Discounted Cash Flow Valuation: Many a slip between the cup and the lip… Aswath Damodaran www.damodaran.com
Some Initial Thoughts " One hundred thousand lemmings cannot be wrong" Graffiti
Misconceptions about Valuation • Myth 1: A valuation is an objective search for “true” value • Truth 1.1: All valuations are biased. The only questions are how much and in which direction. • Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid. • Myth 2.: A good valuation provides a precise estimate of value • Truth 2.1: There are no precise valuations • Truth 2.2: The payoff to valuation is greatest when valuation is least precise. • Myth 3: . The more quantitative a model, the better the valuation • Truth 3.1: One’s understanding of a valuation model is inversely proportional to the number of inputs required for the model. • Truth 3.2: Simpler valuation models do much better than complex ones.
Approaches to Valuation • Discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. • Relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like earnings, cashflows, book value or sales. • Contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics.
Discounted Cash Flow Valuation • What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. • Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. • Information Needed: To use discounted cash flow valuation, you need • to estimate the life of the asset • to estimate the cash flows during the life of the asset • to estimate the discount rate to apply to these cash flows to get present value • Market Inefficiency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets.
DCF Choices: Equity Valuation versus Firm Valuation Firm Valuation: Value the entire business Equity valuation: Value just the equity claim in the business
Operating Leases at The Gap in 2003 • The Gap has conventional debt of about $ 1.97 billion on its balance sheet and its pre-tax cost of debt is about 6%. Its operating lease payments in the 2003 were $978 million and its commitments for the future are below: Year Commitment (millions) Present Value (at 6%) 1 $899.00 $848.11 2 $846.00 $752.94 3 $738.00 $619.64 4 $598.00 $473.67 5 $477.00 $356.44 6&7 $982.50 each year $1,346.04 Debt Value of leases = $4,396.85 (Also value of leased asset) • Debt outstanding at The Gap = $1,970 m + $4,397 m = $6,367 m • Adjusted Operating Income = Stated OI + OL exp this year - Deprec’n = $1,012 m + 978 m - 4397 m /7 = $1,362 million (7 year life for assets) • Approximate OI = $1,012 m + $ 4397 m (.06) = $1,276 m
Capitalizing R&D Expenses: SAP in 2004 • R & D was assumed to have a 5-year life. Year R&D Expense Unamortized portion Amortization this year Current 1020.02 1.00 1020.02 -1 993.99 0.80 795.19 € 198.80 -2 909.39 0.60 545.63 € 181.88 -3 898.25 0.40 359.30 € 179.65 -4 969.38 0.20 193.88 € 193.88 -5 744.67 0.00 0.00 € 148.93 Value of research asset = € 2,914 million Amortization of research asset in 2004 = € 903 million Increase in Operating Income = 1020 - 903 = € 117 million
II. Get the big picture (not the accounting one) when it comes to cap ex and working capital • Capital expenditures should include • Research and development expenses, once they have been re-categorized as capital expenses. • Acquisitions of other firms, whether paid for with cash or stock. • Working capital should be defined not as the difference between current assets and current liabilities but as the difference between non-cash current assets and non-debt current liabilities. • On both items, start with what the company did in the most recent year but do look at the company’s history and at industry averages.
Acquisitions and Growth • If you want to count the growth from acquisitions, you have to count the cost of acquisitions as part of capital expenditures. If you count the growth but not the acquisitions, you will over value the company. • You have the alternative of completely ignoring acquisitions for both growth and cap ex. If you do so, you are assuming that acquisitions are value neutral (and that you pay a fair price on every acquisition). • The most difficult part of dealing with acquisitions is that they tend to be volatile; in some cases, a firm may do an acquisition once every three or four years. You have to normalize acquisition costs over multiple years.
Is Beta an Adequate Measure of Risk for a Private Firm? The owners of most private firms are not diversified. Beta measures the risk added on to a diversified portfolio. Therefore, using beta to arrive at a cost of equity for a private firm will • Under estimate the cost of equity for the private firm • Over estimate the cost of equity for the private firm • Could under or over estimate the cost of equity for the private firm
Total Risk versus Market Risk • Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively simple one, since the R squared of the regression measures the proportion of the risk that is market risk. Total Beta = Market Beta / Correlation of the sector with the market • To estimate the beta for Kristin Kandy, we begin with the bottom-up unlevered beta of food processing companies: • Unlevered beta for publicly traded food processing companies = 0.78 • Average correlation of food processing companies with market = 0.333 • Unlevered total beta for Kristin Kandy = 0.78/0.333 = 2.34 • Debt to equity ratio for Kristin Kandy = 0.3/0.7 (assumed industry average) • Total Beta = 2.34 ( 1- (1-.40)(30/70)) = 2.94 • Total Cost of Equity = 4.50% + 2.94 (4%) = 16.26%
IV. And the past is not always a good indicator of the future • It is standard practice to use historical premiums as forward looking premiums. : Arithmetic average Geometric Average Stocks - Stocks - Stocks - Stocks - Historical Period T.Bills T.Bonds T.Bills T.Bonds 1928-2005 7.83% 5.95% 6.47% 4.80% 1964-2005 5.52% 4.29% 4.08% 3.21% 1994-2005 8.80% 7.07% 5.15% 3.76% • An alternative is to back out the premium from market prices: • Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 8.47%-4.39% = 4.08%
Implied Premium for Brazil - February 2006 • Using the Bovespa as our measure of Brazilian equity, we estimated the following: • Level of index = 38364 • FCFE for stocks in index in 2005 = 4.73% of index level • Expected growth rate (in US $) in earnings & FCFE for next 5 years = 10.00% • Growth rate beyond year 5 = 4.50% • Risk free rate= 4.50% • Solving for the level of the index, we get • Expected return on Brazilian stocks = 10.73% • Implied equity risk premium for Brazil = 10.73% - 4.50% = 6.23%
V. There is a downside to globalization… • Emerging markets offer growth opportunities but they are also riskier. If we want to count the growth, we have to also consider the risk. • Consider, for example, Brazil as a country. There are two simple assessments of country risk that we can use for it - • A country rating from S&P, Moody’s or IBCA and an associated default spread for that rating. • The default spread between a dollar denominated bond issued by the Brazilian government and the treasury bond rate.
A blended approach… • Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads. • Another is to multiply the bond default spread by the relative volatility of stock and bond prices in that market. Using this approach in 2003: • Country risk premium = Default spread on country bond* Country Equity / Country Bond • Standard Deviation in Bovespa (Equity) = 29.24% • Standard Deviation in Brazil C-Bond = 24.15% • Default spread on C-Bond = 6.50% • Country Risk Premium for Brazil = 6.50% (29.24%/24.15%) = 7.87% • Using the same approach in 2006 would yield a much lower country risk premium: • Country risk premium = 2.00% (27.15%/15.56%) = 3.49%
VI. And it is not just emerging market companies that are exposed to this risk.. • If we treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales) E(Return)=Riskfree Rate+ b (US premium) + l (Country ERP) • The easiest and most accessible data is on revenues. Most companies break their revenues down by region. One simplistic solution would be to do the following: = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm • Consider, for instance, Embraer, Embratel and Ambev, all of which are incorporated and traded in Brazil. Embraer gets 3% of its revenues from Brazil, Embratel gets almost all of its revenues in Brazil and Ambev gets about 92% of its revenues in Brazil. The average Brazilian company gets about 77% of its revenues in Brazil: • LambdaEmbraer = 3%/ 77% = .04 • LambdaEmbratel = 100%/77% = 1.30 • LambdaAmbev = 92%/77% = 1.19 • There are two implications • A company’s risk exposure is determined by where it does business and not by where it is located • Firms might be able to actively manage their country risk exposures
Estimating Lambdas: Stock Returns versus C-Bond Returns ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond ReturnAmbev = 0.0290+ 0.4136 ReturnC Bond ReturnPetrobras= -0.0308 + 0.6600 ReturnC Bond ReturnVale = 0.02169 + 0.3760.ReturnC Bond
VII. Discount rates can (and often should) change over time… • The inputs into the cost of capital - the cost of equity (beta), the cost of debt (default risk) and the debt ratio - can change over time. For younger firms, they should change over time. • At the minimum, they should change when you get to your terminal year to inputs that better reflect a mature firm.
But you can get a bonus from using existing assets more efficiently… • When the return on equity or capital is changing, there will be a second component to growth, positive if the return is increasing and negative if the return is decreasing. • If ROCt is the return on capital in period t and ROCt+1 is the return on capital in period t+1, the expected growth rate in operating income will be: Expected Growth Rate = ROCt+1 * Reinvestment rate +(ROCt+1 – ROCt) / ROCt • For example, a company whose return on capital increases from 5% to 7.5% in a year will report an earnings growth rate of 50%, even with no new investment. If it happens over 5 years, there will be approximately 10% higher growth each for those five years.
And if margins are changing, start with revenues… and keep your life simple Year Revenues Growth Operating Margin EBIT Tr12m $1,117 -36.71% -$410 1 $2,793 150% -13.35% -$373 2 $5,585 100% -1.68% -$94 3 $9,774 75% 4.16% $407 4 $14,661 50% 7.08% $1,038 5 $19,059 30% 8.54% $1,628 6 $23,862 25.2% 9.27% $2,212 7 $28,729 20.4% 9.64% $2,768 8 $33,211 15.6% 9.82% $3,261 9 $36,798 10.8% 9.91% $3,646 10 $39,006 6% 9.95% $3,883 TY(11) $41,346 10.00% $4,135
IX. All good things come to an end..And the terminal value is not an ATM…
Growth, Reinvestment and Terminal Value: Back to Embraer Return on capital = 8.76% Reinvestment Rate = g/8.76%
1a. The Value of Cash • The simplest and most direct way of dealing with cash and marketable securities is to keep it out of the valuation - the cash flows should be before interest income from cash and securities, and the discount rate should not be contaminated by the inclusion of cash. (Use betas of the operating assets alone to estimate the cost of equity). • Once the operating assets have been valued, you should add back the value of cash and marketable securities.
Should you ever discount cash for its low returns? • There are some analysts who argue that companies with a lot of cash on their balance sheets should be penalized by having the excess cash discounted to reflect the fact that it earns a low return. • Excess cash is usually defined as holding cash that is greater than what the firm needs for operations. • A low return is defined as a return lower than what the firm earns on its non-cash investments. • This is the wrong reason for discounting cash. If the cash is invested in riskless securities, it should earn a low rate of return. As long as the return is high enough, given the riskless nature of the investment, cash does not destroy value. • There is a right reason, though, that may apply to some companies…
1b. Dealing with Holdings in Other firms • Holdings in other firms can be categorized into • Minority passive holdings, in which case only the dividend from the holdings is shown in the balance sheet • Minority active holdings, in which case the share of equity income is shown in the income statements • Majority active holdings, in which case the financial statements are consolidated.
How to value holdings in other firms.. In a perfect world.. • In a perfect world, we would strip the parent company from its subsidiaries and value each one separately. The value of the combined firm will be • Value of parent company + Proportion of value of each subsidiary • To do this right, you will need to be provided detailed information on each subsidiary to estimated cash flows and discount rates.
Two compromise solutions… • The market value solution: When the subsidiaries are publicly traded, you could use their traded market capitalizations to estimate the values of the cross holdings. You do risk carrying into your valuation any mistakes that the market may be making in valuation. • The relative value solution: When there are too many cross holdings to value separately or when there is insufficient information provided on cross holdings, you can convert the book values of holdings that you have on the balance sheet (for both minority holdings and minority interests in majority holdings) by using the average price to book value ratio of the sector in which the subsidiaries operate.
2. Other Assets that have not been counted yet.. • Unutilized assets: If you have assets or property that are not being utilized (vacant land, for example), you have not valued it yet. You can assess a market value for these assets and add them on to the value of the firm. • Overfunded pension plans: If you have a defined benefit plan and your assets exceed your expected liabilities, you could consider the over funding with two caveats: • Collective bargaining agreements may prevent you from laying claim to these excess assets. • There are tax consequences. Often, withdrawals from pension plans get taxed at much higher rates. Do not double count an asset. If you count the income from an asset in your cashflows, you cannot count the market value of the asset in your value.
3. A Discount for Complexity:An Experiment Company A Company B Operating Income $ 1 billion $ 1 billion Tax rate 40% 40% ROIC 10% 10% Expected Growth 5% 5% Cost of capital 8% 8% Business Mix Single Business Multiple Businesses Holdings Simple Complex Accounting Transparent Opaque • Which firm would you value more highly?