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Chapter 18
VALUATION AND CAPITAL BUDGETING FOR THE
LEVERED FIRM
SLIDES
CHAPTER ORGANIZATION
18.1 Adjusted Present Value Approach
18.2 Flow to Equity Approach
Step 1: Calculating Levered Cash Flow (LCF)
Step 2: Calculating Rs
Step 3: Valuation
18.3 Weighted Average Cost of Capital Method
18.4 A Comparison of the APV, FTE, and WACC Approaches
A Suggested Guideline
18.1 Key Concepts and Skills
18.2 Chapter Outline
18.3 Adjusted Present Value Approach
18.4 APV Example
18.5 APV Example
18.6 Flow to Equity Approach
18.7 Step One: Levered Cash Flows
18.8 Step One: Levered Cash Flows
18.9 Step Two: Calculate RS
18.10 Step Three: Valuation
18.11 WACC Method
18.12 WACC Method
18.13 WACC Method
18.14 A Comparison of the APV, FTE, and WACC Approaches
18.15 Summary: APV, FTE, and WACC
18.16 Summary: APV, FTE, and WACC
18.17 Valuation When the Discount Rate Must Be Estimated
18.18 Beta and Leverage: No Corporate Taxes
18.19 Beta and Leverage: With Corporate Taxes
18.20 Beta and Leverage: With Corporate Taxes
18.21 Summary
18.22 Summary
18.23 Quick Quiz
18.5 Valuation When the Discount Rate Must Be Estimated
18.6 APV Example
18.7 Beta and Leverage
The Project Is Not Scale-Enhancing
ANNOTATED CHAPTER OUTLINE
Slide 18.0 Chapter 18 Title Slide
Slide 18.1 Key Concepts and Skills
Slide 18.2 Chapter Outline
18.1. Adjusted Present Value Approach
Slide 18.3 Adjusted Present Value Approach
The Adjusted-Present-Value (APV) for a project with debt
financing is:
APV = NPV + NPVF.
APV has the conceptual advantage of separating the value of the
unlevered investment from the value of financing side-effects.
NPV is the net present value of the project to an all-equity firm:
NPV = PVUCF – Initial investment for entire project
PVUCF: PV of Unlevered Cash Flows (UCF)
UCF = CF from oper. – Capital Spending – Added NWC
Discount rate: R0 (Unlevered cost of capital)
NPVF is the net present value of financial side effects, which
include:
tax subsidy to debt
the costs of issuing new debt and equity securities
the costs of financial distress arising from the use of
debt
subsidies to debt financing
Students have already seen one of these side-effects: the tax shield
from debt in MM's Proposition I, VL = VU + TCB.
Slide 18.4 –
Slide 18.5 APV Example
An Example of APV and the Tax Subsidy to Debt
Since students are familiar with the Modigliani-Miller
assumptions, our example takes advantage of the simplicity in the
MM world. Suppose PMM, Inc. has an investment that costs
$10,000,000 with expected EBIT (cash flows from operations) of
$3,030,303 per year forever. The investment can be financed either
with $10,000,000 in equity or with $5,000,000 of 10% debt and
$5,000,000 of internally generated (equity) cash flows. The
discount rate on an all-equity-financed project in this risk class is
20%. The firm's marginal tax rate is 34%.
1. All-equity value
Annual after-tax cash flows to unlevered equity are (EBIT)(1- Tc)
= ($3,030,303)(1-.34) = $2,000,000. The net present value of the
project if financed with internal equity is therefore:
NPV = ($2,000,000 / .2) – $10,000,000 = $0
Since NPV = $0, the all-equity firm should be indifferent to
accepting or rejecting the project.
2. Financing side-effect: Tax Subsidy
Note that in the MM world, all cash flows are perpetual and even
debt does not have a maturity date. In the real world, the interest
expense on debt is tax deductible but repayment of principal is not.
In our example, the annual interest payment is RBB = (.10)
($5,000,000) = $500,000. The annual tax subsidy is TC × RB × B =
(.34)(.10)($5,000,000) = $170,000, and the present value of this
financing side-effect discounted at 10% (the market cost of debt)
is:
NPVF =$170,000/(0.10) = $1,700,000.
The Adjusted Present Value of the project is then
APV = NPV + NPVF = $0 + $ 1,700,000 = $ 1,700,000
After including the value of the tax subsidy, stockholders can
expect to gain $1,700,000. The firm should accept the project if it
is financed with $5,000,000 in debt at 10%.
Of course, with perpetual cash flows and no bankruptcy costs, this
is simply the result of MM Proposition I with the value of tax
benefits equal to TCB = $1,700,000. The value of the unlevered
firm is the value of the investment because this is a zero NPV
project, i.e. VU = $1,000,000 and the value of the levered firm is VL
= VU + TCB = $10,000,000 + $1,700,000. The value of debt is VB =
$5,000,000, and the entire subsidy is captured by stockholders, VS
= $6,700,000.
Lecture Tip: This is a difficult chapter. The easiest-to-spot mistake
students want to make is to value every project as a perpetuity
because “that’s how the book does it.” That is why the PowerPoint
slides employ a finite life project as an example. Although this
creates assumption problems (and values are not always equal
across approaches), the benefit is to illustrate a more traditional
project.
18.2. Flow to Equity Approach
Slide 18.6 Flow to Equity Approach
Consider again the MM world and the PPM, Inc. example to
illustrate the Flow-to-Equity (FTE) approach. The three steps in
the FTE approach are as follows:
.A Step 1: Calculating Levered Cash Flow (LCF)
Slide 18.7 –
Slide 18.8 Step One: Levered Cash Flows
Recall that the expected EBIT of the project is $3,030,303. If PPM
Inc. financed the project with $5,000,000 debt at 10% interest, the
net after-tax cash flows to stockholders is:
Cash Flows to Levered Equity = ($3,030,303 – $500,000)(1 – .34)
= $1,670,000
.B Step 2: Calculating RS
Slide 18.9 Step Two: Calculating RS
Since this example is in the MM world, we can use MM
Proposition II (with corporate taxes) to estimate the cost of levered
equity:
Rs = R0 + (B/SL) (1 –tC) (R0 – RB).
The only unknown factor is the optimal debt-to-equity ratio, B/SL.
If we assume that B/SL is 50/67, then the cost of levered equity is:
Rs = 20% + (50/67) (1 – .34) (20% – 10%) = 24.925%
.C Step 3: Valuation
Slide 18.10 Step Three: Valuation
The value of the project to levered equity = $1,670,000 / 0.24925 =
$6,700,000.
The project’s initial cost is $10,000,000, and PPM, Inc. plans to
borrow $5,000,000, implying that $5,000,000 will be from equity.
Therefore, the NPV to stockholders under the FTE approach is
$6,700,000 – $5,000,000 = $1,700,000.
Lecture Note: An observant student may point out that the debt-to-equity
ratio should be 1, not 50/67, in step 2. This is the “trick” that
allows us to obtain the same NPV under both the APV and the FTE
approach. If our “foresight” does not tell us that the debt-to-equity
ratio is 50/67, we need SL to determine RS in step 2, but we will not
know SL until step 3 and we need RS to determine SL. This is a
simultaneity problem that does not have an easy solution. In
practice, the FTE approach seldom generates the same result as
the APV method. The simultaneity problem affects both the FTE
approach and the WACC approach (next section) when the target
debt-to-equity ratio is based on market values. (Note: Chapter 17
discussed how companies determine their capital structure in the
real world.)
18.3. Weighted Average Cost of Capital Method
Slide 18.11 –
Slide 18.13 WACC Method
A firm's overall WACC is a market value weighted average of the
after-tax cost of debt and cost of equity:
RWACC = [B/(B+S)]RB(1 – TC) + [S/(B + S)]RS
The intuition of the WACC approach is simple and appealing. If a
project's expected after-tax return is higher than the weighted
average of the after-tax required returns on debt and equity capital,
it is a positive NPV project. This approach was discussed in prior
chapters, but is reviewed here for comparison.
Continuing the previous example, the weighted average cost of
capital for a levered firm in the MM world is:
B = $5,000,000
S = $6,700,000
RB = 10%
RS = 24.925%
TC = 34%
RWACC = (5,000,000/11,700,000)(.10)(.64) +
(6,700,000/11,700,000)(.24925) = 17.094%
The present value of the after-tax cash flows to the firm discounted
at RWACC is:
PVWACC = ($3,030,303)(1 –.34)/.17094 = $11,700,000
and the
NPVWACC = $11,700,000 – $10,000,000 = $1,700,000.
Of course, this is the same firm value as in the APV and FTE
approaches. Note that the cost of equity, RS, is the same as in the
FTE approach and is based on a debt/equity ratio of 50/67. Hence,
the WACC approach faces the same simultaneity problem as the
FTE approach. This example illustrates that APV, FTE and WACC
are different but complementary ways of valuing the firm. Each
method accounts for the tax benefits of financial leverage
differently, but the value of the benefits is the same under each
approach in the MM world.
Lecture Note: It is important to remind students that the firm's
WACC is only appropriate as a discount rate for a project when:
1. The project has similar systematic business risk as the firm.
2. The project and firm have the same debt capacity.
That is, the WACC formula gives the right discount rate only for
projects that have the same asset and liability mix as the firm, such
as a scale-enhancing expansion of existing firm assets. In practice,
a project's systematic business risk may be different from that of
the firm. A project's debt capacity can also be different than the
average debt capacity of the firm. Each project should be treated
as if it were a mini-firm, with its own proportion of debt and equity
and its own capital costs.
A convenient feature of the WACC approach is that it is often easy
to obtain estimates of RS, RB, B and S. For a publicly traded firm,
the market values of debt and equity can be obtained from the
financial press.
18.4. A Comparison of the APV, FTE, and WACC Approaches
Slide 18.14 A Comparison of the APV, FTE, and WACC Approaches
Slide 18.15 Summary: APV, FTE, and WACC
These three methods for calculating the value of a proposed project
should be viewed as complementary. The following table
summarizes the similarities and differences between the three
methods.
APV WACC FTE
Initial Investment All All Equity Portion
Cash Flows UCF UCF LCF
Discount Rates R0 RWACC RS
PV of financing
effects Yes No No
.A A Suggested Guideline
Slide 18.16 Summary: APV, FTE, and WACC
We suggest the following guideline for choosing between these
models:
Use the WACC or the FTE methods if the target
debt ratio will be constant throughout the life of the project.
Use the APV method if the debt level will be
constant through out the life of the project.
18.5. Valuation When the Discount Rate Must Be Estimated
Slide 18.17 Valuation When the Discount Rate Must Be Estimated
A scale-enhancing project is one where the project is similar to
those of the existing firm.
In the real world, executives would make the assumption that the
business risk of the non-scale-enhancing project would be about
equal to the business risk of firms already in the business.
No exact formula exists for this. Some executives might select a
discount rate slightly higher on the assumption that the new project
is somewhat riskier since it is a new entrant.
18.6. APV Example
Consider the APV example used earlier, with the following
extensions:
a. Subsidized (or below-market-rate) financing
Suppose a municipal government decides that the investment is
socially (and politically) desirable and agrees to raise the
$5,000,000 debt financing as a municipal bond, or 'muni.' PPM,
Inc. can effectively borrow $5,000,000 at the municipality's
borrowing rate, RB = 7%. (Interest income on a muni is exempt
from Federal tax, so the muni rate is typically below the rate on
corporate debt.)
The good news is that the firm is able to borrow at a below-market
rate. The bad news is that this lower interest rate reduces the value
of the tax shield on debt financing. The total present value of both
subsidies is:
NPVF(Municipal Loan)
= Amount borrowed – PV(after-tax interest payments) – PV(loan
repayments)
= $5,000,000 – (1 –.34)(.07)($5,000,000)/(.10) – $0
= $5,000,000 – $2,310,000 – $0 = $2,690,000
The NPVF of $2,690,000 can be decomposed into the tax subsidy
and the below market-rate subsidy. The annual interest expense
through the municipal government is only $350,000. The
opportunity cost (and, therefore, the appropriate discount rate) is
10%, PPM’s cost of debt. Hence, the present value of the tax shield
from debt is ($350,000)(.34)/(0.10) = $1,190,000. (Note: the tax
subsidy is smaller than in the original example, i.e., $1,700,000,
because the interest expense through the municipal government is
lower.)
The second component of the subsidy is the below market-rate
funds provided through the municipal government. The value of
the municipal bond is $350,000 / (0.1) = $3,500,000. If PPM, Inc.
obtains the funds at their normal borrowing rate, the value of debt
would be $5,000,000. The saving through the municipal
government is $1,500,000 ($5,000,000 – $3,500,000).
The total NPVF(Municipal Loan) = PV(tax subsidy) + PV(interest
rate subsidy) = $1,190,000 + $1,500,000 = $2,690,000.
Given the subsidized financing, the APV of the project is:
APV = NPV + NPVF
= $0 + $2,690,000
= $2,690,000
The project is now very attractive.
b. Flotation Costs
When a company raises funds through external debt or equity, it
must incur flotation costs. Assume that the municipal government
no longer sponsored the project and PPM, Inc. must obtain
$5,000,000 with new debt at the market interest rate of 10%.
Flotation costs are 12.5% of gross proceeds.
Since the company must have $5,000,000 in net proceed, it must
raise $5,000,000/(1 –0.125) = $5,714,286. The $714,286 flotation
cost is a cash expense today. The U.S. tax code allows this expense
to be amortized over five years, resulting in a ($714,286/5 years) =
$142,857 deduction per year. Annual tax shields from amortization
of the flotation costs are (.34)($142,857) = $48,571. The net
present value of the after-tax flotation cost is:
NPV(flotation cost) = –$714,286 + $48,571 × [1 – (1/1.1)5]/.1
= –$714,286 + $184,124 = –$530,162
The APV of the project is now:
APV = NPV + NPVF(tax subsidy) + NPVF(issue costs)
= $0 + $1,700,000 – $530,162 = $1,169,838
c. Costs of Financial Distress
Firms should continue to exploit tax shields on interest until the
benefits are offset by the marginal costs of financial distress. This
means that financial distress costs are likely to be non-trivial for an
optimally-financed firm. Unfortunately, financial economists are
no help here. This is bad news for financial managers attempting to
account for costs of financial distress in their analyses.
18.7. Beta and Leverage
Slide 18.18 Beta and Leverage: No Corporate Taxes
The No-tax Case
In a world without taxes, the asset beta of a levered firm is simply
the weighted average of the betas of debt and equity:
ASSET = (Debt/Asset) Debt + (Equity/Asset) Equity
If corporate debt is risk-free, i.e. Debt = 0 then:
ASSET = (Equity/Asset) Equity
Note: this equation is just a rearrangement of equation 18.3 in the
text: Equity = (1 + Debt/Equity)*ASSET.
Slide 18.19 –
Slide 18.20 Beta and Leverage: With Corporate Taxes
The Corporate-tax case
In a world with corporate taxes and risk-free corporate debt, the
relationship between levered equity beta and unlevered beta is:
Equity = [1 + (1 – TC) B/SL]*Unlevered Firm.
In this case, since corporate debt is risk-free, the tax shield benefit
from debt is also risk-free. The systematic risk of the firm is an
average of Unlevered Firm and the risk-free tax shield weighted
according to their market values. Therefore, Levered Firm is lower than
Unlevered Firm. Consequently, the risk of levered equity increases at a
lower rate when there is corporate tax. This is the same result as
MM’s proposition II with tax and without tax.
If corporate debt is not risk-free, the relationship between levered
equity beta and unlevered beta becomes:
Equity Unlevered Firm + (1 – TC) Unlevered Firm - Debt) B/SL.
These two formulas combine assumptions of the CAPM and the
MM Model. Recall that in the MM world with corporate tax, the
optimal capital structure policy is to use 100% debt because the
costs of financial distress are assumed to be zero. Consequently,
applying the levered beta equations to real-world situations that
differ markedly from the MM assumptions can be hazardous (see
Fuller and Kerr [1981] and Butler, Mohr and Simonds [1991]).
This is especially true when the debt/equity ratio changes over
time, as in a LBO.
.A The Project Is Not Scale-Enhancing
If the project is not scale-enhancing (i.e., not within same industry
as existing firm), then we would begin with an industry asset beta,
as opposed to that of the specific firm.
Slide 18.21 –
Slide 18.22 Summary
Slide 18.23 Quick Quiz
To access Appendix 18A (The Adjusted Present Value Approach to Valuing Leveraged
Buyouts) go to www.mhhe.com/rwj.
