VALUATION AND FINANCINGCHAPTER 16

LEARNING OBJECTIVES 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.

Beta of a levered firm’s equity will increase as debt is introduced in the firm’s capital structure.

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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:

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a e d

E D

V V

Asset Cost of Capital

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:

Cost of equity of a levered firm with risky debt as follows:

We can rewrite Equation as follows to decompose risk premium into business risk and financial risk:

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.

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( )e a a d

D

E

e f p a a d

Dk r r

E

e f p a p a d

Dk r r r

E

Risk-free Debt, Equity Beta and Cost of Equity

For calculating the cost of equity of a levered firm with risk-less debt:

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Unlevering and Relevering Beta

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:

You should now relever the equity beta to reflect the new debt-equity ratio:

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(If 0)

a e d

a e d

E D

V VE

V

Unlevering and Relevering Beta

You should now relever the equity beta to reflect the new debt-equity ratio:

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( )

1/

e a a d

ae a

E

SD

E V E

Example10

Corporate Taxes, Interest Tax Shields and Beta

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).

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Example: Cost of Equity12

Corporate Taxes, Interest Tax Shields and Beta

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.

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Example: Effect of Interest Tax Shield on Asset Beta14

Summary of Methods of Calculating Asset Beta and Equity Beta 15

Free Cash Flow and WACC

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 pure-

equity 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.

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Constant Capital Structure and Debt Rebalancing

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.

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Adjusting the Firm’s WACC for the Project’s Risk and Debt Capacity

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 after-

tax weighted average cost of debt and the cost of equity.

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Limitations of the WACC

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 ORFLOW-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 ECFsthe 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:

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Interest Free Cash FlowsTax Shield

Capital cash flows (CCF) Free cash flows Interest tax shield

( )(1 ) Capex

(1 ) Capexd d

d

EBIT k D T k D DEP NWC

EBIT T DEP NWC Tk D

Adjusted Present Value (APV)

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.

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Adjusted Present Value (APV)

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).

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APV and Subsidized Financing

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 The 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).

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Miles and Ezzell’s Formula for Adjusted Cost of Capital

We can use the Miles–Ezzell formula when debt ratio is fixed and the amount of debt rebalances.

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* 1

1a

a dd

D kk k Tk

V k

CHOICE OF THE APPROPRIATE VALUATION APPROACH27

Comparison of FCF, CCF and APV Valuation Approaches

Valuation of a Firm

The value of a firm depends on the expected cash flows and the discount rate.

Value of the firm is given as follows:

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:

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1 0(1 )

nt

tt

FCFV

k

(1 ) ( )NCF FCF SALES p T DEP w f SALES

Estimating Free Cash Flows

1. Sales projections 2. Estimate of expenses 3. Estimate of depreciation 4. Capital expenditure 5. Estimates of increase in net working capital 6. Treatment of interest expenses 7. Tax rate 8. Inflation

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Horizon Period and Terminal Value

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:

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1 0 0(1 ) (1 )

Ht H

t Ht

FCF TVV

k k

Methods of Valuing Terminal Value 1. Constant perpetual cash flows 2. Growing perpetual cash flows 3. Price-earnings (P/E) ratio 4. Market-to-book value (M/B) ratio5. Replacement cost of assets

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Value of the Firm’s Equity

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.

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Growth Patterns and the Firm Value

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

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Comparative Firms Valuation Approach

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-to-book 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.

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Balance Sheet Approach to Firm Valuation 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.

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