The Investment Principle Aswath Damodaran Stern School of Business
First Principles • Invest in projects that yield a return greater than the minimum acceptable hurdle rate. • The hurdle rate should be higher for riskier projects and reflect the financing mix used - owners’ funds (equity) or borrowed money (debt) • Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects. • Choose a financing mix that minimizes the hurdle rate and matches the assets being financed. • If there are not enough investments that earn the hurdle rate, return the cash to stockholders. • The form of returns - dividends and stock buybacks - will depend upon the stockholders’ characteristics.
What is a investment or a project? • Any decision that requires the use of resources (financial or otherwise) is a project. • Broad strategic decisions • Entering new areas of business • Entering new markets • Acquiring other companies • Tactical decisions • Management decisions • The product mix to carry • The level of inventory and credit terms • Decisions on delivering a needed service • Lease or buy a distribution system • Creating and delivering a management information system
Measuring Returns Right: The Basic Principles • Use cash flows rather than earnings. You cannot spend earnings. • Use “incremental” cash flows relating to the investment decision, i.e., cashflows that occur as a consequence of the decision, rather than total cash flows. • Use “time weighted” returns, i.e., value cash flows that occur earlier more than cash flows that occur later. The Return Mantra: “Time-weighted, Incremental Cash Flow Return”
Steps in Investment Analysis • Estimate a hurdle rate for the project, based upon the riskiness of the investment • Estimate revenues and accounting earnings on the investment. • Measure the accounting return to see if the investment measures up to the hurdle rate. • Convert accounting earnings into cash flows • Use the cash flows to evaluate whether the investment is a good investment. • Time weight the cash flows • Use the time-weighted cash flows to evaluate whether the investment is a good investment. • Consider all side-costs and side-benefits when analyzing project.
The Essence of Discount Rates: The notion of a benchmark • Since financial resources are finite, there is a hurdle that projects have to cross before being deemed acceptable. • This hurdle will be higher for riskier projects than for safer projects. • A simple representation of the hurdle rate is as follows: Hurdle rate = Riskless Rate + Risk Premium • The two basic questions that every risk and return model in finance tries to answer are: • How do you measure risk? • How do you translate this risk measure into a risk premium?
1. The Nominal versus Real Choice & A Currency for your analysis • A project can be analyzed in nominal terms (in which case inflation is incorporated into both your cashflows and your discount rate) or in real terms. When inflation is high and volatile, analysts may find it easier to do everything in real terms. • If an analysis is nominal, you have to pick the currency to do the analysis is. Any project can be analyzed in any currency. In choosing a currency to do the analysis, you should consider: • Where the project will be located and what currency its costs and revenues will be in. (The costs may be in one currency and the revenues may be in another or more than one currency) • How easy it will be to obtain fundamental information on risk free rates and risk premiums in that currency.
2. Risk Free Rate • For an investment to be risk free, it has to fulfill two conditions: • There can have no default risk • There can be no reinvestment risk • Using this principle strictly, there can be no one risk free rate for any investment that delivers cash flows at different points in time. The right risk free rate for each cash flow will be the interest rate on a zero-coupon default free government bond maturity on the same date as the cash flow.
Some common sense rules on risk free rates • Currency with default free entity: If you are working with a currency where a default free entity exists ($ or Euro), use the interest rate on a government bond with roughly the same duration as the project as the riskfree rate for all cashflows. • Currency with no default free entity: There are two solutions when there is no default free entity: • Approach 1: Subtract default spread from local government bond rate: Government bond rate in local currency terms - Default spread for Government in local currency • Approach 2: Use forward rates and the riskless rate in an index currency (say Euros or dollars) to estimate the riskless rate in the local currency. • Real Risk free rate: To obtain a real riskfree rate, you can try the following: • from an inflation-indexed government bond, if one exists • set equal, approximately, to the long term real growth rate of the economy in which the valuation is being done.
3. Determine a debt ratio and a cost of debt for the project • Most projects do not carry debt on their own. Instead, the parent company borrows money, using its general assets as collateral, and uses this money to fund the projects. • Some projects are large enough and have assets that are separable from the firm. These projects sometimes borrow on their own assets, with no recourse against the parent company.
What debt ratio should you use for a project? Case 1: Single business company with several, small and similar projects Company’s cost of debt and debt ratio Case 2: Diverse company with large projects with different risk exposures Average debt ratio for the industry in which the project is and the cost of debt for the company Case 3: Large project which carries its own debt (with no or limited recourse to parent company assets) Estimated debt ratio for the project and cost of debt for the project
What is debt? • General Rule: Debt generally has the following characteristics: • Commitment to make fixed payments in the future • The fixed payments are tax deductible • Failure to make the payments can lead to either default or loss of control of the firm to the party to whom payments are due. • As a consequence, debt should include • Any interest-bearing liability, whether short term or long term. • Any lease obligation, whether operating or capital.
Estimating the Cost of Debt • If the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate. • If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt. • If the firm is not rated, • and it has recently borrowed long term from a bank, use the interest rate on the borrowing or • estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt • If you are estimating the cost of debt for a project, you usually have to use a synthetic rating. • The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation.
Estimating Synthetic Ratings • The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest Expenses • Consider InfoSoft, a private firm with EBIT of $2000 million and interest expenses of $ 315 million Interest Coverage Ratio = 2,000/315= 6.15 • Based upon the relationship between interest coverage ratios and ratings, we would estimate a rating of A for the firm. • You can estimate synthetic ratings for individual projects that will be carrying their own debt.
Interest Coverage Ratios, Ratings and Default Spreads Interest Coverage Ratio Rating Default Spread > 12.5 AAA 0.20% 9.50 - 12.50 AA 0.50% 7.50 – 9.50 A+ 0.80% 6.00 – 7.50 A 1.00% 4.50 – 6.00 A- 1.25% 3.50 – 4.50 BBB 1.50% 3.00 – 3.50 BB 2.00% 2.50 – 3.00 B+ 2.50% 2.00 - 2.50 B 3.25% 1.50 – 2.00 B- 4.25% 1.25 – 1.50 CCC 5.00% 0.80 – 1.25 CC 6.00% 0.50 – 0.80 C 7.50% < 0.65 D 10.00%
Costs of Debt for Boeing, the Home Depot and InfoSoft Boeing Home Depot InfoSoft Bond Rating AA A+ A Rating is Actual Actual Synthetic Default Spread over treasury 0.50% 0.80% 1.00% Market Interest Rate 5.50% 5.80% 6.00% Marginal tax rate 35% 35% 42% Cost of Debt 3.58% 3.77% 3.48% The treasury bond rate is 5%.
Everyone uses historical premiums, but.. • The historical premium is the premium that stocks have historically earned over riskless securities. • Practitioners never seem to agree on the premium; it is sensitive to • How far back you go in history… • Whether you use T.bill rates or T.Bond rates • Whether you use geometric or arithmetic averages. • For instance, looking at the US: Arithmetic average Geometric Average Stocks - Stocks - Stocks - Stocks - Historical Period T.Bills T.Bonds T.Bills T.Bonds 1928-2002 7.67% 6.25% 5.73% 4.53% 1962-2002 5.17% 3.66% 3.90% 2.76% 1992-2002 6.32% 2.15% 4.69% 0.95%
Two Ways of Estimating Country Risk Premiums… • Default spread on Country Bond: In this approach, the country risk premium is based upon the default spread of the bond issued by the country (but only if it is denominated in a currency where a default free entity exists. • Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar denominated C.Bond at the end of September 2003 was 6.01%. (10.18%-4.17%) • Relative Equity Market approach: The country risk premium is based upon the volatility of the market in question relative to U.S market. Country risk premium = Risk PremiumUS* Country Equity / US Equity Using a 4.53% premium for the US, this approach would yield: Total risk premium for Brazil = 4.53% (33.37%/18.59%) = 8.13% Country risk premium for Brazil = 8.13% - 4.53% = 3.60% (The standard deviation in weekly returns from 2001 to 2003 for the Bovespa was 33.37% whereas the standard deviation in the S&P 500 was 18.59%)
And a third 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. In this approach: • Country risk premium = Default spread on country bond* Country Equity / Country Bond • Standard Deviation in Bovespa (Equity) = 33.37% • Standard Deviation in Brazil C-Bond = 26.15% • Default spread on C-Bond = 6.01% • Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%%
Implied Equity Risk Premiums • An implied equity risk premium is a forward looking estimate, based upon how stocks are priced today and expected cashflows in the future. • On January 1, 2003, the S&P was trading at 879.82. • Treasury bond rate = 3.81% • Expected Growth rate in earnings (next 5 years) = 8% (Consensus estimate for S&P 500 earnings) • Expected growth rate after year 5 = 3.81% • Dividends + stock buybacks = 3.29% of index (in latest year) Year 1 Year 2 Year 3 Year 4 Year 5 Expected Dividends = $31.25 $33.75 $36.45 $39.37 $42.52 + Stock Buybacks Expected dividends + buybacks in year 6 = 42.52 (1.0381) = $ 44.14 879.82 = 31.25/(1+r) + 33.75/(1+r)2+ + 36.45/(1+r)3 + 39.37/(1+r)4 + (42.52+(44.14/(r-.0381))/(1+r)5 Solving for r, r = 7.91%. (Only way to do this is trial and error) Implied risk premium = 7.91% - 3.81% = 4.10%
Decomposing Boeing’s Beta Segment Revenues Estimated Value bunlevered Weight Weighted b Levered Beta Commercial Aircraft $ 26,929 $ 30,160 0.91 70.39% 0.6405 1.06 ISDS $ 18,125 $ 12,688 0.80 29.61% 0.2369 0.93 Firm $ 42,848 100.00% 0.88 1.01 • The values were estimated based upon the revenues in each business and the typical multiple of revenues that other firms in that business trade for. • The unlevered betas for each business were estimated by looking at other publicly traded firms in each business, averaging across the betas estimated for these firms, and then unlevering the beta using the average debt to equity ratio for firms in that business. Unlevered Beta = Average Beta / (1 + (1-tax rate) (Average D/E)) • Using Boeing’s current market debt to equity ratio of 25% Boeing’s Beta = = 0.88 (1+(1-.35)(.25)) = 1.014
Estimating The Home Depot’s Bottom-up Beta • Average Beta of comparable firms = 0.93 • D/E ratio of comparable firms = (200+2076)/16,232 = 14.01% • Unlevered Beta for comparable firms = 0.93/(1+(1-.35)(.1401)) = 0.86
Beta for InfoSoft, a Private Software Firm The following table summarizes the unlevered betas for publicly traded software firms. Grouping Number of Beta D/E Ratio Unlevered Firms Beta All Software 264 1.45 3.70% 1.42 Small-cap Software 125 1.54 10.12% 1.45 Entertainment Software 31 1.50 7.09% 1.43 • We will use the beta of entertainment software firms as the unlevered beta for InfoSoft. • We will also assume that InfoSoft’s D/E ratio will be similar to that of these publicly traded firms (D/E = 7.09%) • Beta for InfoSoft = 1.43 (1 + (1-.42) (.0709)) = 1.49 (We used a tax rate of 42% 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 / √R squared • In the InfoSoft example, where the market beta is 1.10 and the average R-squared of the comparable publicly traded firms is 16%, • Total Beta = 1.49/√0.16 = 3.725 • Total Cost of Equity = 5% + 3.725 (5.5%)= 25.49% • This cost of equity is much higher than the cost of equity based upon the market beta because the owners of the firm are not diversified.
Estimating a beta for a project Case 1: Single business company with several, small and similar projects Company’s levered beta Case 2: Diverse company with large projects with different risk exposures Levered beta for the industry in which the project operates. (Alternatively, you can use an unlevered beta for the industry in which the project operates and use the company’s debt to equity ratio to lever up) Case 3: Large project which carries its own debt (with no or limited recourse to parent company assets) Levered beta estimated using unlevered beta for publicly traded firms comparable to the project and the debt to equity ratio for project.
Estimating Cost of Capital: Boeing • Equity • Cost of Equity = 5% + 1.01 (5.5%) = 10.58% • Market Value of Equity = $32.60 Billion • Equity/(Debt+Equity ) = 82% • Debt • After-tax Cost of debt = 5.50% (1-.35) = 3.58% • Market Value of Debt = $ 8.2 Billion • Debt/(Debt +Equity) = 18% • Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17%
Boeing’s Divisional Costs of Capital Boeing Aerospace Defense Cost of Equity 10.58% 10.77% 10.07% Equity/(Debt + Equity) 79.91% 79.91% 79.91% Cost of Debt 3.58% 3.58% 3.58% Debt/(Debt + Equity) 20.09% 20.09% 20.09% Cost of Capital 9.17% 9.32% 8.76%
Cost of Capital: InfoSoft and The Home Depot The Home Depot InfoSoft Cost of Equity 9.78% 25.49% Equity/(Debt + Equity) 95.45% 93.38% Cost of Debt 3.77% 3.48% Debt/(Debt + Equity) 4.55% 6.62% Cost of Capital 9.51% 24.03%
In summary: Estimating cost of capital for a project • If a firm is in only one business, and all of its investments are homogeneous: • Use the company’s costs of equity and capital to evaluate its investments. • If the firm is in more than one business, but investments within each of business are similar: • Use the divisional costs of equity and capital to evaluate investments made by that division • If a firm is planning on entering a new business: • Estimate a cost of equity for the investment, based upon the riskiness of the investment • Estimate a cost of debt and debt ratio for the investment based upon the costs of debt and debt ratios of other firms in the business
Analyzing Project Risk: Three Examples • The Home Depot: A New Store • The Home Depot is a firm in a single business, with homogeneous investments (another store). • We will use The Home Depot’s cost of equity (9.78%) and capital (9.51%) to analyze this investment. • Boeing: A Super Jumbo Jet (capable of carrying 400+ people) • We will use the cost of capital of 9.32% that we estimated for the aerospace division of Boeing. • InfoSoft: An Online Software Store • We will estimate the cost of equity based upon the total beta for online retailers (5.25). We will also assume that the online software company will not borrow any money (reflecting industry practices) • Cost of capital = Cost of equity = 33.875%
Choosing a Hurdle Rate • Either the cost of equity or the cost of capital can be used as a hurdle rate, depending upon whether the returns measured are to equity investors or to all claimholders on the firm (capital) • If returns are measured to equity investors, the appropriate hurdle rate is the cost of equity. • If returns are measured to capital (or the firm), the appropriate hurdle rate is the cost of capital.
II. The Estimation Process: Sources of Information/ Estimation • Experience and History: If a firm has invested in similar projects in the past, it can use this experience to estimate revenues and earnings on the project being analyzed. • Market Testing: If the investment is in a new market or business, you can use market testing to get a sense of the size of the market and potential profitability. • Macro economic/ Sector forecasters: There are services that provide forecasts of varying accuracy/ reliability on what they think will happen to the economy or a particular sector. • Market Data: There are some cases where market prices provide information that can be used in forecasts. This is especially the case when you are forecasting interest rates, exchange rates and commodity prices.
Three approaches to estimation • Expected value approach: In this approach, we estimate the expected revenues and earnings of a project. While these are point estimates, they presumably incorporate all the information you have on other scenarios. • Simulation: In this approach, we estimate a statistical distribution (and the parameters of the distribution) for each variable. We then run simulations drawing from the distribution and compute the return on each simulation. The output is a distribution of the decision variable (NPV, IRR, ROC etc.) • Scenario Analysis: In this approach, we define scenarios for key variables and probabilities of each occurring. We then compute the revenues and earnings under scenario. The output is the decision variable under each scenario.
The Home Depot’s New Store: Experience and History • The Home Depot has 700+ stores in existence, at difference stages in their life cycles, yielding valuable information on how much revenue can be expected at each store and expected margins. • At the end of 1999, for instance, each existing store had revenues of $ 44 million, with revenues starting at about $ 40 million in the first year of a store’s life, climbing until year 5 and then declining until year 10.
Projections for The Home Depot’s New Store -Expected Value Analysis • For revenues, we will assume • that the new store being considered by the Home Depot will have expected revenues of $ 40 million in year 1 (which is the approximately the average revenue per store at existing stores after one year in operation) • that these revenues to grow 5% a year • that our analysis will cover 10 years (since revenues start dropping at existing stores after the 10th year). • For operating margins, we will assume • The operating expenses of the new store will be 90% of the revenues (based upon the median for existing stores)
The Simulation Alternative • Instead of using the expected values for each variable and arriving at a set of expected cashflows for the analysis, we could have enriched the analysis by assuming a distribution for each of the key variables - revenues, margins and growth, for instance. • Steps in a simulation • Step 1: Determine the variables that you will be estimating distributions/parameters for. • Step 2: Choose the statistical distribution for each of the variables and esitmate the parameters of the distribution. • Step 3: Run your first simulation, drawing one outcome from each distribution. • Step 4: Repeat process. The number of simulations run will depend upon how many variables are being simulated and the range of outcomes. • Step 5: Compute your decision variable (NPV, IRR, ROIC) for each simulation and report the findings in a distribution.
What simulations do and what they do not… • Simulations do • Provide richer information about a project’s outcomes to decision makers. • Provide information about potentially dangerous outcomes (for the firm), in terms of worst case scenarios. (Violation of lending covenants, Failure to make interest payments etc.) • A measure of “outcome variability” that can be compared across mutually exclusive investments • Simulations do not • Adjust cash flows for risk (They generate expected cashflows) • Provide better estimates of the expected value or NPV of an investment.
When simulations make sense and when they do not.. • Simulations make sense • When there is sufficient information to estimate the correct statistical distributions for each variables and the parameters of those distributions. This is most likely to be the case for firms that • Take the same kind of investment over and over again (like the Home Depot) • Have done extensive market testing of a product or service and generated output from the testing which can be used in the distribution • When there is a lower bound constraint, which if violated, can lead to the project ending. (An example would be capital ratio constraints at banks…) • Simulations don’t make sense • When the distributions chosen and the parameters used are arbitrary. It is garbage in, garbage out.
Scenario Analysis: Boeing Super Jumbo • We consider two factors: • Actions of Airbus (the competition): Produces new large capacity plane to match Boeing’s new jet, Improves its existing large capacity plane (A-300) or abandons this market entirely. • Much of the growth from this market will come from whether Asia. We look at a high growth, average growth and low growth scenario. • In each scenario, • We estimate the number of planes that Boeing will sell under each scenario. • We estimate the probability of each scenario.
Scenario Analysis • The following table lists the number of planes that Boeing will sell under each scenario, with the probabilities listed below each number. Airbus New Airbus A-300 Airbus abandons large plane large airplane High Growth in Asia 120 150 200 (0.125) (0.125) (0.00) Average Growth in Asia 100 135 160 (0.15) (0.25) (0.10) Low Growth in Asia 75 110 120 (0.05) (0.10) (0.10) Expected Value = 120*0.125+150*.125+200*0+100*.15+135*.25 +160*.10+ 75*.05+110*.10+120*10 = 125 planes
III. Measures of return: Accounting Earnings • Principles Governing Accounting Earnings Measurement • Accrual Accounting: Show revenues when products and services are sold or provided, not when they are paid for. Show expenses associated with these revenues rather than cash expenses. • Operating versus Capital Expenditures: Only expenses associated with creating revenues in the current period should be treated as operating expenses. Expenses that create benefits over several periods are written off over multiple periods (as depreciation or amortization)