Valuation and Taxes

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Valuation and Taxes
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The Effects of Taxes on Valuation

• Learning Objectives
• Effects of Corporate Taxes on Capital Budgeting
• Adjusted Present Value (APV) Method
• Weighted Average Cost of Capital (WACC)

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• Introduction
• Firms can create value by choosing the right
  financing policy
• Later in the semester well carefully analyze why
  and how (capital structure analysis)
• Now, we focus on the tax effects of financing on
  valuation of projects
• Remark
• It is not the differences in the risk of equity
  and debt that make the debt/equity mix relevant
  for valuation
• It is the fact that cash flows to equity and debt
  are differently treated for tax purposes that
  makes the debt/equity mix relevant

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2. Effects of Corporate Taxes on Capital
Budgeting

• (a) Cash flow effects
• A projects value depends on its total cash
  flows (to be shared between creditors and
  shareholders)
• Taxes reduce projects total cash flows
• Since interest payments are treated as an
  expense, debt financing reduces taxes paid and
  so increases after-tax total cash flows (tax
  shields of debt)
• Useful cash flow decomposition
• CF after taxes Unlevered CF Tax subsidy due
  to debt
• where unlevered CF is the cash flow that would
  be generated by the project if the firm was all
  equity financed (i.e., this is simply the free
  cash flow of the project)

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• How to compute unlevered CF?
• If the starting point is earnings
• Unlevered CF EBIT
• or equivalently,
• Unlevered CF Pretax CF - Earnings x Tax Rate

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• (b) Risk effects
• Start with CF decomposition
• CF after taxes Unlevered CF Tax subsidy
• Risk of tax subsidy of debt is different from the
  risk of unlevered CF, so we need to discount them
  at different rates
• Unlevered CF reflects business risk
• Tax subsidy is risk-free if EBIT never falls
  below interest expense. Otherwise it is risky
  too, but this risk differs from the business
  risk.
• What are the proper discount rates for these two
  components?

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Lets look at firms balance sheet
Liabilities
Assets
We know that Let TC be the corporate tax
rate. If debt is static, perpetual, and
risk-free, then Since

when debt is risk-free
we get
Unlevered beta
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Why is useful?

• It allows us to use the comparison method in the
  presence of taxes
• Obtain ?E and D/E for comparison firms, then
  compute ?UA
• ?UA reflects the systematic risk of the core
  business
• Using ?UA in the CAPM equation, we get rUA the
  cost of capital for the project that would apply
  if the firm is all equity financed
• rUA the rate that should be used for
  discounting unlevered cash flows
• Key input for the APV method
• Also useful in calculating WACC from comparison
  firms

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• Example Unlevered Cost of Capital
• Comparison Firms ?E
  D E
• Churchs Chicken 0.75
  0.004 0.096
• McDonalds 1.00
  2.300 7.700
• Wendys 1.08
  0.210 0.790
• rf 4 and the market risk premium is 8.4
• Corporate tax rate 34
• Debt of comparison firms is risk free
• What is the unlevered cost of capital estimated
  from the above comparison data?

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Answer 1. Use to find
unlevered asset betas 2.
Compute the average of betas 3. Apply CAPM
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• Remark Other debt policies
• What if the firm changes D dynamically to keep a
  constant D/E ratio?
• Debt is perfectly correlated with unlevered
  assets (UA)
• Value of tax savings correlated with prior
  period's UA, so approximately
• (i) and (ii)
• Intuition
• First period tax shield is risk free its value
  is and has ß 0
• Remainder of tax shield has ß ßUA
• ßTX is a weighted average of these two betas ,
  but as periods become very short, the zero beta
  part becomes insignificant so
• ßTX ßUA ßA
• In this case, to unlever betas dont use
  but use
  theversion without taxes

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• Example
• The unlevered beta of a firm comparable to Firm X
  is 1.08. Firm X has 20 debt and 80 equity.
  Assume a 35 tax rate.
• What is the appropriate beta for Firm Xs equity
  if
• a) the debt amount will remain the same over
  time?
• b) the debt to equity ratio will stay constant
  (i.e., debt will grow with unlevered assets)?
• Answer
• a)
• b)
• Why is the equity beta higher in part b?
• The financing policy in part b generates riskier
  tax shields relative to part a. Since equity
  holders are the residual claimants, they bear
  this additional risk, and this causes a higher
  equity beta

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3. Adjusted Present Value (APV) Method

• Valuation by components
• Compatible with other valuation methods
• Flexible Approach Can be used with debt levels
  or tax rates that change over time

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Implementation of APV

• Step 1 Separate cash flows into
• Unlevered CF (as if the firm is all-equity
  financed)
• - This is just the free cash flows
• (b) Tax shields
• Step 2 Find the cost of capital (discount rate)
  for each component
• - For unlevered CF, use unlevered cost of
  capital
• - For tax shields, you need a separate
  discount rate
• Step 3 Calculate the PV of each components and
  add these PVs to obtain project PV

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• To find the tax subsidies we need to know the
  debt capacity of the project
• Debt capacity Marginal amount by which a firm
  can increase its debt when it adopts the project
• What determines debt capacity?
• Depends on the financial policy of the firm
• For now we take debt capacity as given (We will
  examine this issue extensively when we focus on
  capital structure in the second part of the
  course)
• Debt Capacity is a dynamic concept
• May change over time and may depend on the
  profitability of the project
• These issues are easier to address within the APV
  framework than with WACC

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• Example APV with risk-free tax shields
• Consider a project with an unlevered cost of
  capital of 14 (i.e., if financed entirely with
  equity). The project is expected to generate the
  following Unlevered CF over the next four years
• Unlevered Cash Flows
• Year 1 Year 2 Year 3 Year 4
• 100 100 1,000 1,000
• Financing plan
• Initial investment is financed with equity in the
  first two years
• After 2 years, the firm will repurchase some of
  its equity and borrow 750 in debt at 8 per year
  (during the last two years of the project)
• The debt is paid off at the end of year 4
• The corporate tax rate is 34
• Find the PV of the project given the financing
  plan

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• Answer
• Compute the present value assuming all equity
  financing
• Compute the debt tax shields generated by debt
  financing
• Add the two components

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• What is the proper discount rate for Risky Debt
  Tax Shields?
• In practice, often the risk-free rate is used
• Risk-free rate will misvalue the tax shields for
  two reasons
• The firm may not be able to take advantage of
  interest tax shields (future EBITs may fall
  below interest payments)
• Firms financing plans can be flexible the firm
  may increase or decrease debt levels (and hence
  the tax shields) in the future
• Two possible solutions
• Expected return of tax shield derived from the
  beta of the debt
• If there is uncertainty about the evolution of
  debt levels, use the derivatives valuation
  (i.e., real options) approach
• - We will see how to do this later on when we
  study real options

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• Example NPV when Debt Tax Shields are Risky
• Calculate the NPV of the following project
• CAPM holds Expected market return 13 and rf
  5
• Initial investment outlay 100M
• Unlevered CF 20M for the next 10 years
• Beta of Unlevered CF is ?UA 1
• Corporate tax rate is 30
• Financing plan
• Project adds 80M to the firms debt capacity
  during its life
• Risky firm debt yields 8 and has beta of 0.25
• On average the company will use 75 of debt tax
  shield
• Assume that beta of tax-shield coincides with
  beta of debt

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• Answer
• 1. PV of the firms UnleveredCF
• 2. PV of the firms tax shields
• a) Expected tax shield
• b) Discount rate
• c) Compute PV of the firms tax shields
• 3. Add PVs and subtract the cost of investment
  to find the NPV

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4. Weighted Average Cost of Capital (WACC)

• Alternative method to incorporate taxes into
  valuation
• Widely used in practice
• Appropriate if projects evaluated have the same
  risks and same debt as the firm as a whole
• WACC is easier to calculate for the whole firm
  than for a single project
• Procedure
• Estimate a projects expected unlevered CF
• Discount unlevered CF at a single rate (i.e.,
  WACC)

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• What is WACC?
• Weighted average of the after-tax expected return
  paid by the firm on its debt and equity
• Why using WACC method may be reasonable?
• 1. Tracking Portfolio Revisited Good projects
  are those that create value by delivering
  future cash flows cheaper than financial assets
  do
• 2. When the project has the same risk and the
  same debt capacity as the firm (i.e., when
  the project is typical), its tracking portfolio
  includes the equity and the debt of the firm
  mixed in the same proportions as in firms
  capital structure

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• Formally
• Consider a project that requires investing C0 to
  produce CF in perpetuity
• Debt Equity to finance project
• A good project should produce CF to cover
  after-tax interest charges and provide the
  required compensation for equity holders
• Hence the project creates value if and only if

Tax Saving
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How to calculate WACC

• Cost of Equity Financing
• Use either CAPM, APT or historical equity returns
• If comparison method is used, need to first
  delever and then relever
• If the firms own historical data is used, and
  the leverage has been stable, then need not to
  adjust for leverage

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• 2. Cost of Debt Financing
• a) Default-Free Debt
• Use Yield-To-Maturity (YTM)
• YTM Discount rate that makes discounted value of
  promised future bond payments equal to the market
  price of the bond
• Good estimate if debt is highly-rated, and not
  callable or convertible
• b) Risky Debt
• YTM overstates cost
• Two alternatives
• Subtract expected losses from default and
  recalculate yields
• Use betas of debt (and then CAPM or APT)
• Junk debt betas range from 0.3 to 0.5

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• Example
• Firm X has outstanding debt that matures in one
  year
• Debt has 8 coupon rate over 1 face value, to be
  paid at the end of the year
• Debt is currently trading for 96 cents on the
  dollar
• If firm X defaults, bondholders are expected to
  recover 90 cents on the dollar
• There is a 15 chance of default
• Estimate the cost of debt,
• Answer
• Find YTM (i.e., return with no default) 2.
  Find the return with default
• 3. Cost of debt (i.e., expected return on debt)
  is the weighted average of returns in the two
  possible outcomes

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• 3. Tax Rate Tc
• If debt is risk-free then Tc Tmarginal
• If debt is risky then Tmarginal cannot be used
• If the probability of fully using the tax shields
  (i.e., the average utilization rate) is stable
  over time
• which gives the tax savings component of WACC
• 2. If probability changes over time
• Not clear if correction overestimates or
  underestimates Tc
• A precise value is very hard to find
• Should use APV

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• Example WACC with risk-free debt
• A 20 debt-80 equity firm borrows at 8
  (risk-free)
• CAPM holds Expected market return 14 and the
  beta of equity 1.2
• Interest is fully tax deductible and corporate
  tax rate is 34
• Find WACC
• Answer
• hence

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• Example continued WACC with risky debt
• Compute WACC when
• Firms bonds have a 15 YTM, and a beta of 0.5
• Interest payments are tax deductible with
  probability 0.75
• Answer
• We need to compute
• Now the expected return on debt is
• The expected tax savings due to leverage are
• Hence WACC is

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• Example Delevering and relevering betas
• A year from today, the project will produce 5 M
  Unlevered CF
• A comparable business has been identified with
  equity beta 1.2 and D/E1.4
• You plan to use D/E1
• Corporate tax rate is 35
• CAPM holds Expected market return 12, rf 4
  
• Both firms have static, perpetual, risk-free debt
• What is the PV of the project?

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• Answer
• Step 1 Obtain the unlevered beta from comparable
  business (delevering)
• Step 2 Obtain the firm equity beta from the
  unlevered beta (relevering)
•  
• Step 3 Get the expected equity return from
  equity beta
• rErf ?E (rM rf) 4 1.04 x (12 4)
  12.32
•  
• Step 4 Calculate WACC
•  Step 5 Calculate PV using unlevered expected CF
  and WACC
• PV5,000,000/(10.0746) 4,652,894

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• Remarks
• and are forward looking expected
  returns, not the expected returns at the time
  the firm has raised financing
• Project WACC and firm WACC are different
• If project risk differs significantly from the
  overall firm risk, using firm WACC based on
  existing projects will give the wrong answer
• Either use project-level WACC, or use marginal
  WACC the WACC that correctly values the whole
  firm after the adoption of the new project

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• Example Project WACC vs. firm WACC
• Company X spends 213,333 per year to lease its
  office space
• X is all-equity financed and has a WACC rE
  20
• X can buy its office space for 1,000,000
• If it decides to buy the building, X will finance
  the purchase with a mortgage obtained at rf 8
  (suppose mortgage is perpetual)
• Marginal tax rate 25
• Should the company buy the building?

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• Answer
• 1. It makes sense to buy if owning costs are
  less than leasing costs
• Leasing costs (1 0.25) x 213,333 160,000
  per year
• Owning cost 0.08 (1 0.25) x 1,000,000
  60,000 per year
• Clearly it makes sense to buy the building
• 2. What happens if you use firms WACC to
  evaluate project?
• But this is wrong!!
• 3. What is the correct WACC?
• Finding WACC in this case is more complicated
  than it looks

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• One may be tempted to say the project is
  all-debt financed, therefore,
• But this is wrong too. Although the cost of the
  project is paid by issuing debt, this is only
  part of projects value. Since we know that the
  project NPV is positive, the PV the project
  generates includes 1 million debt plus some
  surplus accruing to equity holders V D E , D
  1 million, and V gt 1 million, therefore E gt
  0.
• So we should put some weight on equity too in
  calculating WACC.
• But what is the correct weight?
• b) Here the calculation has some circularity. We
  want to find PV. Yet the weight on equity in WACC
  is E/V (PV 1 million)/PV i.e., it is a
  function of PV too

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Rearranging this equation gives the
following Solving this gives PV 2,250,000.
Now we can plug this into WACC Conclusion
When the project risk differs significantly from
the overall firm risk, finding the correct WACC
is a non-trivial task.
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• Example Marginal WACC
• Company X is all-equity financed with a market
  value of 1M and beta 2
• X consists of a project that gives perpetual cash
  flows with expected values that do not change
  with the horizon
• CAPM holds Market premium 6 and rf8
• X is considering a risk-free project that costs
  1M and will be financed with additional equity
• The new project will produce 80,000 per year.
  Assume a tax rate of zero
• Questions
• a) What is the expected cash-flow of X before
  undertaking the project?
• b) What is the expected cash-flow of X if
  project is adopted.
• c) Should X undertake the project?

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• Answer
• a) Before the new project WACC 20, hence the
  yearly expected cash-flow is
• b) After the new project is adopted
• E(CF) 200,000 80,000 280,000
• c) There are two ways to calculate the NPV of the
  new project. Since the project is risk-free,
  obviously the appropriate rate is the risk-free
  rate, 8. There is no tax adjustment, since the
  firm is all-equity financed. Therefore the NPV is
• Hence shareholders are indifferent between
  investing and not investing. Now, lets try to
  value the firm using WACC. After project
  adoption, the firm consists of 2 projects the
  old project with beta 2, and the new project
  with beta 0. Since shareholders are invested 1
  million in each, each project is 50 of the firm
  value. Hence the firm beta is the average of 2
  and 0, which is 1. Given CAPM, this implies a
  WACC of 14. Using this WACC,

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shareholders will invest only if the PV of the
new firm minus the cost of the new project
exceeds the value of the firm without the new
project Since the firm has market value of
1 million without the project, shareholders are
indifferent between investing and not investing.
WACC 14 gives the right answer. Here, 14 is
the marginal WACC the cost of capital that
applies if the firm adopts the project. A common
mistake here would be to apply beta 2 and a
resulting WACC 20 in evaluating the new
project. But notice that beta 2 reflects the
risk of the old project of the firm. The new
project reduces overall firm risk, since it is
risk-free. Therefore, if we desire to use a
company-wide WACC, the return on equity in WACC
calculation should be based on the new risk
profile of the firm.
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• WACC and leverage effects
• a) Without taxes firm WACC is independent of
  leverage
• Portfolio theory intuition
• Without taxes (and no other effects of debt on
  cash flows) return on assets must coincide with
  return on liabilities
• b) With taxes firm WACC depends on leverage and
  on financing plan
• If debt is static, and perpetual, firm WACC
  decreases with leverage
• b) If debt is kept at a constant ratio of
  project value
• c) With more complicated financing plans WACC is
  very impractical and difficult to compute

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• On the practical use of APV vs. WACC
• - APV is easy to understand, and easy to adapt
• - Useful for flexible financing plans (debt
  ratio changing over time)
• - Required for LBOs and when there are
  financing subsidies
• - WACC requires that the project is a carbon
  copy of the firm in terms of risk and debt
  capacity
• Advantages of WACC
• 1. WACC is very intuitive a project should earn
  a higher return than the cost of capital
• 2. WACC is easy to implement in a company
  where capital budgeting is decentralized