
8.43
0
Finding expected interest payments
• Given debt levels (in $millions):
time
0
1
2
3
4
Debt
30.62
23.71
16.32
8.43
0
• We calculate interest payments and tax shield
with tax rate of 40% and interest of 6%
time
0
1
2
3
4
interest
0
1.84
1.42
0.97
0.505
0.73
0.57
0.39
0.20
Tax shield
Discounting interest tax shield
One more example
• Example – Avco is considering an acquisition
of another firm in the same industry. Expected
FCF’s will increase by $3.8 million @ t=1, and
will grow at annual rate of 3% from then on.
The purchase price is $80 million will be
financed with $50 million in new debt initially.
Avco maintain a constant D/E ratio for the
acquisition.
Valuation the acquisition using APV
Valuation using WACC
Project-based cost of capital
Project-based cost of capital
how to find WACC of project?
• Up to now we assumed that the project is in the
same line of business as the rest of the firm and
that it is financed while maintaining the same
capital structure
• This allowed us to assume that the cost of capital
of the project equals the firm’s WACC
• Sometimes these assumptions do not apply
• Consider GE
– GE Commercial Finance, GE Aviation, GE Healthcare,
GE Energy, NBC Universal, among others
Project-based cost of capital
Comparable firms
Firm
project
rU (comp. firms) = rU (project)
Project-based cost of capital
Calculating WACC for project
• Identify comparable firms in the same industry of
the project (comparable risk)
• Calculate average unleveraged cost of capital of
comparable firms
• Use this as the project’s unleveraged cost of
capital
• Given debt cost of capital you can calculate the
project equity cost of capital
• Then, given tax rate and firm’s capital structure
you can calculate WACC for the project
Project-based cost of capital
Numerical example
• Suppose now that Avco launches a new plastics
manufacturing division with different market risk
than its main packaging business
• WACC of Avco is no longer relevant to us
• Instead, we estimate the unlevered cost of capital
(rU) of other plastic manufacturers
• Remember this represents the underlying risk of
the firm’s assets before we account for leverage
effects
Step one: calculate unlevered cost of
capital for comparable firms
• You identify two single-division plastics firms
that have similar business risk
Step two: calculate equity cost of
capital for project
• Back to our project
• Remember, our project will be financed with debt
and equity and therefore we will benefit from the
interest tax shield
• Suppose Avco maintains its capital structure
(equal mix of debt and equity) when adopting the
project, and that it will continue to borrow at 6%
• Then, Avco’s equity cost of capital is
Step 3: calculate WACC for project
• Once we have the equity cost of capital, the
debt cost of capital, and marginal tax rate we
can compute the project’s WACC
Changing Capital Structure and
WACC
Levering up and WACC
• What happens to WACC when the firm
increases leverage?
Example page 592
• Consider a firm with debt-to-equity ratio of
25%, debt cost of capital of 6.67%, equity cost
of capital of 12%, and tax rate of 40%
• Its current WACC is,
Levering up and WACC
• Example continued
• Now suppose that the firm changes its debtto-equity ratio to 50%
• What is wrong with the calculation:
rWACC (new) = 0.5 x 12% + 0.5 x 6.67% x (0.6) = 9%
Levering up and WACC
• Two things can happen when levering up
– First with higher leverage payments to equity holders
bear more risk
– Second with higher leverage the required rate of
return on the firm’s debt by investors might increase
• Suppose that now debt holders require 7.34%
instead of 6.67%
• To recalculate the firm’s WACC lets go back and
calculate the firm’s unlevered cost of capital
Levering up and WACC
Assigned problems
• Problems page 611-618
• 2, 5,14