Frameworks for Valuation:

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Chapter 6
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• Frameworks for Valuation
• Adjusted Present Value (APV)

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Adjusted Present Value

• There are five well-known frameworks for valuing
  a company using discounted flows.
• In theory, each framework will generate the same
  value. In practice, the ease of implementation
  and the interpretation of results varies across
  frameworks.
• In this presentation, we examine how to value a
  company using adjusted present value (APV)

Frameworks for Valuation
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Why Use APV?

• When building an enterprise DCF or
  economic-profit valuation, most financial
  analysts discount all future flows at a constant
  weighted average cost of capital (WACC). Using a
  constant WACC, however, assumes the company
  manages its capital structure to a target
  debt-to-value ratio.
• In cases where the capital structure is expected
  to change significantly, assuming a constant cost
  of capital can lead to misvaluation. In these
  situations, do not embed capital structure in the
  cost of capital, but instead model capital
  structure explicitly.
• The adjusted present value (APV) model separates
  the value of operations into two components the
  value of operations as if the company were
  all-equity financed and the value of tax shields
  that arise from debt financing

Enterprise value as if the company were
all-equity financed
Present value of debt-related tax shields
APV

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APV Valuation Free Cash Flow

• To value a company using APV, start with a
  forecast of free cash flow (FCF). APV-based free
  cash flow is identical to that of enterprise DCF.
• Rather than discount free cash flow at the WACC,
  discount free cash flow at the unlevered cost of
  capital, the cost of capital of an all-equity
  company. We discuss the unlevered cost of
  capital later in this presentation.

Home Depot Unlevered Valuation
Discount free cash flow at the unlevered cost of
equity. For Home Depot, the unlevered cost of
equity is estimated at 9.3 percent.
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APV Valuation Interest Tax Shields

• Next, compute the present value of
  financing-related benefits, such as interest tax
  shields (ITS). Interest tax shields can be
  discounted at either the unlevered cost of equity
  or the cost of debt, depending on your
  perspective of their risk.

Home Depot Interest Tax Shield




To forecast the interest tax shield, first
forecast the level of debt.
A forecast of the marginal tax rate is also
required. Be careful a company must be
profitable to capture tax shields!
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APV Valuation Putting It All Together

• To conclude the APV-based valuation, sum the
  present value of free cash flow and the present
  value of interest tax shields (ITS). This leads
  to the value of operations.

Home Depot Valuation ( million)
Present value of FCF using unlevered cost of
equity
73,557
Present value of interest tax shields (ITS)
2,372
Present value of FCF and ITS
75,928
1.041
Midyear adjustment factor
Value of operations
79,384

• The value of operations for Home Depot is the
  same for both enterprise DCF and APV (79,384
  million). This occurs because we assumed the cost
  of capital for the tax shields (ktax) is equal to
  the unlevered cost of equity (ku). We used this
  assumption when deriving the unlevered cost of
  equity and while discounting the tax shields.

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A Critical Component Unlevered Cost of Equity

• The adjusted present value (APV) model separates
  the value of operations into two components the
  value of operations as if the company were
  all-equity financed and the value of tax shields
  that arise from debt financing

Discounted free cash flow at the unlevered cost
of capital
Discounted tax shields at the unlevered cost of
equity or the cost of debt

• But how do we define the unlevered cost of
  equitythat is, the cost of equity when the firm
  has no leverage, when it is unobservable? We
  rely on the tools of economists Franco Modigliani
  and Merton Miller.

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Modigliani and Miller

• In the 1950s, economists Modigliani and Miller
  (MM) postulated that the value of a firms
  claims must equal the value of its assets.
• They also argued that the weighted average risk
  of a companys financial claims must equal the
  weighted average.

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The Levered and Unlevered Cost of Equity

• Lets start with MMs risk formula

• Multiply both sides by enterprise value. This
  eliminates each fractions denominator.

• Next, use the first equation from the previous
  slide to eliminate Vu (an unobservable value

• Redistribute the terms on the left to collect
  like terms.

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The Levered and Unlevered Cost of Equity
(Continued)

• Dividing the final equation on the previous slide
  by E leads to the generalized cost of equity
  equation

The cost of equity
A premium for increasing leverage
The unlevered cost of equity
A discount for the tax deductibility of interest
payments

• The cost of levered equity (which can be measured
  via regression) is a function of the underlying
  economic risk, the amount of leverage, and tax
  deductibility of interest.

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The Levered and Unlevered Cost of Equity

• The levered cost of equity (ke) is related to the
  unlevered cost of equity via the following
  equation

• Each of the variables can be estimated except the
  risk of tax shields. Most practitioners assume
  ktax ku. This is consistent with a constant
  D/V ratio. When ktax ku, the final term
  disappears and the equation simplifies to

• Many academics assume ktax kd. This leads to
  an alternative representation

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Levered Cost of Equity

• The grid below summarizes the formulas that can
  be used to estimate the levered cost of equity.
  The top row in the exhibit contains formulas that
  assume ktax equals ku. The bottom row contains
  formulas that assume ktax equals kd. The formulas
  on the left side are flexible enough to handle
  any future capital structure but require valuing
  the tax shields separately. The formulas on the
  right side assume the dollar level of debt is
  fixed over time.

Dollar level of debt fluctuates
Dollar level of debt is constant
Tax shields have same risk as operating
assets ktax ku
Tax shields have same risk as debt ktax kd
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Unlevered Cost of Equity

• Since the unlevered cost of equity is
  unobservable, equations on the previous slide
  must be arranged to solve for the unlevered cost
  of equity. Depending on risk of tax shields and
  how the companys debt fluctuates, the formula
  will vary.

Dollar level of debt fluctuates
Dollar level of debt is constant
Tax shields have same risk as operating
assets ktax ku
Tax shields have same risk as debt ktax kd
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Unlevering Example

• Question
• SampleCo maintains a debt-to-value ratio of 1/3.
  If the companys cost of debt is 6 percent, its
  cost of equity is 12 percent, and the marginal
  tax rate is 30 percent, what is the companys
  unlevered cost of equity?
• Solution
• Since the company maintains a constant capital
  structure, we can assume ktax ku. Therefore,
  ku equals