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CHAPTER 16
VALUATION AND FINANCING
LEARNING OBJECTIVES
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 Understand
the relationship between leverage, beta and the cost of
capital.
 Explain the unlevering and levering of beta for calculating the cost
of capital.
 Discuss the utility and limitations of WACC in evaluating an
investment project.
 Compare the free cash flow (FCF) approach and the capital cash
flow (CCF) approach of investment evaluation.
 Focus on the advantages of using the adjusted present value (APV)
approach in project evaluation.
 Explain the methodology for determining the value of the firm and
the value of equity.
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BETA, COST OF CAPITAL AND
CAPITAL STRUCTURE
 The
opportunity cost of capital of a firm depends on its
business risk. Hence, the opportunity cost of capital of a
levered firm and an unlevered firm, belonging to the same
homogeneous (business) risk class, will be the same.
of a levered firm’s equity will increase as debt is
introduced in the firm’s capital structure.
 Beta
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Asset Beta

The unlevered beta is a measure of the business risk of the firm.
 A firm has a portfolio of assets, and therefore, the asset beta of a
firm, a is the weighted average of betas of individual assets.


Average asset beta = beta of asset 1  weight of asset 1 + beta of asset
2  weight of asset 2 +…+ beta of asset n  weight of asset n.
A firm’s assets are generally financed by debt and equity.
Therefore, a firm’s asset beta is also equal to the weighted average
of the firm’s equity beta and debt beta. Assuming no corporate tax,
the beta of assets will be as follows:
E
D
a  e  d
V
V
Asset Cost of Capital
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 The
asset or opportunity cost of capital is the same
as the pre-tax WACC. Hence,
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

Equity Beta and Cost of Equity
Equity beta of a levered firm:
D
e  a  (a  d )
E
Cost of equity of a levered firm with risky debt as follows:
D

ke  rf  rp   a    a   d  
E


We can rewrite Equation as follows to decompose risk premium into
business risk and financial risk:
D
ke  rf  rp  a  rp   a   d 
E

You may notice that shareholders of the levered firm demand premium
equal to rpβa for assuming the business risk and additional premium equal to
rp(βa – βd)D/E for assuming the financial risk.
Risk-free Debt, Equity Beta and Cost of Equity
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 For
calculating the cost of equity of a levered firm
with risk-less debt:
Unlevering and Relevering Beta
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 The
equity beta of the firm will change when its financial
risk has changed. Two steps are involved in estimating the
new equity beta of the firm:

You should unlever the firm’s equity beta. This means that you
should estimate the firm’s asset beta:
E
D
 d 
V
V
E
a  e 
(If  d  0)
V
a  e 

You should now relever the equity beta to reflect the new debtequity ratio:
Unlevering and Relevering Beta
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
You should now relever the equity beta to reflect
the new debt-equity ratio:
E
S
a
 D
e 
  a 1  
E /V
 E
e  a  (a  d ) 
Example
10
Corporate Taxes, Interest Tax Shields and
Beta
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Fixed debt-to-value ratio
 The beta of the interest tax shields will be equal to
the asset beta. This implies that interest tax shield
will not reduce the risk of the firm.
 The asset beta of the levered firm (1) will be
equal to the asset beta of the unlevered firm (u).
Example: Cost of Equity
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Corporate Taxes, Interest Tax Shields and
Beta
13
Fixed amount of debt
 The interest tax shields are as safe or risky as
debt is. Hence the beta of the interest tax shields
will be equal to the beta of debt. We discount the
interest tax shields by the cost of debt.
 The equality of the betas of the interest tax
shields and debt under the fixed debt assumption
means that a levered firm
(or project) will
have lower systematic risk. Therefore, the asset
beta should be adjusted for the tax effects of
debt.
Example: Effect of Interest Tax Shield on Asset
Beta
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Summary of Methods of Calculating Asset Beta
and Equity Beta
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Free Cash Flow and WACC
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 FCF is calculated as follows:
 FCF = EBIT (1 – T) + DEP – NWC – CAPEX
 FCFs are unlevered cash flows, which
are
available for serving both equity shareholders
and debt holders.
 WACC is the ‘levered’ cost of capital. How can
you determine the ‘unlevered’ cost of capital?

The opportunity or the asset cost of capital of a pureequity firm is the unlevered cost of capital. Under
CAPM, the opportunity cost of capital, ka, can be
calculated. Shown earlier that the opportunity cost of
capital, ka, is also equal to the pre-tax WACC.
Constant Capital Structure and Debt
Rebalancing
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 The
concept of WACC is based on the assumption
that debt is a constant proportion of value.
 This means that as the firm’s or project’s value
changes, the amount of debt is adjusted to maintain
the proportionality of debt.
 WACC assumes that debt is rebalanced to maintain
the constant capital structure.
Adjusting the Firm’s WACC for the Project’s
Risk and Debt Capacity
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The following steps are involved in calculating the
project’s cost of capital:




First, calculate the firm’s opportunity cost of capital
(assuming that MM Proposition I works).
Second, calculate the new cost of debt.
Third, calculate the project’s cost of equity.
Fourth, calculate the project’s cost of capital as the aftertax weighted average cost of debt and the cost of equity.
Limitations of the WACC
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This approach has the following limitations:
 Cash flow patterns
 Business risk
 Debt capacity
 Issue costs
 Financing effects
 We need alternative methodologies than the WACC approach to
evaluate projects that do not have constant debt ratio, have
different cash flow patterns and have several financing effects.
We discuss two alternative approaches – the capital cash flows
(CCF) and the adjusted present value (APV).
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EQUITY CASH FLOWS OR
FLOW-TO-EQUITY APPROACH
 In
the equity cash flow (ECF) approach, ECFs are calculated
net of debt flows
(i.e., interest, interest tax shield and
repayments). Since these residual cash flows include the
effect of debt, they are also called levered cash flows. This
approach discounts ECFsthe cash flows available to
shareholders at the levered cost of equity, ke.
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Capital Cash Flows and the Opportunity
Cost of Capital
 In
this approach capital cash flows are
discounted at the project’s opportunity cost of
capital. Capital cash flows are the free-cash
flows plus the interest tax shields:
Capital cash flows (CCF)  Free cash flows  Interest tax shield
 ( EBIT  kd D)(1  T )  kd D  DEP  NWC  Capex
  EBIT (1  T )  DEP  NWC  Capex   Tkd D
Free Cash Flows
Interest
Tax Shield
Adjusted Present Value (APV)
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
The APV approach can handle any patterns of cash flows (perpetuity or
uneven cash flows) and it can be extended to calculate the adjusted present
value of an investment project incorporating several financing effects. It
divides the net present value of a project into two main parts: the first part
consists of the all-equity NPV or the base-case NPV assuming that the
project is entirely equity financed and the second part consists of the value
of the interest tax shields and other financing effects:


APV = All-equity NPV + Value of financing effects
The application of the APV approach involves the following three steps:



First, find the ‘all-equity NPV’, or the “base-case NPV”.
Second, find the present value of cash flows resulting from the financing of the project.
Each cash flows are discounted by the discount rate appropriate to the risk of each cash
flow.
Third, sum the ‘all-equity NPV’ and the present value of financing effects to arrive at the
project’s NPV.
Adjusted Present Value (APV)
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 Issue Costs:
 APV = All-equity NPV + PV of interest tax shields – Issue
costs

Fixed Debt Ratio:
 Under the assumption of the constant capital structure (fixed debt
ratio), the CCF approach, the modified (compressed) APV approach
and the FCF will give the same value for the project.
 Fixed

Debt:
APV approach considers them less risky and discounts at the cost
of debt (the market interest rate).
APV and Subsidized Financing
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 The
interest tax shields are discounted at the pre-tax
cost of debt, and the after-tax interest subsidies are
discounted at the after-tax cost of debt. The project’s
APV will be as shown below:

APV = Investment + All-equity PV + PV of interest
tax shields + PV of interest subsidies.
Value of the Subsidised Financing
 Amount is equal to the present value of the interest
subsidy.
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THE ADJUSTED COST OF CAPITAL:
CASE OF PERPETUAL CASH FLOWS
project’s NPV will be zero at this rate. The
adjusted cost of capital is equal to the opportunity
cost of capital less the value created by the project
by adding to the firm’s debt capacity. This
minimum rate is the adjusted cost of capital, k*.
 Instead of using APV approach, we can discount a
project’s free cash flows at the adjusted cost of
capital.
 The adjusted cost of capital is the MM formula for
the cost of capital of a levered firm (project).
 The
Miles and Ezzell’s Formula for Adjusted Cost of
Capital
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 We
can use the Miles–Ezzell formula when debt
ratio is fixed and the amount of debt rebalances.
D  1  ka 
k  ka  Tkd 

V 1  k d 
*
CHOICE OF THE APPROPRIATE VALUATION
APPROACH
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Comparison of FCF, CCF and APV Valuation Approaches
Valuation of a Firm
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 The
value of a firm depends on the expected cash flows and
the discount rate.
 Value of the firm is given as follows:
n
FCFt
V
t
t  1 (1  k0 )
where FCF is the free cash flow and k0 is the weighted average
cost of capital (WACC).
 If we assume constant relations of earnings, working capital
and capital expenditure to sales, we can write the equation for
the free cash flows as follows:
NCF  FCF  SALES  p  (1  T )  DEP  ( w  f ) SALES
Estimating Free Cash Flows
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1.
2.
3.
4.
5.
6.
7.
8.
Sales projections
Estimate of expenses
Estimate of depreciation
Capital expenditure
Estimates of increase in net working capital
Treatment of interest expenses
Tax rate
Inflation
Horizon Period and Terminal Value
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 In
the case of a firm, it continuously makes investments that
generate revenues and cash flows, theoretically, forever.
Therefore, the financial analyst assumes a horizon period
because detailed calculations for a long period become quite
intricate. The financial analysis of such projects incorporate
an estimate of the value of cash flows after the horizon period
without involving detailed calculations. Thus, the value of the
firm is given as follows:
H
FCFt
TVH
V 

t
(1  k0 ) H
t  1 (1  k0 )
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Methods of Valuing Terminal Value
1.
2.
3.
4.
5.
Constant perpetual cash flows
Growing perpetual cash flows
Price-earnings (P/E) ratio
Market-to-book value (M/B) ratio
Replacement cost of assets
Value of the Firm’s Equity
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Following steps are involved in the valuation of a firm:








Identify sales growth and profitability assumptions.
Consider depreciation, change in net working capital, capital expenditure and
taxes in estimating the free cash flows.
Estimate the amounts of free cash flows for the horizon period.
Estimate the cash flow patterns beyond the horizon period and determine the
terminal value.
Estimate the firm’s weighted average cost of capital.
Be consistent in treating inflation in the estimation of free cash flows and WACC.
Compute present value cash flows using WACC as the discount rate.
Subtract the value of the outstanding debt from the value of the firm to find out
the value of its equity.
Growth Patterns and the Firm Value
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 The
DCF valuation of a firm makes assumptions
about the growth patterns of the firm during the
horizon period and beyond. Generally, there are
the following four possibilities:




No growth
Constant growth
Two-stage growth
Three-stage growth
Comparative Firms Valuation Approach
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 Identify
the comparable firms based on the criteria of
similar products, size, age, growth and profitability trends.
 For the comparable firms, calculate the firm value as a
ratio of sales, EBIT, free cash flows and market value-tobook value of assets. Sales, EBIT, free cash flow and book
value of assets are assumed as value drivers. Notice that
firm value to EBIT ratio is equivalent of price-earnings
(P/E) ratio.
 Average the ratios of the comparable firms, and apply them
to the sales, EBIT and free cash flow data of the firm.
Balance Sheet Approach to Firm Valuation
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 Balance
sheet or adjusted book value uses assets
and liabilities information to determine the value of
the firm.
 One approach to estimate the adjusted book values
of assets is to determine their current or replacement
costs.