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Valuation

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Aswath Damodaran

1

VALUATION Cynic: A person who knows the price of everything but the value of nothing.. Oscar Wilde

First Principles 2

Maximize the value of the business (firm)

The Investment Decision Invest in assets that earn a return greater than the minimum acceptable hurdle rate

The Financing Decision Find the right kind of debt for your firm and the right mix of debt and equity to fund your operations

The Dividend Decision If you cannot find investments that make your minimum acceptable rate, return the cash to owners of your business

The hurdle rate should reflect the riskiness of the investment and the mix of debt and equity used to fund it.

The return should reflect the magnitude and the timing of the cashflows as welll as all side effects.

The optimal mix of debt and equity maximizes firm value

The right kind of debt matches the tenor of your assets

How much cash you can return depends upon current & potential investment opportunities

How you choose to return cash to the owners will depend on whether they prefer dividends or buybacks

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Three approaches to valuaEon 3

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Intrinsic valuaEon: The value of an asset is a funcEon of its fundamentals – cash flows, growth and risk. In general, discounted cash flow models are used to esEmate intrinsic value. RelaEve valuaEon: The value of an asset is esEmated based upon what investors are paying for similar assets. In general, this takes the form of value or price mulEples and comparing firms within the same business. ConEngent claim valuaEon: When the cash flows on an asset are conEngent on an external event, the value can be esEmated using opEon pricing models. 3

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One tool for esEmaEng intrinsic value: Discounted Cash Flow ValuaEon 4

Value of growth The future cash flows will reflect expectations of how quickly earnings will grow in the future (as a positive) and how much the company will have to reinvest to generate that growth (as a negative). The net effect will determine the value of growth. Expected Cash Flow in year t = E(CF) = Expected Earnings in year t - Reinvestment needed for growth Cash flows from existing assets The base earnings will reflect the earnings power of the existing assets of the firm, net of taxes and any reinvestment needed to sustain the base earnings.

Steady state The value of growth comes from the capacity to generate excess returns. The length of your growth period comes from the strength & sustainability of your competitive advantages.

Risk in the Cash flows The risk in the investment is captured in the discount rate as a beta in the cost of equity and the default spread in the cost of debt.

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Equity ValuaEon 5

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The value of equity is obtained by discounEng expected cashflows to equity, i.e., the residual cashflows aPer meeEng all expenses, tax obligaEons 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

Value of Equity= ∑

CF to Equity t (1+k e )t t=1

where, CF to Equity t = Expected Cashflow to Equity in period t ke = Cost of Equity ¨

The dividend discount model is a specialized case of equity valuaEon, and the value of a stock is the present value of expected future dividends. 5

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Firm ValuaEon 6

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The value of the firm is obtained by discounEng expected cashflows to the firm, i.e., the residual cashflows aPer meeEng all operaEng 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 proporEons. t=n

Value of Firm= ∑

CF to Firm t t t=1 (1+WACC)

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

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Choosing a Cash Flow to Discount 7

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When you cannot esEmate the free cash flows to equity or the firm, the only cash flow that you can discount is dividends. For financial service firms, it is difficult to esEmate free cash flows. For Deutsche Bank, we will be discounEng dividends. If a firm’s debt raEo is not expected to change over Eme, the free cash flows to equity can be discounted to yield the value of equity. For Tata Motors, we will discount free cash flows to equity. If a firm’s debt raEo might change over Eme, free cash flows to equity become cumbersome to esEmate. Here, we would discount free cash flows to the firm. For Vale and Disney, we will discount the free cash flow to the firm.

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The Ingredients that determine value. 8

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I. EsEmaEng Cash Flows 9

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Dividends and Modified Dividends for Deutsche Bank 10

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In 2007, Deutsche Bank paid out dividends of 2,146 million Euros on net income of 6,510 million Euros. In early 2008, we valued Deutsche Bank using the dividends it paid in 2007. In my 2008 valuaEon I am assuming the dividends are not only reasonable but sustainable. In November 2013, Deutsche Bank’s dividend policy was in flux. Not only did it report losses but it was on a pathway to increase its regulatory capital raEo. Rather than focus on the dividends (which were small), we esEmated the potenEal dividends (by esEmaEng the free cash flows to equity aPer investments in regulatory capital) Current 439,851 € 15.13% 66,561 € 76,829 € -1.08% -716 € 2014 453,047 € 15.71% 71,156 € 4,595 € 81,424 € 0.74% 602 € 4,595 € -3,993 € 2015 466,638 € 16.28% 75,967 € 4,811 € 86,235 € 2.55% 2,203 € 4,811 € -2,608 € 2016 480,637 € 16.85% 81,002 € 5,035 € 91,270 € 4.37% 3,988 € 5,035 € -1,047 € 2017 495,056 € 17.43% 86,271 € 5,269 € 96,539 € 6.18% 5,971 € 5,269 € 702 € 2018 509,908 € 18.00% 91,783 € 5,512 € 102,051 € 8.00% 8,164 € 5,512 € 2,652 € Steady state 517,556 € 18.00% 93,160 € 1,377 € 103,605 € 8.00% 8,287 € 1,554 € 6,733 €

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Asset Base Capital ratio Tier 1 Capital Change in regulatory capital Book Equity ROE Net Income - Investment in Regulatory Capital FCFE

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EsEmaEng FCFE (past) : Tata Motors 11

Year

Net Income

2008-­‐09 -­‐25,053₹ 2009-­‐10 29,151₹ 2010-­‐11 92,736₹ 2011-­‐12 135,165₹ 2012-­‐13 98,926₹ Aggregate 330,925₹

Equity Depreciatio Change in Change in Equity Reinvestment Cap Ex

n

WC

Debt

Reinvestment

Rate

99,708₹ 25,072₹ 13,441₹ 25,789₹ 62,288₹ -­‐248.63% 84,754₹ 39,602₹ -­‐26,009₹ 5,605₹ 13,538₹ 46.44% 81,240₹ 46,510₹ 50,484₹ 24,951₹ 60,263₹ 64.98% 138,756₹ 56,209₹ 22,801₹ 30,846₹ 74,502₹ 55.12% 187,570₹ 75,648₹ 680₹ 32,970₹ 79,632₹ 80.50% 592,028₹ 243,041₹ 61,397₹ 120,160₹ 290,224₹ 87.70%

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EsEmaEng FCFF: Disney ¨

In the fiscal year ended September 2013, Disney reported the following: ¤ ¤ ¤ ¤ ¤

OperaEng income (adjusted for leases) = $10,032 million EffecEve tax rate = 31.02% Capital Expenditures (including acquisiEons) = $5,239 million DepreciaEon & AmorEzaEon = $2,192 million Change in non-­‐cash working capital = $103 million = 10,032 (1 -­‐.3102) = $5,239 -­‐ $2,192

=

= = $6,920

= $3,629

=$103

= $3,188

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The free cash flow to the firm can be computed as follows: APer-­‐tax OperaEng Income -­‐ Net Cap Expenditures -­‐ Change in Working Capital = Free Cashflow to Firm (FCFF)

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The reinvestment and reinvestment rate are as follows: ¤ ¤

Reinvestment = $3,629 + $103 = $3,732 million Reinvestment Rate = $3,732/ $6,920 = 53.93%

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II. Discount Rates 13

CriEcal ingredient in discounted cashflow valuaEon. Errors in esEmaEng the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuaEon. ¨ At an intuiEve level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted. ¨ The cost of equity is the rate at which we discount cash flows to equity (dividends or free cash flows to equity). The cost of capital is the rate at which we discount free cash flows to the firm. ¨
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Cost of Equity: Deutsche Bank 2008 versus 2013 14

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In early 2008, we esEmated a beta of 1.162 for Deutsche Bank, which used in conjuncEon with the Euro risk-­‐free rate of 4% (in January 2008) and an equity risk premium of 4.50%, yielded a cost of equity of 9.23%. Cost of Equity Jan 2008 = Riskfree Rate Jan 2008 + Beta* Mature Market Risk Premium

= 4.00% + 1.162 (4.5%) = 9.23%

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In November 2013, the Euro riskfree rate had dropped to 1.75% and the Deutsche’s equity risk premium had risen to 6.12%: Cost of equity Nov ’13 = Riskfree Rate Nov ‘13 + Beta (ERP)

= 1.75% + 1.1516 (6.12%) = 8.80%

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Cost of Equity: Tata Motors 15

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We will be valuing Tata Motors in rupee terms. That is a choice. Any company can be valued in any currency. Earlier, we esEmated a levered beta for equity of 1.1007 for Tata Motor’s operaEng assets . Since we will be discounEng FCFE with the income from cash included in the cash, we recomputed a beta for Tata Motors as a company (with cash): Levered BetaCompany= 1.1007 (1428/1630)+ 0 (202/1630) = 0.964

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With a nominal rupee risk-­‐free rate of 6.57 percent and an equity risk premium of 7.19% for Tata Motors, we arrive at a cost of equity of 13.50%. Cost of Equity = 6.57% + 0.964 (7.19%) = 13.50%

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Current Cost of Capital: Disney ¨

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The beta for Disney’s stock in November 2013 was 1.0013. The T. bond rate at that Eme was 2.75%. Using an esEmated equity risk premium of 5.76%, we esEmated the cost of equity for Disney to be 8.52%: Cost of Equity = 2.75% + 1.0013(5.76%) = 8.52% Disney’s bond raEng in May 2009 was A, and based on this raEng, the esEmated pretax cost of debt for Disney is 3.75%. Using a marginal tax rate of 36.1, the aPer-­‐tax cost of debt for Disney is 2.40%. APer-­‐Tax Cost of Debt = 3.75% (1 – 0.361) = 2.40% The cost of capital was calculated using these costs and the weights based on market values of equity (121,878) and debt (15.961): 121,878 15,961 Cost of capital = 8.52% + 2.40% = 7.81%
(15,961+121,878) (15,961+121,878)
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But costs of equity and capital can and should change over Eme… Year 1 2 3 4 5 6 7 8 9 10 Aswath Damodaran

Beta 1.0013 1.0013 1.0013 1.0013 1.0013 1.0010 1.0008 1.0005 1.0003 1.0000

Cost of Equity 8.52% 8.52% 8.52% 8.52% 8.52% 8.52% 8.51% 8.51% 8.51% 8.51%

APer-­‐tax Cost of Debt Debt RaEo Cost of capital 2.40% 11.50% 7.81% 2.40% 11.50% 7.81% 2.40% 11.50% 7.81% 2.40% 11.50% 7.81% 2.40% 11.50% 7.81% 2.40% 13.20% 7.71% 2.40% 14.90% 7.60% 2.40% 16.60% 7.50% 2.40% 18.30% 7.39% 2.40% 20.00% 7.29% 17

III. Expected Growth 18

Expected Growth

Net Income

Operating Income

Retention Ratio= 1 - Dividends/Net Income

X

Return on Equity Net Income/Book Value of Equity

Reinvestment Rate = (Net Cap Ex + Chg in WC/EBIT(1-t)

X

Return on Capital = EBIT(1-t)/Book Value of Capital

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EsEmaEng growth in EPS: Deutsche Bank in January 2008 19

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In 2007, Deutsche Bank reported net income of 6.51 billion Euros on a book value of equity of 33.475 billion Euros at the start of the year (end of 2006), and paid out 2.146 billion Euros as dividends. 6,510 Return on Equity = Net Income = = 19.45% Book Value of Equity 33,475

RetenEon RaEo = 1 − Dividends = 1 −2,146 = 67.03%
2007 2006


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Net Income

6,510

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If Deutsche Bank maintains the return on equity (ROE) and retenEon raEo that it delivered in 2007 for t€ long run: he Expected Growth Rate ExisEng Fundamentals = 0.6703 * 0.1945 = 13.04% If we replace the net income in 2007 with average net income of $3,954 million, from 2003 to 2007: Average Net Income 3,954 Normalized Return on Equity = Book Value of Equity = 33,475 = 11.81% Normalized RetenEon RaEo = 1 − Dividends = 1 −2,146 = 45.72% Net Income 3,954 Expected Growth Rate Normalized Fundamentals = 0.4572 * 0.1181 = 5.40% 2003-07 2006





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EsEmaEng growth in Net Income: Tata Motors 20

Equity Reinvestment Rate

-­‐248.63% 46.44% 64.98% 55.12% 80.50% 87.70% Cap Ex

Year

2008-­‐09 2009-­‐10 2010-­‐11 2011-­‐12 2012-­‐13 Aggregate Net Income

-­‐25,053₹ 29,151₹ 92,736₹ 135,165₹ 98,926₹ 330,925₹ 99,708₹ 84,754₹ 81,240₹ 138,756₹ 187,570₹ 592,028₹ Change in Depreciation

WC

25,072₹ 39,602₹ 46,510₹ 56,209₹ 75,648₹ 243,041₹ 13,441₹ -­‐26,009₹ 50,484₹ 22,801₹ 680₹ 61,397₹ Change in Debt

25,789₹ 5,605₹ 24,951₹ 30,846₹ 32,970₹ 120,160₹ Equity Reinvestment

62,288₹ 13,538₹ 60,263₹ 74,502₹ 79,632₹ 290,224₹

Year

2008-­‐09 2009-­‐10 2010-­‐11 2011-­‐12 2012-­‐13 Aggregate

BV of Equity at Net Income start of the year -­‐25,053₹ 91,658₹ 29,151₹ 63,437₹ 92,736₹ 84,200₹ 135,165₹ 194,181₹ 98,926₹ 330,056₹ 330,925₹ 763,532₹

ROE -­‐27.33% 45.95% 110.14% 69.61% 29.97% 43.34%

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Reinvestment rate ROE Expected growth

Average values: 2013 value 2008-­‐2013 80.50% 87.70% 29.97% 43.34% 24.13% 38.01%

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ROE and Leverage 21

A high ROE, other things remaining equal, should yield a higher expected growth rate in equity earnings. ¨ The ROE for a firm is a funcEon of both the quality of its investments and how much debt it uses in funding these investments. In parEcular ROE = ROC + D/E (ROC -­‐ i (1-­‐t)) where, ROC = (EBIT (1 -­‐ tax rate)) / (Book Value of Capital) BV of Capital = BV of Debt + BV of Equity -­‐ Cash D/E = Debt/ Equity raEo

i = Interest rate on debt t = Tax rate on ordinary income. ¨
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Decomposing ROE 22

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Assume that you are analyzing a company with a 15% return on capital, an aPer-­‐tax cost of debt of 5% and a book debt to equity raEo of 100%. EsEmate the ROE for this company.

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Now assume that another company in the same sector has the same ROE as the company that you have just analyzed but no debt. Will these two firms have the same growth rates in earnings per share if they have the same dividend payout raEo? Will they have the same equity value? 22

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EsEmaEng Growth in EBIT: Disney ¨

We started with the reinvestment rate that we computed from the 2013 financial statements: (3,629 + 103) = 53.93% 10,032 (1-.3102) Reinvestment rate = We computed the reinvestment rate in prior years to ensure that the 2013 values were not unusual or outliers.

We compute the return on capital, using operaEng income in 2013 and capital invested at the start of the year: EBIT (1-t) 10, 032 (1-.361) = Return on Capital2013 = (BV of Equity+ BV of Debt - Cash) (41,958+ 16,328 - 3,387) = 12.61%
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Disney’s return on capital has improved gradually over the last decade and has levelled off in the last two years.

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If Disney maintains its 2013 reinvestment rate and return on capital for the next five years, its growth rate will be 6.80 percent. Expected Growth Rate from ExisEng Fundamentals = 53.93% * 12.61% = 6.8%

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When everything is in flux: Changing growth and margins 24

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The elegant connecEon between reinvestment and growth in operaEng income breaks down, when you have a company in transiEon, where margins are changing over Eme. If that is the case, you have to esEmate cash flows in three steps: ¤

Forecast revenue growth and revenues in future years, taking into account market potenEal and compeEEon. ¤ Forecast a “target” margin in the future and a pathway from current margins to the target. ¤ EsEmate reinvestment from revenues, using a sales to capital raEo (measuring the dollars of revenues you get from each dollar of investment).

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Here is an example: Baidu’s Expected FCFF 25

Revenue Year! Base year! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10! ! 25.00%! 25.00%! 25.00%! 25.00%! 25.00%! $28,756 ! 48.72%! $14,009 !16.31%! $11,724 ! ! 2.64! ! ! $35,945 ! 47.35%! $17,019 !16.31%! $14,243 ! $7,189 ! 2.64! $44,931 ! 45.97%! $20,657 !16.31%! $17,288 ! $8,986 ! 2.64! $56,164 ! 44.60%! $25,051 !16.31%! $20,965 !$11,233 ! 2.64! $70,205 ! 43.23%! $30,350 !16.31%! $25,400 !$14,041 ! 2.64! $87,756 ! 41.86%! $36,734 !16.31%! $30,743 !$17,551 ! 2.64! $2,722 ! $11,521 ! $3,403 ! $13,885 ! $4,253 ! $16,712 ! $5,316 ! $20,084 ! $6,646 ! $24,097 ! $6,878 ! $28,267 ! $6,577 ! $32,107 ! $5,649 ! $35,289 ! $4,082 ! $37,503 ! $1,974 ! $38,505 ! growth! Revenues! Operating Margin! EBIT! Chg in Sales/ Reinvestm ent! FCFF! Tax rate! EBIT (1-t)!Revenues! Capital!

20.70%! $105,922 ! 40.49%! $42,885 !18.05%! $35,145 !$18,166 ! 2.64! 16.40%! $123,293 ! 39.12%! $48,227 !19.79%! $38,685 !$17,371 ! 2.64! 12.10%! $138,212 ! 37.74%! $52,166 !21.52%! $40,938 !$14,918 ! 2.64! 7.80%! 3.50%! $148,992 ! 36.37%! $54,191 !23.26%! $41,585 !$10,781 ! 2.64! $154,207 ! 35.00%! $53,972 !25.00%! $40,479 ! $5,215 ! 2.64!

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IV. Gevng Closure in ValuaEon 26

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Since we cannot esEmate cash flows forever, we esEmate cash flows for a “growth period” and then esEmate a terminal value, to capture the value at the end of the period: t=N CF t + Terminal Value Value = ∑ (1+r)N (1+r)t t=1

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When a firm’s cash flows grow at a “constant” rate forever, the present value of those cash flows can be wriwen as: Value = Expected Cash Flow Next Period / (r -­‐ g) where, r = Discount rate (Cost of Equity or Cost of Capital) g = Expected growth rate forever.

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This “constant” growth rate is called a stable growth rate and cannot be higher than the growth rate of the economy in which the firm operates. 26

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Gevng to stable growth… 27

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A key assumpEon in all discounted cash flow models is the period of high growth, and the pawern of growth during that period. In general, we can make one of three assumpEons: ¤ ¤ ¤

there is no high growth, in which case the firm is already in stable growth there will be high growth for a period, at the end of which the growth rate will drop to the stable growth rate (2-­‐stage) there will be high growth for a period, at the end of which the growth rate will decline gradually to a stable growth rate(3-­‐stage)

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The assumpEon of how long high growth will conEnue will depend upon several factors including: ¤ ¤ ¤

the size of the firm (larger firm -­‐> shorter high growth periods) current growth rate (if high -­‐> longer high growth period) barriers to entry and differenEal advantages (if high -­‐> longer growth period)

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Choosing a Growth Period: Examples 28

Disney Firm size/market Firm is one of the largest size players in the entertainment and theme park business, but the businesses are being redefined and are expanding. Vale The company is one of the largest mining companies in the world, and the overall market is constrained by limits on resource availability. Current excess Firm is earning more than its Returns on capital are returns cost of capital. largely a function of commodity prices. Have generally exceeded the cost of capital. Competitive Has some of the most Cost advantages advantages recognized brand names in the because of access to world. Its movie business now low-cost iron ore houses Marvel superheros, reserves in Brazil. Pixar animated characters & Star Wars. Tata Motors Firm has a large market share of Indian (domestic) market, but it is small by global standards. Growth is coming from Jaguar division in emerging markets. Firm has a return on capital that is higher than the cost of capital. Baidu Company is in a growing sector (online search) in a growing market (China).

Firm earns significant excess returns.

Has wide distribution/service network in India but competitive advantages are fading there.Competitive advantages in India are fading but Landrover/Jaguar has strong brand name value, giving Tata pricing power and growth potential. Length of high- Ten years, entirely because of None, though with Five years, with much of growth period its strong competitive normalized earnings the growth coming from advantages/ and moderate excess outside India. returns.

Early entry into & knowledge of the Chinese market, coupled with government-imposed barriers to entry on outsiders.

Ten years, with strong excess returns.

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Valuing Vale in November 2013 (in US dollars)
Let's start with some history & estimate what a normalized year will look like

Year 2009 2010 2011 2012 2013+(TTM) Normalized

Operating+Income+($) Effective+tax+rate+ BV+of+Debt BV+of+Equity Cash Invested+capital Return+on+capital $6,057 27.79% $18,168 $42,556 $12,639 $48,085 9.10% $23,033 18.67% $23,613 $59,766 $11,040 $72,339 25.90% $30,206 18.54% $27,668 $70,076 $9,913 $87,831 28.01% $13,346 18.96% $23,116 $78,721 $3,538 $98,299 11.00% $15,487 20.65% $30,196 $75,974 $5,818 $100,352 12.25% $17,626 20.92% 17.25%
Estimate the costs of equity & capital for Vale

Unlevered, beta,of, Peer,Group, Value,of, Business Sample,size business Revenues EV/Sales Business Metals'&'Mining 48 0.86 $9,013 1.97 $17,739 Iron'Ore 78 0.83 $32,717 2.48 $81,188 Fertilizers 693 0.99 $3,777 1.52 $5,741 Logistics 223 0.75 $1,644 1.14 $1,874 Vale,Operations 0.8440 $47,151 $106,543 Market D/E = 54.99% Marginal tax rate = 34.00% (Brazil) Levered Beta = 0.844 (1+(1-.34)(.5499)) = 1.15 Cost of equity = 2.75% + 1.15 (7.38%) = 10.87%

Proportion, of,Vale 16.65% 76.20% 5.39% 1.76% 100.00%

%"of"revenues ERP US & Canada 4.90% 5.50% Brazil 16.90% 8.50% Rest of Latin America 1.70% 10.09% China 37.00% 6.94% Japan 10.30% 6.70% Rest of Asia 8.50% 8.61% Europe 17.20% 6.72% Rest of World 3.50% 10.06% Vale ERP 100.00% 7.38% Vale's rating: ADefault spread based on rating = 1.30% Cost of debt (pre-tax) = 2.75% + 1.30% = 4.05%

Cost of capital = 11.23% (.6452) + 4.05% (1-.34) (.3548) = 8.20% Assume that the company is in stable growth, growing 2% a year in perpetuity !"#$%"&'("$'!!"#$ = ! !"#$%!!"!!"#$%&'()!!""#$" = ! ! 2% =! = 11.59%! !"# 17.25% Value of operating assets + Cash & Marketable Securities - Debt Value of equity Value per share Stock price (11/2013) = $202,832 = $ 7,133 = $ 42,879 = $167,086 =$ 32.44 = $ 13.57

17,626! 1 − .2092 1 − !. 1159 = $202,832! . 082 − .02

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EsEmaEng Stable Period Inputs aPer a high growth period: Disney Respect the cap: The growth rate forever is assumed to be 2.5. This is set lower than the riskfree rate (2.75%). ¨ Stable period excess returns: The return on capital for Disney will drop from its high growth period level of 12.61% to a stable growth return of 10%. This is sEll higher than the cost of capital of 7.29% but the compeEEve advantages that Disney has are unlikely to dissipate completely by the end of the 10th year. ¨ Reinvest to grow: Based on the expected growth rate in perpetuity (2.5%) and expected return on capital forever aPer year 10 of 10%, we compute s a stable period reinvestment rate of 25%: ¨ Reinvestment Rate = Growth Rate / Return on Capital = 2.5% /10% = 25% ¨ Adjust risk and cost of capital: The beta for the stock will drop to one, reflecEng Disney’s status as a mature company.

¨
¤ ¤ ¤

Cost of Equity = Riskfree Rate + Beta * Risk Premium = 2.75% + 5.76% = 8.51% The debt raEo for Disney will rise to 20%. Since we assume that the cost of debt remains unchanged at 3.75%, this will result in a cost of capital of 7.29% Cost of capital = 8.51% (.80) + 3.75% (1-­‐.361) (.20) = 7.29%

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V. From firm value to equity value per share 31

Approach used

Discount dividends per share at the cost of equity

Discount aggregate FCFE at the cost of equity

To get to equity value per share

Present value is value of equity per share

Present value is value of aggregate equity. Subtract the value of equity options given to managers and divide by number of shares.

PV = Value of operating assets

+ Cash & Near Cash investments

+ Value of minority cross holdings

- Debt outstanding

= Value of equity

- Value of equity options

=Value of equity in common stock

/ Number of shares

31

Discount aggregate FCFF at the cost of capital

Aswath Damodaran

Valuing Deutsche Bank in early 2008 32

¨

To value Deutsche Bank, we started with the normalized income over the previous five years (3,954 million Euros) and the dividends in 2008 (2,146 million Euros). We assumed that the payout raEo and ROE, based on these numbers will conEnue for the next 5 years: ¤ Payout raEo = 2,146/3954 = 54.28% ¤ Expected growth rate = (1-­‐.5428) * .1181 = 0.054 or 5.4% ¤ Cost of equity = 9.23%

Aswath Damodaran

32

Deutsche Bank in stable growth 33

¨

At the end of year 5, the firm is in stable growth. We assume that the cost of equity drops to 8.5% (as the beta moves to 1) and that the return on equity also drops to 8.5 (to equal the cost of equity). Stable Period Payout RaEo = 1 – g/ROE = 1 – 0.03/0.085 = 0.6471 or 64.71% Expected Dividends in Year 6 = Expected Net Income5 *(1+gStable)* Stable Payout RaEo

= €5,143 (1.03) * 0.6471 = €3,427 million Terminal Value = Expected Dividends6 3,247

(Cost of Equity-g)

=

(.085-.03)

= 62, 318 million Euros

PV of Terminal Value =

¨ ¨

Terminal Value n 62,318 = = 40, 079 mil Euros (1+Cost of Equity High growth )n (1.0923)5

Value of equity = €9,653+ €40,079 = €49,732 million Euros Value of equity per share= Value of Equity = 49,732 = 104.88 Euros/share
# Shares 474.2

Stock was trading at 89 Euros per share at the Eme of the analysis.

Aswath Damodaran

33

Valuing Deutsche Bank in 2013 34

Current Risk Adjusted Assets (grows 3% a year for next 5 years) Tier 1 Capital ratio (increases from 15.13% to 18.00% over next 5 years Tier 1 Capital (Risk Adjusted Assets * Tier 1 Capital Ratio) Change in regulatory capital (Tier 1) Book Equity ROE (expected to improve from -1.08% to 8.00% in year 5) Net Income (Book Equity * ROE) - Investment in Regulatory Capital FCFE Terminal value of equity Present value Cost of equity Value of equity today = Number of shares outstanding = Value per share = Stock price in November 2013 = 439,851 € 1 453,047 € 2 466,638 € 3 480,637 € 4 495,056 € 5 509,908 € Steady state 517,556 €

15.13% 66,561 €

15.71% 71,156 € 4,595 € 81,424 €

16.28% 75,967 € 4,811 € 86,235 €

16.85% 81,002 € 5,035 € 91,270 €

17.43% 86,271 € 5,269 € 96,539 €

18.00% 91,783 € 5,512 € 102,051 €

18.00% 93,160 € 1,377 € 103,605 €

76,829 €

-1.08% -716 €

0.74% 602 € 4,595 € -3,993 € -3,669.80 € 8.80%

2.55% 2,203 € 4,811 € -2,608 € -2,202.88 € 8.80%

4.37% 3,988 € 5,035 € -1,047 € -812.94 € 8.80%

6.18% 5,971 € 5,269 € 702 €

8.80% 63,486.39 € 1019.50 62.27 € 35.46 €

8.00% 8,164 € 5,512 € 2,652 € 103,582.19 € 500.72 € 69,671.28 € 8.80% 8.80%

8.00% 8,287 € 1,554 € 6,733 €

8.00%

Aswath Damodaran

34

Valuing Tata Motors with a FCFE model in November 2013: The high growth period 35

¨

We use the expected growth rate of 24.13%, esEmated based upon the 2013 values for ROE (29.97%) and equity reinvestment rate (80.5%): ¨

Expected growth rate = 29.97% * 80.5% = 24.13% Cost of equity = = 6.57% + 0.964 (7.19%) = 13.50%

¨

The cost of equity for Tata Motors is 13.50%: The expected FCFE for the high growth period
Current

98,926₹ 80.50% 79,632₹ 19,294₹ 1 24.13% 122,794₹ 80.50% 98,845₹ 23,949₹ 21,100₹ 2 24.13% 152,420₹ 80.50% 122,693₹ 29,727₹ 23,075₹ 3 24.13% 189,194₹ 80.50% 152,295₹ 36,899₹ 25,235₹ 4 24.13% 234,841₹ 80.50% 189,039₹ 45,802₹ 27,597₹

¨

5 24.13% 291,500₹ 80.50% 234,648₹ 56,852₹ 30,180₹

Expected growth rate Net Income Equity Reinvestment Rate Equity Reinvestment FCFE PV of FCFE@13.5%

Aswath Damodaran

Sum of PV of FCFE = 127,187₹

35

Stable growth and value…. 36

¨

¨

APer year five, we will assume that the beta will increase to 1 and that the equity risk premium will decline to 6.98% percent (as the company becomes more global). The resulEng cost of equity is 13.55 percent. Cost of Equity in Stable Growth = 6.57% + 1(6.98%) = 13.55% We will assume that the growth in net income will drop to 6% and that the return on equity will drop to 13.55% (which is also the cost of equity).

Equity Reinvestment Rate Stable Growth = 6%/13.55% = 44.28% FCFE in Year 6 = ₹291,500(1.06)(1 – 0.4428) = ₹ 136,822million Terminal Value of Equity = ₹136,822/(0.1355 – 0.06) = ₹ 2,280,372 million

¨

To value equity in the firm today

Value of equity = PV of FCFE during high growth + PV of terminal value 5 = ₹742,008 million = ₹127,187 + 2,280,372/1.1355 ¤ Dividing by 2694.08 million shares yields a value of equity per share of ₹275.42, about 40% lower than the stock price of ₹427.85 per share.

Aswath Damodaran

36

Baidu: My valuation (November 2013)
Last%12%months Last%year
Revenues Operating income or EBIT Operating Margin Revenue Growth Sales/Capital Ratio ¥28,756 ¥14,009 48.72% 28.92% 2.64 ¥22,306 ¥11,051 49.54%

Revenue growth of 25% a year for 5 years, tapering down to 3.5% in year 10

Pre-tax operating margin decreases to 35% over time

Sales to capital ratio maintained at 2.64 (current level)

Stable Growth g = 3.5% Cost of capital = 10% ROC= 15%; Reinvestment Rate=3.5%/15% = 23.33% Terminal Value10= 32,120/(.10-035) = ¥494,159

Operating assets ¥291,618 + Cash 43,300 - Debt 20,895 Value of equity 314,023 / No of shares 2088.87 Value/share ¥150.33

Revenue growth Revenues Operating Margin EBIT Tax rate EBIT (1-t) - Reinvestment FCFF

1 25.00% ¥35,945 47.35% ¥17,019 16.31% ¥14,243 ¥2,722 ¥11,521

3 25.00% ¥44,931 45.97% ¥20,657 16.31% ¥17,288 ¥3,403 ¥13,885

3 25.00% ¥56,164 44.60% ¥25,051 16.31% ¥20,965 ¥4,253 ¥16,712

4 25.00% ¥70,205 43.23% ¥30,350 16.31% ¥25,400 ¥5,316 ¥20,084

5 25.00% ¥87,756 41.86% ¥36,734 16.31% ¥30,743 ¥6,646 ¥24,097

6 20.70% ¥105,922 40.49% ¥42,885 18.05% ¥35,145 ¥6,878 ¥28,267

7 16.40% ¥123,293 39.12% ¥48,227 19.79% ¥38,685 ¥6,577 ¥32,107

8 12.10% ¥138,212 37.74% ¥52,166 21.52% ¥40,938 ¥5,649 ¥35,289

9 7.80% ¥148,992 36.37% ¥54,191 23.26% ¥41,585 ¥4,082 ¥37,503

10 3.50% ¥154,207 35.00% ¥53,972 25.00% ¥40,479 ¥1,974 ¥38,505

Term yr EBIT (1-t) 41,896 - Reinv 9.776 FCFF 32,120

Cost of capital = 12.91% (.9477) + 3.45% (.0523) = 12.42%

Cost of capital decreases to 10% from years 6-10

Cost of Equity 12.91%

Cost of Debt (3.5%+0.8%+0.3%)(1-.25) = 3.45%

Weights E = 94.77% D = 5.23%

In November 2013, the stock was trading at ¥160.06 per share.

Riskfree Rate: Riskfree rate = 3.5%

+

Beta 1.356

X

ERP 6.94%

Unlevered Beta for Businesses: 1.30

D/E=5.52%

37

Aswath Damodaran

Disney: Inputs to ValuaEon High Growth Phase Length of Period Tax Rate 5 years 31.02% (Effective) 36.1% (Marginal) Return on Capital Reinvestment Rate 12.61% Transition Phase 5 years 31.02% (Effective) 36.1% (Marginal) Declines linearly to 10% Stable Growth Phase Forever after 10 years 31.02% (Effective) 36.1% (Marginal) Stable ROC of 10%

53.93% (based on normalized Declines gradually to 25% 25% of after-tax operating acquisition costs) as ROC and growth rates income. drop: Reinvestment rate = g/ ROC = 2.5/10=25%

Expected

Growth ROC * Reinvestment Rate = Linear decline to Stable 2.5% 0.1261*.5393 = .068 or 6.8% 11.5% Beta = 1.0013, ke = 8.52%% Pre-tax Cost of Debt = 3.75% Cost of capital = 7.81% Growth Rate of 2.5% Rises linearly to 20.0% Beta changes to 1.00; 20% Beta = 1.00; ke = 8.51%

Rate in EBIT Debt/Capital Ratio Risk Parameters

Cost of debt stays at 3.75% Cost of debt stays at 3.75% Cost of capital declines Cost of capital = 7.29% gradually to 7.29%

Aswath Damodaran

38

Current Cashflow to Firm EBIT(1-t)= 10,032(1-.31)= 6,920 - (Cap Ex - Deprecn) 3,629 - Chg Working capital 103 = FCFF 3,188 Reinvestment Rate = 3,732/6920 =53.93% Return on capital = 12.61%

Disney - November 2013
Reinvestment Rate 53.93% Return on Capital 12.61% Expected Growth .5393*.1261=.068 or 6.8% Stable Growth g = 2.5%; Beta = 1.00; Debt %= 20%; k(debt)=3.75 Cost of capital =7.29% Tax rate=36.1%; ROC= 10%; Reinvestment Rate=2.5/10=25% Terminal Value10= 9,086/(.0729-.025) = 189,738
8 9 10 $11,156 $11,531 $11,819 $4,080 $3,550 $2,955 $7,076 $7,981 $8,864
Cost of capital declines gradually to 7.29%

First 5 years Op. Assets 125,484 + Cash: 3,931 + Non op inv 2,849 - Debt 15,961 - Minority Int 2,721 =Equity 113,582 -Options 869 Value/Share $ 62.26
EBIT/*/(1/2/tax/rate) /2/Reinvestment FCFF 1 $7,391 $3,985 $3,405 2 $7,893 $4,256 $3,637 3 $8,430 $4,546 $3,884 4 $9,003 $4,855 $4,148 5 $9,615 $5,185 $4,430

Growth declines gradually to 2.75%

6 $10,187 $4,904 $5,283

7 $10,704 $4,534 $6,170

Term Yr 12,114 3,029 9,086

Cost of Capital (WACC) = 8.52% (0.885) + 2.40% (0.115) = 7.81%

Cost of Equity 8.52%

Cost of Debt (2.75%+1.00%)(1-.361) = 2.40% Based on actual A rating

Weights E = 88.5% D = 11.5%

In November 2013, Disney was trading at $67.71/share

Riskfree Rate: Riskfree rate = 2.75%

+

Beta 1.0013

X

ERP for operations 5.76%

Unlevered Beta for Sectors: 0.9239

D/E=13.10%

Aswath Damodaran

Investment decision affects risk of assets being finance and financing decision affects hurdle rate The Investment Decision Invest in projects that earn a return greater than a minimum acceptable hurdle rate Existing Investments ROC = 12.61% Current EBIT (1-t) $ 6,920 New Investments Return on Capital 12.61% The Dividend Decision If you cannot find investments that earn more than the hurdle rate, return the cash to the owners of the businesss. The Financing Decision Choose a financing mix that minimizes the hurdle rate and match your financing to your assets. Financing Choices Mostly US $ debt with duration of 6 years

Strategic investments determine length of growth period

Reinvestment Rate 53.93%

Financing Mix D=11.5%; E=88.5%

Expected Growth Rate = 12.61% * 53.93%= 6.8%

Cost of capital = 8.52% (.885) + 2.4% (.115) = 7.81%

Aswath Damodaran

Year Expected+Growth EBIT+(15t) Reinvestment FCFF Terminal+Value Cost+of+capital 1 6.80% $7,391 $3,985 $3,405 7.81% 2 6.80% $7,893 $4,256 $3,637 7.81% 3 6.80% $8,430 $4,546 $3,884 7.81% 4 6.80% $9,003 $4,855 $4,148 7.81% 5 6.80% $9,615 $5,185 $4,430 7.81% 6 5.94% $10,187 $4,904 $5,283 7.71% 7 5.08% $10,704 $4,534 $6,170 7.60% 8 4.22% $11,156 $4,080 $7,076 7.50% 9 3.36% $11,531 $3,550 $7,981 7.39% 10 2.50% $11,819 $2,955 $8,864 $189,738 7.29% Value of operating assets of the firm = Value of Cash & Non-operating assets = Value of Firm = Market Value of outstanding debt = Minority Interests Market Value of Equity = Value of Equity in Options = Value of Equity in Common Stock = Market Value of Equity/share =

PV $3,158 $3,129 $3,099 $3,070 $3,041 $3,367 $3,654 $3,899 $4,094 $94,966 $125,477 $6,780 $132,257 $15,961 $2,721 $113,575 $972 $112,603 $62.56

Disney: Corporate Financing Decisions and Firm Value

Ways of changing value… Are you investing optimally for future growth? How well do you manage your existing investments/assets? Growth from new investments Growth created by making new investments; function of amount and quality of investments Efficiency Growth Growth generated by using existing assets better Is there scope for more efficient utilization of exsting assets?

Cashflows from existing assets Cashflows before debt payments, but after taxes and reinvestment to maintain exising assets

Expected Growth during high growth period

Stable growth firm, with no or very limited excess returns

Are you building on your competitive advantages?

Length of the high growth period Since value creating growth requires excess returns, this is a function of - Magnitude of competitive advantages - Sustainability of competitive advantages

Are you using the right amount and kind of debt for your firm?

Cost of capital to apply to discounting cashflows Determined by - Operating risk of the company - Default risk of the company - Mix of debt and equity used in financing

Aswath Damodaran

41

Current Cashflow to Firm EBIT(1-t)= 10,032(1-.31)= 6,920 - (Cap Ex - Deprecn) 3,629 - Chg Working capital 103 = FCFF 3,188 Reinvestment Rate = 3,732/6920 =53.93% Return on capital = 12.61%

Disney (Restructured)- November 2013
Reinvestment Rate More selective acquisitions & 50.00% payoff from gaming Expected Growth .50* .14 = .07 or 7% Return on Capital 14.00% Stable Growth g = 2.75%; Beta = 1.20; Debt %= 40%; k(debt)=3.75% Cost of capital =6.76% Tax rate=36.1%; ROC= 10%; Reinvestment Rate=2.5/10=25%

First 5 years Op. Assets 147,704 + Cash: 3,931 + Non op inv 2,849 - Debt 15,961 - Minority Int 2,721 =Equity 135,802 -Options 972 Value/Share $ 74.91
1 EBIT * (1 - tax rate) $7,404 - Reinvestment $3,702 Free Cashflow to Firm $3,702 2 $7,923 $3,961 $3,961 3 $8,477 $4,239 $4,239 4 $9,071 $4,535 $4,535

Growth declines gradually to 2.75%

Terminal Value10= 9,206/(.0676-.025) = 216,262
8 $11,299 $3,955 $7,344 9 $11,683 $3,505 $8,178 10 $11,975 $2,994 $8,981

5 $9,706 $4,853 $4,853

6 $10,298 $4,634 $5,664

7 $10,833 $4,333 $6,500

Term Yr 12,275 3,069 9,206

Cost of Capital (WACC) = 8.52% (0.60) + 2.40%(0.40) = 7.16%

Cost of capital declines gradually to 6.76%

Cost of Equity 10.34%

Cost of Debt (2.75%+1.00%)(1-.361) = 2.40% Based on synthetic A rating

Weights E = 60% D = 40%

In November 2013, Disney was trading at $67.71/share Move to optimal debt ratio, with higher beta.

Riskfree Rate: Riskfree rate = 2.75%

+

Beta 1.3175

X

ERP for operations 5.76%

Unlevered Beta for Sectors: 0.9239

D/E=66.67%

Aswath Damodaran

First Principles 43

Maximize the value of the business (firm)

The Investment Decision Invest in assets that earn a return greater than the minimum acceptable hurdle rate

The Financing Decision Find the right kind of debt for your firm and the right mix of debt and equity to fund your operations

The Dividend Decision If you cannot find investments that make your minimum acceptable rate, return the cash to owners of your business

The hurdle rate should reflect the riskiness of the investment and the mix of debt and equity used to fund it.

The return should reflect the magnitude and the timing of the cashflows as welll as all side effects.

The optimal mix of debt and equity maximizes firm value

The right kind of debt matches the tenor of your assets

How much cash you can return depends upon current & potential investment opportunities

How you choose to return cash to the owners will depend on whether they prefer dividends or buybacks

Aswath Damodaran

43

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