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Discounted Cash Flow Valuation: Basics

Aswath Damodaran

Aswath Damodaran

1

Discounted Cashflow Valuation: Basis for Approach

t = n CF t Value = ∑ t t = 1( 1 +r)

where CFt is the cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and t is the life of the asset. Proposition 1: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset. Proposition 2: Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later; the latter may however have greater growth and higher cash flows to compensate.

Aswath Damodaran

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Equity Valuation ...view middle of the document...

Value of Firm = CF to Firm t ∑1 ( 1 +WACC) t t=

t=n

where, CF to Firmt = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of Capital

Aswath Damodaran

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Firm Value and Equity Value

n

o o o

o n o o o

To get from firm value to equity value, which of the following would you need to do? Subtract out the value of long term debt Subtract out the value of all debt Subtract the value of all non-equity claims in the firm, that are included in the cost of capital calculation Subtract out the value of all non-equity claims in the firm Doing so, will give you a value for the equity which is greater than the value you would have got in an equity valuation lesser than the value you would have got in an equity valuation equal to the value you would have got in an equity valuation

Aswath Damodaran

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Cash Flows and Discount Rates

Assume that you are analyzing a company with the following cashflows for the next five years. Year CF to Equity Int Exp (1-t) CF to Firm 1 $ 50 $ 40 $ 90 2 $ 60 $ 40 $ 100 3 $ 68 $ 40 $ 108 4 $ 76.2 $ 40 $ 116.2 5 $ 83.49 $ 40 $ 123.49 Terminal Value $ 1603.0 $ 2363.008 n Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) n The current market value of equity is $1,073 and the value of debt outstanding is $800.

n

Aswath Damodaran

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Equity versus Firm Valuation

Method 1: Discount CF to Equity at Cost of Equity to get value of equity n Cost of Equity = 13.625% n PV of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 + 76.2/1.136254 + (83.49+1603)/1.136255 = $1073 Method 2: Discount CF to Firm at Cost of Capital to get value of firm Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5% WACC = 13.625% (1073/1873) + 5% (800/1873) = 9.94% PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 + (123.49+2363)/1.09945 = $1873 n PV of Equity = PV of Firm - Market Value of Debt = $ 1873 - $ 800 = $1073

Aswath Damodaran

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First Principle of Valuation

n n

Never mix and match cash flows and discount rates. The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.

Aswath Damodaran

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The Effects of Mismatching Cash Flows and Discount Rates

Error 1: Discount CF to Equity at Cost of Capital to get equity value

PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 + (83.49+1603)/1.09945 = $1248 Value of equity is overstated by $175.

Error 2: Discount CF to Firm at Cost of Equity to get firm value

PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 + (123.49+2363)/1.136255 = $1613 PV of Equity = $1612.86 - $800 = $813 Value of Equity is understated by $ 260.

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