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- 1. Valuation in 30 minutes, give or take a few… Aswath Damodaran www.damodaran.com 1
- 2. DCF Choices: Equity Valuation versus Firm ValuationFirm Valuation: Value the entire business Assets LiabilitiesExisting Investments Fixed Claim on cash flowsGenerate cashflows today Assets in Place Debt Little or No role in managementIncludes long lived (fixed) and Fixed Maturity short-lived(working Tax Deductible capital) assetsExpected Value that will be Growth Assets Equity Residual Claim on cash flowscreated by future investments Significant Role in management Perpetual Lives Equity valuation: Value just the equity claim in the business 2
- 3. More generally… The value of any business is a function of.. Are you investing optimally for Determinants of Firm Value future growth? Is there scope for more efficient utilization of exsting Growth from new investments Efficiency Growth assets?How well do you manage your Growth created by making new Growth generated byexisting investments/assets? investments; function of amount and using existing assets quality of investments better Cashflows from existing assets Cashflows before debt payments, Expected Growth during high growth period but after taxes and reinvestment to Stable growth firm, maintain exising assets with no or very limited excess returns Length of the high growth period Are you building on your Since value creating growth requires excess returns, this is a function of competitive advantages? - Magnitude of competitive advantages - Sustainability of competitive advantages Cost of capital to apply to discounting cashflows Are you using the right Determined by amount and kind of - Operating risk of the company debt for your firm? - Default risk of the company - Mix of debt and equity used in financing 3
- 4. Estimating cash ﬂows to a business Cash flows can be measured to Just Equity InvestorsAll claimholders in the firmEBIT (1- tax rate) Net Income Dividends - ( Capital Expenditures - Depreciation) - (Capital Expenditures - Depreciation) + Stock Buybacks- Change in non-cash working capital - Change in non-cash Working Capital= Free Cash Flow to Firm (FCFF) - (Principal Repaid - New Debt Issues) - Preferred Dividend 4
- 5. And discount rates… Cost of Equity: Rate of Return demanded by equity investors Cost of Equity = Riskfree Rate+ Beta X (Risk Premium) Has to be default free, in Historical Premium Implied Premium the same currency as cash 1. Mature Equity Market Premium: Based on how equity is flows, and defined in same Average premium earned by or priced today terms (real or nominal) as stocks over T.Bonds in U.S. and a simple valuation thecash flows 2. Country risk premium = model Country Default Spread* ( Equity/ Country bond) Cost of Capital: Weighted rate of return demanded by all investors Cost of borrowing should be based upon (1) synthetic or actual bond rating Marginal tax rate, reflecting (2) default spread tax benefits of debt Cost of Borrowing = Riskfree rate + Default spreadCost of Capital = Cost of Equity (Equity/(Debt + Equity)) + Cost of Borrowing (1-t) (Debt/(Debt + Equity)) Cost of equity based upon bottom-up Weights should be market value weights beta 5
- 6. Where does growth come from? To grow, a company has to reinvest. How much it will have to reinvest depends in large part on how fast it wants to grow and what type of return it expects to earn on the reinvestment. – Reinvestment rate = Growth Rate/ Return on Capital Expected Growth Net Income Operating Income Retention Ratio= Return on Equity Reinvestment Return on Capital = 1 - Dividends/Net X Net Income/Book Value of Rate =(Net Cap X EBIT(1-t)/Book Value of Income Equity Ex + Chg in Capital WC/EBIT(1-t) 6
- 7. All good things come to an end… stable growth and beyond.." No matter how great a company’s products and management are, two forces operate to drag the company’s growth rate down towards the growth rate of the economy. The ﬁrst is scale. As companies grow, they get larger, and as they get larger, it becomes more difﬁcult to grow. The second is competition. Both forces also operate to pull down the return on capital for a company towards its cost of capital. Mature companies earn much lower returns on capital, relative to their cost of capital. From a mechanical standpoint, this effectively allows us to stop estimating cash ﬂows at some point and estimate a terminal value, by assuming that cash ﬂows will grow at a constant rate forever beyond that point. The “mature” company that we visualize should have a mature company’s cost of capital and a mature company’s return on capital. 7
- 8. Closing Thoughts on Valuation Valuation is simple. We choose to make it complex. The biggest enemies of good valuations are biases and preconceptions that you bring into the valuations. You cannot value equity precisely. Be ready to be wrong and do not take it personally. Making a model bigger will not necessarily make it better. 8
- 9. DCF Choices: Equity Valuation versus Firm Valuation Firm Valuation: Value the entire business Assets Liabilities Existing Investments Fixed Claim on cash flows Generate cashflows today Assets in Place Debt Little or No role in management Includes long lived (fixed) and Fixed Maturity short-lived(working Tax Deductible capital) assets Expected Value that will be Growth Assets Equity Residual Claim on cash flows created by future investments Significant Role in management Perpetual Lives Equity valuation: Value just the equity claim in the businessAswath Damodaran 6
- 10. DCF Choices: Equity Valuation versus Firm ValuationFirm Valuation: Value the entire business Assets LiabilitiesExisting Investments Fixed Claim on cash flowsGenerate cashflows today Assets in Place Debt Little or No role in managementIncludes long lived (fixed) and Fixed Maturity short-lived(working Tax Deductible capital) assetsExpected Value that will be Growth Assets Equity Residual Claim on cash flowscreated by future investments Significant Role in management Perpetual Lives Equity valuation: Value just the equity claim in the business 2
- 11. More generally… The value of any business is a function of.. Are you investing optimally for Determinants of Firm Value future growth? Is there scope for more efficient utilization of exsting Growth from new investments Efficiency Growth assets?How well do you manage your Growth created by making new Growth generated byexisting investments/assets? investments; function of amount and using existing assets quality of investments better Cashflows from existing assets Cashflows before debt payments, Expected Growth during high growth period but after taxes and reinvestment to Stable growth firm, maintain exising assets with no or very limited excess returns Length of the high growth period Are you building on your Since value creating growth requires excess returns, this is a function of competitive advantages? - Magnitude of competitive advantages - Sustainability of competitive advantages Cost of capital to apply to discounting cashflows Are you using the right Determined by amount and kind of - Operating risk of the company debt for your firm? - Default risk of the company - Mix of debt and equity used in financing 3
- 12. Valuation with Inﬁnite Life DISCOUNTED CASHFLOW VALUATION Expected Growth Cash flows Firm: Growth in Firm: Pre-debt cash Operating Earnings flow Equity: Growth in Equity: After debt Net Income/EPS Firm is in stable growth: cash flows Grows at constant rate forever Terminal Value CF1 CF2 CF3 CF4 CF5 CFn Value ......... Firm: Value of Firm Forever Equity: Value of Equity Length of Period of High Growth Discount Rate Firm:Cost of Capital Equity: Cost of EquityAswath Damodaran 7
- 13. DISCOUNTED CASHFLOW VALUATION Cashflow to Firm Expected Growth EBIT (1-t) Reinvestment Rate - (Cap Ex - Depr) * Return on Capital - Change in WC Firm is in stable growth: = FCFF Grows at constant rate forever Terminal Value= FCFF n+1/(r-gn) FCFF1 FCFF2 FCFF3 FCFF4 FCFF5 FCFFnValue of Operating Assets .........+ Cash & Non-op Assets Forever= Value of Firm Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))- Value of Debt= Value of Equity Cost of Equity Cost of Debt Weights (Riskfree Rate Based on Market Value + Default Spread) (1-t) Riskfree Rate : - No default risk Risk Premium - No reinvestment risk Beta - Premium for average + - Measures market risk X - In same currency and risk investment in same terms (real or nominal as cash flows Type of Operating Financial Base Equity Country Risk Business Leverage Leverage Premium PremiumAswath Damodaran 8
- 14. Cap Ex = Acc Cap Ex(1218) + Acquisitions (3975) + R&D (2216) Amgen: Status Quo Return on Capital Current Cashflow to Firm Reinvestment Rate 16% EBIT(1-t)= :7336(1-.28)= 6058 60% Expected Growth - Nt CpX= 6443 in EBIT (1-t) Stable Growth - Chg WC 37 .60*.16=.096 g = 4%; Beta = 1.10; = FCFF - 423 9.6% Debt Ratio= 20%; Tax rate=35% Reinvestment Rate = 6480/6058 Cost of capital = 8.08% =106.98% ROC= 10.00%; Return on capital = 18.26% Reinvestment Rate=4/10=40% Growth decreases Terminal Value10= 7300/(.0808-.04) = 179,099 First 5 years gradually to 4%Op. Assets 94214 Year 1 2 3 4 5 6 7 8 9 10 Term Yr+ Cash: 1283 EBIT $9,221 $11,195 $7,975 $8,741 $9,580 $10,392 $11,157 $11,853 $12,460 $12,958 16898- Debt 8272 EBIT (1-t) $6,639 $7,276 $7,975 $8,741 $9,580 $10,392 $11,157 $11,853 $12,460 $12,958 12167=Equity 87226 - Reinvestment $3,983 $4,366 $4,785 $5,244 $5,748 $5,820 $5,802 $5,690 $5,482 $5,183 4867-Options 479 = FCFF $2,656 $2,911 $3,190 $3,496 $3,832 $4,573 $5,355 $6,164 $6,978 $7,775 7300Value/Share $ 74.33 Cost of Capital (WACC) = 11.7% (0.90) + 3.66% (0.10) = 10.90% Debt ratio increases to 20% Beta decreases to 1.10 On May 11,2007, Cost of Equity Amgen was trading Cost of Debt at $63.65/share 11.70% (4.78%+..85%)(1-.35) Weights = 3.66% E = 90% D = 10% Riskfree Rate: Risk Premium Riskfree rate = 4.78% Beta 4% + 1.73 X Unlevered Beta for Sectors: 1.59 D/E=11.06%Aswath Damodaran 9
- 15. Avg Reinvestment rate = 36.94% SAP: Status Quo Reinvestment Rate Return on Capital 19.93% Current Cashflow to Firm 57.42% Expected Growth EBIT(1-t) : 1414 in EBIT (1-t) Stable Growth - Nt CpX 831 g = 3.41%; Beta = 1.00; - Chg WC - 19 .5742*.1993=.1144 11.44% Debt Ratio= 20% = FCFF 602 Cost of capital = 6.62% Reinvestment Rate = 812/1414 ROC= 6.62%; Tax rate=35% =57.42% Reinvestment Rate=51.54% Growth decreases Terminal Value10= 1717/(.0662-.0341) = 53546 First 5 years gradually to 3.41%Op. Assets 31,615 Year 1 2 3 4 5 6 7 8 9 10 Term Yr+ Cash: 3,018 EBIT 2,483 2,767 3,083 3,436 3,829 4,206 4,552 4,854 5,097 5,271 5451- Debt 558 EBIT(1-t) 1,576 1,756 1,957 2,181 2,430 2,669 2,889 3,080 3,235 3,345 3543- Pension Lian 305 - Reinvestm 905 1,008 1,124 1,252 1,395 1,501 1,591 1,660 1,705 1,724 1826- Minor. Int. 55 = FCFF 671 748 833 929 1,035 1,168 1,298 1,420 1,530 1,621 1717=Equity 34,656-Options 180Value/Share106.12 Cost of Capital (WACC) = 8.77% (0.986) + 2.39% (0.014) = 8.68% Debt ratio increases to 20% Beta decreases to 1.00 On May 5, 2005, SAP was trading at Cost of Equity Cost of Debt 122 Euros/share 8.77% (3.41%+..35%)(1-.3654) Weights = 2.39% E = 98.6% D = 1.4% Riskfree Rate: Risk Premium Euro riskfree rate = 3.41% Beta 4% Country Risk + 1.26 X + Lambda Premium 0.10 X 2.50% Unlevered Beta for Sectors: 1.25 D/E=1.6%Aswath Damodaran 10
- 16. Discounted Cash Flow Valuation: Basics Aswath DamodaranAswath Damodaran 1
- 17. Discounted Cashflow Valuation: Basis for Approach t =n CF Value = t 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 2
- 18. Equity Valuation versus Firm Valuation n Value just the equity stake in the business n Value the entire business, which includes, besides equity, the other claimholders in the firmAswath Damodaran 3
- 19. I.Equity Valuation n The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm. t=n CF to Equityt Value of Equity = (1+ k )t t=1 e where, CF to Equityt= Expected Cashflow to Equity in period t ke = Cost of Equity n The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends.Aswath Damodaran 4
- 20. II. Firm Valuation n The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions. t=n CF to Firm t Value of Firm = = t 1(1+WACC)t where, CF to Firmt = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of CapitalAswath Damodaran 5
- 21. Firm Value and Equity Value n To get from firm value to equity value, which of the following would you need to do? o Subtract out the value of long term debt o Subtract out the value of all debt o Subtract the value of all non-equity claims in the firm, that are included in the cost of capital calculation o Subtract out the value of all non-equity claims in the firm n Doing so, will give you a value for the equity which is o greater than the value you would have got in an equity valuation o lesser than the value you would have got in an equity valuation o equal to the value you would have got in an equity valuationAswath Damodaran 6
- 22. Cash Flows and Discount Rates n 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.Aswath Damodaran 7
- 23. 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 = $1073Aswath Damodaran 8
- 24. First Principle of Valuation n Never mix and match cash flows and discount rates. n 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 9
- 25. 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. Error 3: Discount CF to Firm at Cost of Equity, forget to subtract out debt, and get too high a value for equity Value of Equity = $ 1613 Value of Equity is overstated by $ 540Aswath Damodaran 10
- 26. Discounted Cash Flow Valuation: The Steps n Estimate the discount rate or rates to use in the valuation • Discount rate can be either a cost of equity (if doing equity valuation) or a cost of capital (if valuing the firm) • Discount rate can be in nominal terms or real terms, depending upon whether the cash flows are nominal or real • Discount rate can vary across time. n Estimate the current earnings and cash flows on the asset, to either equity investors (CF to Equity) or to all claimholders (CF to Firm) n Estimate the future earnings and cash flows on the firm being valued, generally by estimating an expected growth rate in earnings. n Estimate when the firm will reach “stable growth” and what characteristics (risk & cash flow) it will have when it does. n Choose the right DCF model for this asset and value it.Aswath Damodaran 11
- 27. Generic DCF Valuation Model DISCOUNTED CASHFLOW VALUATION Expected Growth Cash flows Firm: Growth in Firm: Pre-debt cash Operating Earnings flow Equity: Growth in Equity: After debt Net Income/EPS Firm is in stable growth: cash flows Grows at constant rate forever Terminal Value CF1 CF2 CF3 CF4 CF5 CFn Value ......... Firm: Value of Firm Forever Equity: Value of Equity Length of Period of High Growth Discount Rate Firm:Cost of Capital Equity: Cost of EquityAswath Damodaran 12
- 28. EQUITY VALUATION WITH DIVIDENDS Dividends Expected Growth Net Income Retention Ratio * * Payout Ratio Return on Equity = Dividends Firm is in stable growth: Grows at constant rate forever Terminal Value= Dividend n+1/(ke-gn) Dividend1 Dividend2 Dividend3 Dividend4 Dividend5 Dividendn Value of Equity ......... Forever Discount at Cost of Equity Cost of Equity Riskfree Rate : - No default risk Risk Premium - No reinvestment risk Beta - Premium for average - In same currency and + - Measures market risk X risk investment in same terms (real or nominal as cash flows Type of Operating Financial Base Equity Country Risk Business Leverage Leverage Premium PremiumAswath Damodaran 13
- 29. Financing Weights EQUITY VALUATION WITH FCFE Debt Ratio = DR Cashflow to Equity Expected Growth Net Income Retention Ratio * - (Cap Ex - Depr) (1- DR) Return on Equity Firm is in stable growth: - Change in WC (!-DR) Grows at constant rate = FCFE forever Terminal Value= FCFE n+1/(ke-gn) FCFE1 FCFE2 FCFE3 FCFE4 FCFE5 FCFEn Value of Equity ......... Forever Discount at Cost of Equity Cost of Equity Riskfree Rate : - No default risk Risk Premium - No reinvestment risk Beta + X - Premium for average - In same currency and - Measures market risk risk investment in same terms (real or nominal as cash flows Type of Operating Financial Base Equity Country Risk Business Leverage Leverage Premium PremiumAswath Damodaran 14
- 30. VALUING A FIRM Cashflow to Firm Expected Growth EBIT (1-t) Reinvestment Rate - (Cap Ex - Depr) * Return on Capital Firm is in stable growth: - Change in WC Grows at constant rate = FCFF forever Terminal Value= FCFFn+1/(r-gn) FCFF1 FCFF2 FCFF3 FCFF4 FCFF5 FCFFnValue of Operating Assets .........+ Cash & Non-op Assets Forever= Value of Firm Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))- Value of Debt= Value of Equity Cost of Equity Cost of Debt Weights (Riskfree Rate Based on Market Value + Default Spread) (1-t) Riskfree Rate : - No default risk Risk Premium - No reinvestment risk Beta - Premium for average + X - In same currency and - Measures market risk risk investment in same terms (real or nominal as cash flows Type of Operating Financial Base Equity Country Risk Business Leverage Leverage Premium PremiumAswath Damodaran 15

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