Introduction
Equity valuation is the central skill of successful investing. By having a reliable estimate of underlying value, an investor can determine whether a stock is undervalued, overvalued, or fairly valued. Finding undervalued stocks is the key to generating above-average investment returns over time.
One of the most theoretically sound methods of stock valuation is discounted cash flow valuation, or DCF valuation. Although several variations of DCF exist, this article focuses on a method known as the enterprise DCF model.
Under the enterprise DCF model, investors focus on cash flows available to all of the firm’s capital providers, including both debt and equity capital. Investors value the firm by discounting the firm’s estimated future cash flows at a rate that reflects the riskiness of the firm’s debt and equity. Investors then calculate the value of the equity by subtracting debt and other non-equity claims. Finally, investors calculate the per-share value by dividing total equity value by the number of outstanding common shares.
The purpose of DCF valuation is not to produce a precise estimate of value. Precision is impossible when the value of a business depends on future cash flows, competitive conditions, capital allocation, interest rates, and management decisions. Rather, the purpose of DCF valuation is to develop a reasonable approximation of intrinsic value that can be compared against the current market price.
Used carefully, DCF valuation can help investors think like business owners. Used carelessly, it can create a false sense of accuracy.
Free Cash Flow
The relevant cash flow measure used in DCF valuation is called free cash flow.
Free cash flow is the cash flow available to the firm’s capital providers after the firm has made all necessary expenditures to maintain and operate the business. Investors calculate free cash flow by adding depreciation and amortization to net operating profits after taxes, or NOPAT, and then subtracting investments in working capital and capital expenditures.
A simplified version of the formula is:
Free Cash Flow = NOPAT + Depreciation and Amortization – Increase in Net Working Capital – Capital Expenditures
Free cash flow differs from accounting earnings because it attempts to measure the cash that can ultimately be used for debt repayment, dividends, share repurchases, acquisitions, reinvestment, or other value-creating uses.
For value investors, free cash flow is central because the value of any business ultimately depends on the cash it can generate for its capital providers over time.
Net Operating Profits After Taxes
The first component of free cash flow is net operating profits after taxes, or NOPAT.
To calculate NOPAT, investors begin by normalizing the company’s income statement. This means identifying and eliminating, or provisioning for, nonrecurring gains, losses, and expenses. Investors must also identify areas of a company’s accounting that require management estimates, such as reserves for uncollectible receivables, warranty reserves, restructuring reserves, and similar items. Investors should determine whether such estimates are comparable to prior periods and industry norms.
Investors must also determine whether a company is following applicable accounting guidelines for revenue and expense recognition. These adjustments are made because investors are interested in a company’s sustainable earnings, untainted by nonrecurring events, aggressive accounting estimates, or unusual items that do not reflect normal operations.
The adjusted income statement gives investors three important pieces of information used in calculating free cash flow:
- Revenue;
- Cost of goods sold; and
- Operating expenses.
The net result of these three components is the company’s operating profit, usually referred to as earnings before interest and taxes, or EBIT.
Investors then multiply EBIT by one minus the company’s tax rate, which gives the after-tax operating profit the company would have earned if it had no debt.
NOPAT = EBIT × (1 – Tax Rate)
This calculation focuses on the profitability of the company’s operations before considering how the company is financed. By excluding interest expense, NOPAT allows investors to compare companies with different capital structures.
Investors should exercise judgment in selecting the appropriate tax rate. In some cases, the company’s effective tax rate may be appropriate. In other cases, a normalized statutory or expected long-term tax rate may better reflect the company’s sustainable tax burden.
Depreciation and Amortization
The next step in calculating free cash flow is to identify a company’s depreciation and amortization.
Depreciation is the periodic expensing of the cost of tangible assets, while amortization is the periodic expensing of certain intangible assets. Both measures require estimates of the asset’s useful life and salvage value. These measures are non-cash accounting charges, which is why investors add them back to NOPAT.
Investors can often find depreciation and amortization in a company’s statement of cash flows. In some cases, additional detail may be available in the footnotes or management’s discussion and analysis.
Although depreciation and amortization are non-cash charges in the period reported, investors should not assume they are economically meaningless. Depreciation often reflects real asset wear and eventual replacement needs. A business that requires large ongoing capital expenditures may not be as cash-generative as its accounting earnings suggest.
For this reason, depreciation and amortization should be analyzed together with capital expenditures, asset age, maintenance needs, and the company’s reinvestment requirements.
Capital Expenditures and Working Capital
All companies must invest a portion of their earnings in maintaining their current state and growing their revenues. What most distinguishes free cash flow from accounting earnings is the subtraction of these investments from operating earnings.
A company’s net working capital is the difference between current operating assets and current operating liabilities.
Current operating assets include items such as:
- Accounts receivable;
- Inventory; and
- Prepaid expenses.
Current operating liabilities include items such as:
- Accounts payable;
- Customer deposits; and
- Accrued liabilities.
Investors subtract from NOPAT an increase in net working capital because an increase in working capital is a use of cash. A company can also have negative working capital, which may represent a source of cash and would be added to NOPAT.
Working capital analysis is important because reported earnings can grow even when cash is being absorbed by receivables or inventory. A company that must continually invest large amounts in working capital to support growth may generate less free cash flow than its income statement suggests.
Capital expenditures, or CapEx, represent a company’s acquisition or improvement of long-term assets. CapEx takes two forms:
- Maintenance capital expenditures; and
- Growth capital expenditures.
Maintenance CapEx refers to expenditures necessary for the company to maintain its current capacity. Growth CapEx refers to discretionary expenditures a company makes to expand its operations.
A complicating factor in determining capital expenditures is that companies may make large capital investments in some years while making few capital investments in others. Investors generally deal with this by analyzing CapEx relative to sales over several years and then using an average in their free cash flow calculations.
Ideally, investors would distinguish between maintenance CapEx and growth CapEx. In practice, companies generally disclose total capital expenditures, not the portion required merely to maintain the business. Investors must therefore use judgment. Historical depreciation, asset age, management commentary, industry capital intensity, and competitor comparisons can all help investors estimate maintenance capital needs.
Additional Considerations in Free Cash Flow Analysis
Free cash flow is the primary source of a company’s ability to increase shareholder wealth. A company that generates free cash flow can pay dividends, repurchase shares, invest in growth, make acquisitions, or pay down debt. These uses of free cash flow can, under the right conditions, accrue value to common stockholders.
The investor’s calculation of past free cash flows should be merely one consideration in assessing future free cash flows. Once investors have calculated historical free cash flows, they should then determine:
- How probable it is that the company can maintain or grow its free cash flows;
- How management has used cash in the past; and
- How management intends to use cash in the future.
In other words, investors must ask whether management consists of good capital allocators.
In answering these questions, investors should consider Graham and Dodd’s statement: “Quantitative data are useful only to the extent that they are supported by a qualitative survey of the enterprise.”
Assessing a company’s ability to generate future cash flows involves more than an assessment of past financial statements. An investor must assess the industry, management’s priorities, competitive threats, reinvestment opportunities, and the durability of the company’s economic position.
A spreadsheet may calculate value, but judgment determines whether the inputs are reasonable.
Valuing the Firm
Investors generally have two options for building a DCF valuation.
The first option is to calculate a single free cash flow estimate representing the investor’s estimate of the company’s sustainable cash flow. Investors then divide this figure by a capitalization rate, calculated by subtracting a sustainable growth rate from a risk-appropriate discount rate. This approach is known as a single-stage model.
The formula for calculating firm value using the single-stage model is:
Firm Value = FCF ÷ (r – g)
Where:
- FCF is the sustainable free cash flow estimate;
- r is the discount rate; and
- g is the sustainable growth rate.
The single-stage model is most useful for stable companies whose cash flows are mature, recurring, and capable of being estimated with some confidence. It is less useful for companies experiencing rapid growth, major cyclical swings, or significant business-model transitions.
The second option is to calculate the firm’s value using a two-stage DCF model. Investors use a two-stage DCF model when a company is expected to be in a period of high growth before reaching maturity.
Under the two-stage model, investors calculate the present value of individual cash flows over several years in the high-growth period and add to that a discounted terminal value.
The general structure of a two-stage DCF model is:
Firm Value = Present Value of Explicit Forecast Period Cash Flows + Present Value of Terminal Value
A simplified version is:
Firm Value = FCF₁ ÷ (1 + r) + FCF₂ ÷ (1 + r)² + … + FCFₙ ÷ (1 + r)ⁿ + Terminal Value ÷ (1 + r)ⁿ
Where:
- FCF₁, FCF₂, etc. are the free cash flows in each forecast year;
- r is the discount rate;
- n is the last year in the explicit forecast period; and
- Terminal Value represents the value of cash flows beyond the explicit forecast period.
A common terminal value formula is:
Terminal Value = FCFₙ₊₁ ÷ (r – g)
The purpose of the two-stage model is to account for a rate of growth in revenues and free cash flow that is unsustainable over the long term. By applying this abnormal growth rate to a limited period, usually five to ten years, investors can account for an eventual tapering of the company’s growth rate.
For example, an investor may assume that a company can grow its revenues and free cash flows by 10% for ten years and 2% in perpetuity after ten years.
The two-stage model requires a more explicit cash flow forecast. Each component of free cash flow must be forecast. The investor prepares the forecast by first forecasting revenue. Then the investor forecasts cost of goods sold, operating expenses, depreciation and amortization, taxes, capital expenditures, and working capital requirements.
Cost of goods sold, depreciation and amortization, and capital expenditures are often forecast based on a percentage of revenues, usually informed by historical averages and expected business conditions. Working capital can be projected based on either a percentage of sales or financial statement ratios such as days sales outstanding, days inventory held, and days payable outstanding.
The more detailed the forecast, the greater the need for humility. A detailed DCF model can create the appearance of precision, but the output is only as sound as the assumptions.
The Discount Rate
Since the investor is calculating the present value of cash flows that accrue to all of the firm’s capital providers, the discount rate used must reflect the combined cost of the firm’s debt and equity capital.
This mix is the firm’s weighted average cost of capital, or WACC.
The WACC is designed to reflect the blended required return of the capital providers financing the business. Debt holders require interest payments. Equity holders require a return that compensates them for the risk of owning the residual claim on the company’s cash flows.
Cost of Debt
The investor calculates the firm’s cost of debt by identifying the rate on the firm’s bonds or the rate on bonds of other firms with similar credit ratings and maturities. If public bond yields are not available, investors may estimate the company’s borrowing cost using credit spreads, comparable issuers, bank debt rates, or other market evidence.
This rate is often tax-adjusted to account for the tax deductibility of interest expense:
After-Tax Cost of Debt = Pretax Interest Rate × (1 – Tax Rate)
However, investors should be aware that interest deductibility may be limited for certain companies. Under current U.S. tax rules, Section 163(j) can limit the deductibility of business interest expense for companies subject to the limitation. As a result, highly leveraged companies may not receive the full tax benefit assumed by a simple after-tax cost of debt formula.
For companies with high debt levels or limited interest deductibility, investors should adjust the cost of debt calculation to reflect the portion of interest expense that is deductible and the portion that is not deductible.
Cost of Equity
The firm’s cost of equity is more subjective than its cost of debt because interest rates are observable factors, while equity costs are implied.
The cost of equity represents the minimum return required by the firm’s equity investors. Standard finance textbooks contain many approaches to calculating the cost of equity, including models based on market risk premiums, beta, dividend growth, and other methods.
The important consideration is that equity is the most junior claim on the company’s assets and cash flows and, therefore, must command a higher expected return than the company’s debt.
In practice, many investors take the company’s cost of debt and add a risk premium that reflects the uncertainty of the company’s cash flows. A company with a strong business franchise and stable cash flows will generally command a smaller risk premium than a company with highly uncertain cash flows.
The cost of equity should reflect business risk, financial risk, cyclicality, competitive position, and the predictability of cash flows. Investors should resist the temptation to use an artificially low cost of equity merely to justify a higher valuation.
Calculating the WACC
After investors have calculated the debt and equity costs, they determine the proportional weights for each form of capital. Investors calculate the weights by dividing each component of the capital structure by the firm’s total capital.
For the sake of this discussion, assume the company has only debt and common equity. If the firm has preferred stock, the preferred stock would be an additional component of WACC.
A standard WACC formula is:
WACC = (E ÷ V × Ke) + (D ÷ V × Kd × (1 – Tax Rate))
Where:
- E is the market value of equity;
- D is the market value of debt;
- V is total firm value, or E + D;
- Ke is the cost of equity; and
- Kd is the pretax cost of debt.
Investors can use either market values or book values for debt and equity, although market values are generally preferred when they are available and reliable. Debt should include borrowings, bonds, bank loans, and lease liabilities that function as financing obligations.
Current accounting rules require many leases to be recognized on the balance sheet as right-of-use assets and lease liabilities. Investors should therefore be careful when comparing historical statements prepared under older lease accounting rules with more recent financial statements. For valuation purposes, lease obligations that are economically debt-like should be considered when assessing capital structure, leverage, enterprise value, and WACC.
By using WACC as the discount rate, the investor implicitly assumes that the firm will maintain a similar capital structure. For a firm with high levels of debt, this may be a questionable assumption. However, for firms with moderate or low debt levels, using the current capital structure in the calculation of WACC may be sufficient.
Investors should use WACC as a practical tool, not as an exact scientific measurement. Small changes in the discount rate can produce large changes in estimated value.
Valuing the Equity
After the investor has determined a value for the entire firm, the investor must then calculate the value of the equity.
This requires two broad steps:
- Adding any non-operating assets; and
- Subtracting debt and other non-equity claims from total enterprise value.
Non-operating assets may include excess cash, financial securities, non-operating real estate, investments in unconsolidated entities, or other assets not required to operate the business.
The most common non-equity claims include:
- Debt;
- Lease liabilities that are economically debt-like;
- Preferred stock;
- Noncontrolling interests;
- Outstanding stock options and other dilutive securities;
- Contingent liabilities, such as lawsuits or environmental obligations; and
- Underfunded pension obligations.
Investors will typically source these non-equity claims from the company’s most recent balance sheet, annual report, quarterly report, and footnotes. The footnotes are especially important because many claims and contingencies may not be fully understood from the face of the financial statements alone.
Subtracting non-equity claims from enterprise value yields the value of the equity. The investor then calculates the per-share value by dividing equity value by the total number of outstanding shares, adjusted when appropriate for dilution from options, restricted stock units, convertible securities, or other instruments.
The formula is:
Equity Value = Enterprise Value + Non-Operating Assets – Debt and Other Non-Equity Claims
Per-Share Value = Equity Value ÷ Diluted Shares Outstanding
This per-share amount becomes the basis of comparison against the current market price. A conservative investor will generally consider an investment only when the calculated value is significantly higher than the market price.
Shortcomings of the DCF Approach
Although the DCF approach is the most theoretically sound approach to stock valuation, the model is highly sensitive to the assumptions used, particularly assumptions concerning growth rates and discount rates.
Investors can mitigate this shortcoming in several ways.
First, investors should use conservative assumptions. Conservative assumptions do not mean unrealistically pessimistic assumptions. Rather, they mean assumptions that are reasonable, supportable, and not dependent on an overly favorable future.
Second, investors should build the DCF model using spreadsheet software. By using a spreadsheet, the investor can easily change the inputs in the model and calculate a new value.
Third, investors should create several sets of assumptions. For example, an investor may create three scenarios:
- A base case;
- An optimistic case; and
- A pessimistic case.
Finally, investors can expand the range of values calculated under scenario analysis by discounting each scenario at different discount rates.
By having a range of values, the investor has an expanded basis for judgment. Some investors will attach a probability to each value and calculate a probability-weighted average stock value.
The important point is for investors to exercise caution when using the DCF approach. Investors should understand that DCF is a tool. And while this tool can be very helpful, it can be damaging if used carelessly.
Margin of Safety
Although equity valuation is the central skill behind successful investing, investors can never determine stock values with precision. Investors, therefore, must understand that their valuation work will provide an approximation that may or may not be a sound basis for an investment decision.
Benjamin Graham understood the shortcomings of security valuation. He wrote that security analysis does not seek to determine exactly what the intrinsic value of a given security is. Rather, it needs only to establish whether value is adequate or whether value is considerably higher or lower than the market price. For such purposes, an indefinite and approximate measure of intrinsic value may be sufficient.
For this reason, Graham insisted on a margin of safety.
By considering an investment only when the market price is available at a large enough discount from approximate value, investors can limit the effects of valuation error.
The margin of safety is not merely a mathematical concept. It is a recognition of human limitation. Investors cannot know the future with certainty. They cannot forecast cash flows precisely. They cannot know what discount rate other investors will apply years from now. They cannot know all competitive, regulatory, or technological changes that may affect a business.
The margin of safety exists because valuation is approximate.
Conclusion
Discounted cash flow valuation is the most theoretically sound method of business and equity valuation. It forces investors to think about the cash a business can generate, the capital required to generate that cash, the riskiness of those cash flows, and the claims that stand ahead of common equity.
However, the difficulty of forecasting future cash flows and the sensitivity of the output to the model’s assumptions make DCF valuation especially prone to user error. Investors should use conservative assumptions and make extensive use of scenario analysis when using DCF models.
The goal is not precision. The goal is intelligent approximation.
A sound DCF analysis should help investors think more clearly about the relationship between business quality, free cash flow, risk, growth, capital structure, and intrinsic value. When combined with a margin of safety, DCF valuation can be a useful tool in the value investor’s analytical process.
Sources
Damodaran, Aswath. Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2nd ed. Hoboken: Wiley, 2006.
Graham, Benjamin, and David Dodd. Security Analysis, 6th ed. New York: McGraw-Hill, 2009.
Rosenbaum, Joshua, and Joshua Pearl. Investment Banking: Valuation, Leveraged Buyouts, and Mergers & Acquisitions, 2nd ed. Hoboken: Wiley, 2013.
