Valuation (Part I)

by Tim Koller, Marc Goedhart, and David Wessels

Fundamental Principles of Value Creation
ValuationCompanies create value by investing capital at rates of return greater than the cost of capital. While stock markets might be obsessed with short-term quarterly earnings, business leaders maximize value by focusing on long-term value creation. Market prices, after all, closely track the fundamental performance of a company and the larger economy in the long run. When prices do deviate from fundamentals, they tend to be short-lived and concentrated among a small number of stocks in a particular sector. The value-weighted S&P 500 index, for example, declined by almost 40% in the wake of the Internet Bubble, driven by the collapse of a few large-capitalization companies in technology, media, and telecommunications (or TMT). The median S&P company price, on the other hand, declined only 8% from peak to trough over the same period.

A value manager is someone who focuses on long-term cash flow. Take the case of a hypothetical, laggard company with multiple lines of business. The following steps could be taken to identify value opportunities. (1) A manager can determine if capital is being allocated efficiently by comparing returns on invested capital (ROIC) to capital invested by segment. (2) It can be seen whether improving margins or accelerating revenue growth is more important by conducting a sensitivity analysis by segment. (Realistic assumptions for margins can be found by looking at peers). (3) After determining the value of individual segments using a discounted cash flow (DCF) model, managers might find that some parts of their business are worth more to someone else and therefore worth divesting. (4) A manager might alternatively add value by adding more debt to the company’s balance sheet, thereby leveraging returns and disciplining the company to think harder about generating cash flows. (5) If potential acquisitions are available, the company shouldn’t pay more than the pre-acquisition value plus any potential value created through management improvements and synergies.

Return on invested capital (ROIC) is one of two key drivers of business value. It should not be taken in isolation, however, since it can be increased in the short term at the detriment of the long term (e.g. decreasing R&D spending or cutting back on customer service). Other drivers of profits should also be considered, such as pricing, market share, new products, unit costs, and quality. By itself, ROIC also discloses nothing about the amount of capital invested (i.e. a ROIC of 50% on $1 is a jaw-dropping $0.50). Economic profit, defined as (ROIC – WACC) * invested capital, is the preferred measure, as it can be used to choose strategies that maximize real value. Valuing a company is found by discounting economic profits by the opportunity cost of capital and adding the capital invested today, which equals the same value as using the DCF approach.

The second key driver of cash flow is long-term revenue growth. Taken together with ROIC, value can be expressed using the Key Value Driver Formula:

Key Value Driver Formula

This formula shows that higher growth will generate greater value, but only as long as the return on new invested capital is greater than the cost of capital. If a company already has a high ROIC, then it creates value by increasing growth. Companies with low ROIC create more value by increasing ROIC. You can further divide both sides of the equation by NOPLAT to derive a company’s earnings multiple.

Key Value Earnings Multiple

A helpful feature of the above formula is that the market’s expectations about a company’s long-term growth can be backed out if the ROIC, WACC, and P/E are already known. Although it doesn’t always make sense to use multiples, expressing a DCF valuation as an implied multiple does provide a useful sanity check, forcing you to justify why a multiple is higher or lower in terms of faster growth, higher margins, etc.

Empirical research supports the view that cash flows, driven by revenue growth and return on investment, determine the value of companies.  Over the decade from 1993 to 2003, ROIC and growth accounted for 46% of the variation in market-value-to-capital ratios among 563 U.S. companies. A separate study between 1992 and 1997 found that 40% of companies reporting positive earnings saw their prices subsequently decline. This is because total return to shareholders (TRS) is driven more by performance relative to expectations rather than the reported levels of earnings and growth themselves. In other words, reactions to earnings announcements have less to do with short-term results and more to do with real changes in long-term prospects (though investors do use short-term results as a gauge for long-term corporate performance). Companies are rarely penalized by markets, for example, when they depress current earnings and cash flows by increasing R&D or PP&E spending, so long as companies are expected to create value from it.

Core Valuation Techniques
This section begins with a high-level summary of the most common valuation models, all of which result in the same values by different means. The summary is followed by more detailed explanations of each.

The Enterprise Discounted Cash Flow (DCF) Model is popular among practitioners because it relies solely on cash flows rather than complex accounting-based earnings. To value a company using enterprise DCF, first discount FCF from operations at the WACC (since FCF is available to all investors). Second, estimate the value of non-operating assets and add to the value from operations to determine enterprise value. Third, subtract all non-equity claims from enterprise value. Fourth, divide equity value by undiluted shares outstanding (since the value of employee stock options was already subtracted from enterprise value) to determine the value of common stock.

The Economic Profit (EP) Model is growing in popularity because it highlights in each year whether a company is earning its cost of capital. By comparison, DCF models can show growing FCFs each year while simultaneously hiding that ROIC is possibly falling.

Economic Profit Formula

The Adjusted Present Value (APV) Model is ideal for situations in which a company’s current capital structure is not expected to persist. This model severs as an alternative to adjusting WACC yearly by separating the value of operations into two components. The first component values the company as if it were all-equity financed. This is done by discounting FCF by the unlevered cost of equity. The second component is the value of tax shields that arise from the company’s use of debt financing. If the company’s debt is expected to grow in line with the business, the unlevered cost of equity (ku) can be calculated using the cost of debt (kd), the levered cost of equity (ke) and the current debt-to-equity ratio.

Unlevered Cost of Equity

The value of interest tax shield in a given year is calculated by taking the prior year net debt, multiplied by the expected interest rate, multiplied by the marginal tax rate. Net debt is reported debt, plus capitalized operating leases, less excess cash. If there is a significant probability of default, then each tax shield should be reduced by the cumulative probability of default.

Return on Invested Capital (ROIC) is one of the two primary drivers of a company’s value. Based on empirical evidence, the typical company’s ROIC gradually regresses toward the median ROIC of 9% (excluding goodwill). Some companies, however, are capable of achieving high ROIC persistence over long periods of time. To maintain a high ROIC, companies must have the ability to charge a price premium (through differentiated products), have lower unit costs than its competitors (through economies of scale), or sell more products per dollar of invested capital (through capital efficiency). Companies earning returns in excess of their cost of capital invite competition, but companies can maintain their competitive advantage through patents, strong brands, and capable distribution.

Median ROIC between 1963 and 2003 was 9% without goodwill, oscillating between 6.9% and 10.6%. This variation was tied directly to economic growth (1% increase in GDP translated to 0.2% increase in median ROIC). Median ROICs varied dramatically across industries, with the strongest ROICs (11-18%) occurring across industries that rely on patents and brands while the lowest ROICs (6-8%) were found among more basic industries. Median ROICs also increase consistently with revenue growth since the same underlying factors that determine ROIC (e.g. barriers to entry) also influence growth.

Median Revenue Growth, the second primary driver of value, was 6.3% in real terms over the same period of study. (These results were analyzed using real, rather than nominal, data to eliminate the effect of inflation. For forecasting purposes, expected inflation should be added back in). Median growth rates fluctuated widely between 1.8% and 10.8%. High growth rates also decayed very quickly, meaning that high growth is not sustainable for the typical company and generally only maintained through acquisitions. The reason corporate growth (6.3%) can be higher than real GDP growth (3.3%) can be explained by self-selection (corporations grow faster than their private counterparts), global expansion (corporations generate revenue outside of the U.S.), and the use of medians (GDP is driven by large companies which grow more slowly, whereas the median corporation is small and fast growing).

We now detail how to calculate ROIC and its underlying components correctly. The three fundamentals to ROIC involve understanding that (1) it only includes operating items, (2) the numerator represents income available to all investors, and (3) if an asset (liability) is included in the denominator, its related income (expense) should be included in the numerator.

  • ROIC = NOPLAT / average of starting and ending Invested Capital
  • NOPLAT = Revenue – Operating Expenses + Implied Interest on Operating Lease + R&D Expense – Adjusted Taxes
    • Excludes interest expense and non-operating income, gains or losses
  • Operating Expenses = Cost of Goods Sold (COGS) + Selling, General and Administrative (SG&A) + Depreciation + Amortization
  • Adjusted Taxes = Reported Taxes + Tax Shield on Interest Expense (from debt and capitalized leases) + Tax Shield on Retirement Liabilities – Taxes on Non-Operating Income – Increase in Deferred Taxes
  • Tax Shield on Interest Expense = Interest Expense * Marginal Tax Rate (found in footnotes)
  • Taxes on Non-Operating Income = Non-Operating Line Items * Marginal Tax Rate
  • Invested Capital = Operating Working Capital + Net Property and Equipment + Capitalized Operating Leases and R&D + Net Other Long-Term Operating Assets
    • Optionally, add Goodwill and Acquired Intangibles, inclusive of write-downs, cumulative amortization and pooled goodwill. Ensure that amortization and impairments are not deducted from NOPLAT to maintain consistency. Optionally including Goodwill is used to measure returns to shareholders. Excluding it provides a way to measure internal performance and is useful for peer comparisons.
  • Operating Working Capital = Operating Current Assets – Operating Current Liabilities
  • Operating Current Assets = Working Cash + Net Receivables + Inventories + Prepaid Expenses + Other Current Assets
  • Working Cash = any cash < 2% of sales
    • This varies by industry. Look for a minimum clustering of cash-to-revenue across peers. The remainder cash and marketable securities are considered excess.
  • Operating Current Liabilities = Accounts Payable + Accrued Salaries + Deferred Revenue + Income Taxes Payable + Other Accrued Expenses
  • Net Other Long-Term Operating Assets = Other Long-Term Assets – Other Long-Term Liabilities
    • Use balance sheet totals if assumed to all be operating-related, otherwise subtract out non-operating items as disclosed in footnotes.

For companies that utilize Operating Leases, the expense should be capitalized and added to the balance sheets as an asset and liability (i.e. debt). Invested capital should also be increased by the capitalized value. The implied interest payment is calculated as the capitalized value multiplied by the cost of debt.

Operating Leases

Research and Development (R&D) costs should also be capitalized. Choose an amortization period and restate financials by eliminating R&D expenditures from the income statement and adding it to the balance sheet (assets and equity). Deduct R&D amortization from the respective statements each year. Taxes need not be adjusted.

We can now value a company’s operations using the economic profit model by adding invested capital to the discounted present value of economic profits. Alternatively, if using the DCF model, free cash flows (FCF) still need to be determined.

  • FCF = NOPLAT + Non-Cash Operating Expenses – (Change in Invested Capital – Increase in Foreign Currency Translation Effect)
    • FCF excludes investments in non-operating assets, which should be valued separately.
    • Currency Translations are found in Accumulated Other Comprehensive Income (AOCI).
  • Non-Cash Operating Expenses = Depreciation + Employee Stock Options
    • Do not add back goodwill amortization and impairments.

Given the complexity of the calculations listed above, it is advisable you double-check your work. This can be accomplished by using different methods to calculate the same thing. Although the work is redundant, it helps you avoid errors and omissions. Invested capital can be cross-checked with total funds, NOPLAT can be reconciled to net income, and cash flow available to all investors should equal total financing flows.

  • Total Funds = Invested Capital (including goodwill) + Non-Operating Assets = Debt (including capitalized leases) + Equity + Equity Equivalents
  • Debt = Commercial Paper + Notes Payable + Current Portion of Long-Term Debt + Long-Term Debt + Unfunded Pension and Medical Expenses + Capitalized Leases + Reserves*
    • Only include reserves for the purpose of plant decommissioning and restructuring
  • Equity = Common Stock + Additional Paid-In Capital + Retained Earnings + Accumulated Other Comprehensive Income – Repurchased Stock + Deferred Taxes + Cumulative Amortization and Pooled Goodwill + Reserves†
    • Only include reserves for the purpose of income smoothing
  • NOPLAT = Net Income + Increase in Deferred Taxes + Goodwill Amortization + After-Tax Interest Expense (from debt and capitalized leases) – After-Tax Gains (e.g. Discontinued Operations) – After-Tax Non-Operating Income
  • Cash Flow Available to All Investors = FCF + After-Tax Interest and Gains on Excess Cash and Marketable Securities + After-Tax Income and Gains from Other Non-Operating Assets
  • Total Financing Flow = After-Tax Interest Expenses + Change in Net Debt (including capitalized leases) + Dividends + Net Shares Repurchased + Change in Debt and Debt Equivalents
  • Debt and Debt Equivalents = Accrued Pension Liabilities + Accrued Postretirement Medical Benefits

Non-Operating Assets
All assets (liabilities) not included in the DCF valuation must be valued separately and added to (subtracted from) the enterprise value of a company’s operations. The most frequently encountered non-operating assets include excess cash and marketable securities, illiquid investment, non-consolidated subsidiaries, tax loss carryforwards, discontinued operations, excess real estate, and net pension assets. For excess cash and marketable securities, book values can be used since companies report such assets at their fair market value. Reported book values serve as a reasonable approximation for illiquid investments, such as credit card receivables and loans to other companies.

For non-consolidated subsidiaries that are publicly traded, use market values or build a separate DCF valuation. If financial information is not accessible and the parent has a 20-50% equity stake, project future cash-flows-to-equity (since subsidiary’s net income and approximate book equity are disclosed in parent’s financials) and discount at the subsidiary’s cost of equity. Alternatively, perform a valuation based on a price-to earnings or market-to-book multiple. For equity stakes below 20%, start with the investment’s historical cost and increase by the relative price increase for a portfolio of comparable stocks (i.e. tracking portfolio) over the same holding period.

Tax loss carryforwards (or “net operating losses”) can be valued using the tax rate multiplied by accumulated tax losses. (Alternatively, forecast the balance on a year-by-year basis by adding any future losses and subtracting any future taxable profits. For each year the account is used to offset taxable profits, discount the savings at the cost of debt). Use book values for discontinued operations. Excess real estate (and other unutilized assets) can be valued using the most recent appraisal values or estimated using appraisal multiples (e.g. value per square foot).

Non-Equity Claims
The most common non-operating liabilities (or non-equity claims) include corporate debt, unfunded pension liabilities, preferred stock, certain provisions, contingent liabilities, employee stock options, convertible debt, and minority interests. Corporate debt can include commercial paper, bank loans, corporate bonds, and capital leases. If actively traded, use market values. Otherwise, estimate current value by discounting promised payments at YTM. For fixed-rate debt, book values serve as a reasonable approximation. Do not use book values for pension and post-retirement liabilities. Rather, consult the notes to the balance sheet and use the fair values (fund assets less total pension liabilities) on an after-tax basis. For preferred stock, use market values if traded. Otherwise perform a separate DCF valuation of future preferred dividends discounted at the cost of unsecured debt.

Only two provisions should be deducted from enterprise value: long-term operating provisions (e.g. for plant-decommissioning costs) and non-operating provisions (for restructuring charges resulting from layoffs). Use book values. Do not make adjustments for ongoing operating provisions (e.g. for warranties and product returns) or income-smoothing provisions. Contingent liabilities are discussed separately in the notes and include examples such as pending litigation and loan guarantees. Estimate the associated expected after-tax cash flows and discount at the cost of debt. For employee stock options currently outstanding, values disclosed in the footnotes are a good approximation. More sophisticated valuations involve Black-Scholes option-pricing models or binomial (lattice) models. Market values are suitable for convertible debt, if traded. Otherwise assume all convertible bonds are immediately converted into equity. Minority interests are the inverse of non-consolidated subsidiaries. If the minority stake is publicly listed, deduct the proportional market value owned by outsiders. Alternatively, build a separate valuation using multiples, a DCF approach, or tracking portfolio.

Forecasting Performance
When projecting a company’s performance, detailed forecasts of financial statements should be modeled over 5 to 15 years. Explicit forecasts are best modeled in Excel using successive worksheets, with each one flowing to and driving the next. The most effort should be given to forecasting revenue since it determines almost every other item.

  1. Raw Historical Data: Begin by collecting historical financials from the company’s annual reports. Raw data is often available through third party providers as well. However, these services format data using standardized categories, which often hide important value drivers. Even financial statements themselves combine key information into simplified line items. Therefore, it is always critical to consult the footnotes and disaggregate significant line items.
  2. Integrated Financial Statements: Re-create the historical financials, but link all of the statements together. Line items that are immaterial can be consolidated for simplicity. Be sure to distinguish operating from non-operating expenses (e.g. COGS occasional includes pension items). This worksheet will include future forecasted periods. Formulas for the past and future should be the same.
  3. Forecast Ratios: For each line item, calculate historical ratios and forecast future ones. Most line items are tied directly to revenue or a specific asset or liability. Depreciation should be forecasted as a percentage of net PP&E. Non-operating income is generated by non-operating assets. Interest expense is driven by total debt from the previous year, though it will not affect the company’s valuation. The operating tax rate in a given year is reported taxes, plus non-operating expenses multiplied by the marginal tax rate, less non-operating income multiplied by the marginal tax rate. If operating tax rates differ from the marginal tax rate and this pattern is expected to continue, use the average historical rate. Otherwise, use the marginal rate. Forecast all working capital items in terms of days to forecast the intentions of management. Net PP&E should be forecasted as a percent of revenues (but always calculate the implied capital expenditures – change in net PP&E plus depreciation – to ensure projections are not negative, which implies assets sales and positive cash flow). Hold goodwill constant and assume that deferred taxes increase at the same ratio to operating taxes as historically. Use debt and excess cash as plugs to make the balance sheet balance. (These line items will not affect the enterprise valuation since they are not included as part of FCF).
  4. Market Data & WACC: Include calculations for historical trading multiples, estimates of beta, cost of equity, cost of debt, and WACC.
  5. Reorganized Financials: Calculate NOPLAT (including its reconciliation to net income) and invested capital (including its reconciliation to total funds invested).
  6. ROIC & FCF: After the income statement and balance sheet forecasts are complete, calculate ROIC, economic profit, and FCF. Calculations should only need to be copied across from historical financials. ROIC should remain near current levels if the company has a sustainable advantage, trend toward the industry median, or trend toward the cost of capital.
  7. Valuation Summary: Summarize final results of discounted cash flows and economic profits. Include valuations for non-operating assets, non-equity claims, and equity.

After building the forecasting model, be sure to verify the results. Does the balance sheet balance in every year? Does net income correctly flow into dividends and retained earnings? Does the company reach a steady state at the end of the explicit forecasting period? Are the final results probable? Can you explain significant differences from peer-group companies in terms of value drivers and underlying business characteristics or strategy? End by comparing the valuation results with a back-of-the-envelope value estimate.

Continuing Value
The explicit forecast period should extend for as long as there are ongoing changes to the fundamental assumptions of the company (e.g. ROIC and rate of growth).  Once the company has reached a steady state of operations, a continuing value formula can be used to calculate the company’s expected cash flows beyond the explicit forecast period. The continuing value is then discounted to the present and added to the discounted present value of operations. (If the explicit forecast period is 10 years, then discount the continuing value by 10 years).

When using an enterprise DCF model, the continuing value should be estimated using the key value driver formula.

Continuing Value

Long-term returns on new invested capital (RONIC) should be consistent with expected competitive conditions. Many forecasters set this equal to the cost of capital, except perhaps for companies with patents or strong brands. The best growth rate estimate is probably the long-term rate of growth for the industry (inclusive of inflation). WACC should reflect a sustainable capital structure. Given the highly sensitive nature of continuing value to these parameter inputs, it is helpful to model different scenarios.

Using the economic profit approach, continuing value is the incremental value over the company’s invested capital at the end of the explicit forecast period.

EP Continuing Value

Cost of Capital
The weighted average cost of capital (WACC) is estimated by determining the cost of capital for each source of financing (namely, debt and equity) and then weighting them by their respective target market-based values. (Hybrid securities, such as preferred stock, must additionally be included if material).


Estimating the cost of equity is most commonly performed using the capital asset pricing model (CAPM).


The risk-free rate (rf) is best estimated with 10-year zero-coupon Treasury strips. There are three primary methods for calculating the market risk premium, E(Rm), all of which commonly generate estimates between 4.5% and 5.5%. The first option is to calculate historical excess returns of the market over the risk-free rate. The second option is to use regression analysis to predict the market risk premium based on current market variables, such as the aggregate ratio of dividends to price. The third option is to use a DCF valuation to reverse engineer the market’s cost of capital.

Beta (βi) measures how much the stock and market move together. It is calculated using regression analysis, where returns on the market is the dependent variable and returns on the stock is the independent variable. Best practice suggests using monthly returns over 5 years (i.e. 60 data points) in the estimation. Rolling 60-month betas should also be graphed to examine any significant changes over time. Good proxies for the market include value-weighted, well-diversified portfolios such as the S&P 500 or MSCI World Index. The precision of the beta calculation can be improved by deriving an unlevered industry beta (βu). This is discovered by first calculating the raw betas of several industry competitors. Each of these is then un-levered and the average (or median) is re-levered (βe) to reflect the company’s target capital structure.

Unlevered Beta

If a company has investment grade debt (i.e. BBB or better), the cost of debt is computed by using the yield to maturity (YTM) of the company’s long-term, option-free bonds. The yield is solved for by reverse engineering the discount rate required to set the present value of a bond’s promised cash flows equal to its price.


For companies with only short-term or illiquid bonds, an indirect method can be used to determine the cost of debt. Simply take the average YTM on unsecured, long-term bonds of the same credit rating. For companies with below-investment-grade debt, the CAPM is used instead. In this case, rather than using stock returns as the independent variable, returns on bond indexes are used to determine the beta. The cost of debt equals the beta of an investment-grade bond index, less the beta of a high-yield bond index, all multiplied by the market risk premium. The marginal tax rate (Tm) should be the statutory marginal tax rate, less approximately 5% (to account for average tax-loss carryforwards and investment tax credits).

The current market-value of equity (E) is equal to the company’s stock price multiplied by the number of shares outstanding (excluding any repurchases by the company). If market values of debt (D) are unavailable, a reasonable approximation is to use book values. If interest rates have dramatically changed or the company is in financial distress, each bond should be valuated separately by discounting the promised cash flows (disclosed in the notes of the annual report) at the appropriate YTM. Off-balance-sheet debt, such as operating leases, should additionally be included to the total value of debt.

Multiples provide a useful way to test the plausibility of DCF valuations, if applied carefully. The first challenge of using ratios involves selecting the appropriate peer companies for comparison. A short list can be generated by looking for the competitors listed in the annual report or finding companies with the same industry classification (i.e. using SIC or GICS codes). Reduce the peer group to only the closest competitors with similar growth and ROIC prospects. Only include companies with positive earnings in the peer group. When analyzing a multi-business company, use a separate peer group for each business segment.

To avoid any biases caused by capital structure and non-operating items, use an enterprise-value multiple (e.g. enterprise value / EBITA). The adjusted the enterprise value should equal the market value of debt and equity, less excess cash, less other non-operating assets whose income is not part of EBITA, plus the value of operating leases, plus the present value of outstanding employee grants, plus the after-tax present value of pension liabilities. EBITA should also be adjusted by adding the implied interest expense from operating leases, subtracting the after-tax value of newly issued employee option grants if not already expensed, adding pension interest expense, and subtracting the recognized returns on plan assets (as reported in the footnotes).

Multiples should be based on forward-looking estimates since future performance, rather than past performance, is the basis for value. Empirical evidence shows that multiples based on one- and two-year forecasts outperform multiples based on historical earnings. Price-to-sales multiples should only be used when peers have negative operating profits. Price-earnings-growth (PEG) ratios allow you to expand a company’s comparison group to include competitors with different growth prospects.

Adjusted PEG

One drawback is choosing a time frame for measuring expected growth. Another is that it undervalues companies with low growth rates (e.g. the implied value of a company with constant profits is zero).


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