17.1 Adjusted Present Value Approach

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17.1 Adjusted Present Value Approach

• The value of a project to the firm can be thought
  of as the value of the project to an unlevered
  firm (NPV) plus the present value of the
  financing side effects (NPVF)
• There are four side effects of financing
• The Tax Subsidy to Debt
• The Costs of Issuing New Securities
• The Costs of Financial Distress
• Subsidies to Debt Financing

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APV Example

• Consider a project of the Pearson Company, the
  timing and size of the incremental after-tax cash
  flows for an all-equity firm are
  
• Cash inflows 500,000 per year forever Tc34
• Cash costs 72 of sales Initial Investment
  475,000
  
• The unlevered cost of equity is r0 20

The project would be rejected by an all-equity
firm NPV
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APV Example (continued)

• Now, imagine that the firm finances the project
  with 126,229.5 of debt at rB 10.
  
• Pearsons tax rate is 34, so they have the
  present value of interest tax shield worth TCB
  .34126,229.5 42,918.

• The net present value of the project under
  leverage is

• So, Pearson should accept the project with debt.

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17.2 Flows to Equity Approach

• Discount the cash flow from the project to the
  equity holders of the levered firm at the cost of
  levered equity capital, rS.
  
• There are three steps in the FTE Approach
• Step One Calculate the levered cash flows
• Step Two Calculate rS.
• Step Three Valuation of the levered cash flows
  at rS.

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Step One Levered Cash Flows for Pearson

• UCF LCF (1-Tc)rBB
• Each period, the equity holders must pay interest
  expense. The after-tax cost of the interest is
  BrB(1-TC) 126,229.50.1(1-.34) 8,331.15
  
• LCF 92,400 - 8,331.15 84,068.85

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Step Two Calculate rS for Pearson
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Step Three Valuation for Pearson

• Discount cash flows to equity holders at rS
  22.2

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17.3 WACC Method for Pearson

• To find the value of the project, discount the
  unlevered cash flows at the weighted average cost
  of capital.
  
• Pearson Inc. target debt to value ratio is 1/4

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Valuation for Pearson using WACC

• To find the value of the project, discount the
  unlevered cash flows at the weighted average cost
  of capital

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17.4 A Comparison of the APV, FTE, and WACC
Approaches

• All three approaches attempt the same
  taskvaluation in the presence of debt
  financing.
  
• Guidelines
• Use WACC or FTE if the firms target
  debt-to-value ratio applies to the project over
  the life of the project.
  
• Use the APV if the projects level of debt is
  known over the life of the project.
  
• In the real world, the WACC is the most widely
  used by far.
  

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Summary APV, FTE, and WACC

• 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
• Which approach is best?
• Use APV when the level of debt is constant
• Use WACC and FTE when the debt ratio is constant

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17.5 APV Example

• Worldwide Trousers, Inc. is considering a
  5 million expansion of their existing business.
  The initial expense will be depreciated
  straight-line over 5 years to zero salvage value
  the pretax salvage value in year 5 will be
  500,000. The project will generate pretax
  earnings of 1,500,000 per year, and not change
  the risk level of the firm. The firm can obtain a
  5-year 3,000,000 loan at 12.5 to partially
  finance the project. If the project were financed
  with all equity, the cost of capital would be
  18. The corporate tax rate is 34, and the
  risk-free rate is 4. The project will require a
  100,000 investment in net working capital. 
  Calculate the APV.

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APV Example Cost
Lets work our way through the four terms in this
equation
The cost of the project is not 5,000,000.
We must include the round trip in and out of net
working capital and the after-tax salvage value.
NWC is riskless, so we discount it at rf. Salvage
value should have the same risk as the rest of
the firms assets, so we use r0.
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APV Example PV unlevered project
Turning our attention to the second term,
The PV unlevered project is the present value of
the unlevered cash flows discounted at the
unlevered cost of capital, 18.

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APV Example PV depreciation tax shield
Turning our attention to the third term,
The PV depreciation tax shield is the present
value of the tax savings due to depreciation
discounted at the risk free rate , at rf 4
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APV Example PV interest tax shield
Turning our attention to the last term,
The PV interest tax shield is the present value
of the tax savings due to interest expense
discounted at the firms debt rate, at rD 12.5
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APV Example Adding it all up
Lets add the four terms in this equation
Since the project has a positive APV, it looks
like a go.
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17.6 Beta and Leverage

• Recall that an asset beta would be of the form

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Beta and Leverage No Corp.Taxes

• In a world without corporate taxes, and with
  riskless corporate debt, it can be shown that the
  relationship between the beta of the unlevered
  firm and the beta of levered equity is

• In a world without corporate taxes, and with
  risky corporate debt, it can be shown that the
  relationship between the beta of the unlevered
  firm and the beta of levered equity is

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Beta and Leverage with Corp. Taxes

• In a world with corporate taxes, and riskless
  debt, it can be shown that the relationship
  between the beta of the unlevered firm and the
  beta of levered equity is

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Beta and Leverage with Corp. Taxes

• If the beta of the debt is non-zero, then

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Example 1

• Lee Inc. is considering a project. The market
  value of the firms debt is 100 million, and the
  market value of the firms equity is 200
  million. The debt is considered riskless. The
  corporate tax rate is 34. The beta of firms
  equity is 2. The risk-free rate is 10, and the
  expected market risk premium is 8.5. What would
  the projects discount rate in the case that Lee
  Inc. is all equity?

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Example 2

• Lowes Corp. is considering a 1 million
  investment in a project. The firm estimates
  unlevered after-tax cash flows (UCF) of 300,000
  per year into perpetuity from the project. The
  firm will finance the project with a
  debt-to-value ratio of 0.5.
• The three competitors in this new industry
  are currently unlevered, with betas of 1.2, 1.3,
  and 1.4. Assuming a risk-free rate of 5, a
  market risk premium of 9, and a corporate tax
  rate of 34, what is the net present value of the
  project?

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17.7 Summary and Conclusions

• The APV formula can be written as
• The FTE formula can be written as
• The WACC formula can be written as

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Summary and Conclusions

• Use the WACC or FTE if the firm's target debt to
  value ratio applies to the project over its
  life.
  
• The APV method is used if the level of debt is
  known over the projects life.
  
• The beta of the equity of the firm is positively
  related to the leverage of the firm.