Computing FCFF from Net Income

FCFF is the cash flow available to the company’s suppliers of capital after all operating expenses (including taxes) have been paid and operating investments have been made. The company’s suppliers of capital include bondholders and common shareholders (plus, occasionally, holders of preferred stock, which we ignore until later). Keeping in mind that a noncash charge is a charge or expense that does not involve the outlay of cash, we can write the expression for FCFF as follows:

FCFF = Net income available to common shareholders (NI)
Plus: Net noncash charges (NCC)
Plus: Interest expense × (1 − Tax rate)
Less: Investment in fixed capital (FCInv)
Less: Investment in working capital (WCInv)

This equation can be written more compactly as: FCFF = NI + NCC + Int(1 – Tax rate) – FCInv – WCInv
 
Consider each component of FCFF. The starting point in the equation above is net income available to common shareholders—the bottom line in an income statement. It represents income after depreciation, amortization, interest expense, income taxes, and the payment of dividends to preferred shareholders (but not payment of dividends to common shareholders).

Net noncash charges represent an adjustment for noncash decreases and increases in net income. This adjustment is the first of several that analysts generally perform on a net basis. If noncash decreases in net income exceed the increases, as is usually the case, the adjustment is positive. If noncash increases exceed noncash decreases, the adjustment is negative. The most common noncash charge is depreciation expense. When a company purchases fixed capital, such as equipment, the balance sheet reflects a cash outflow at the time of the purchase. In subsequent periods, the company records depreciation expense as the asset is used. The depreciation expense reduces net income but is not a cash outflow. Depreciation expense is thus one (the most common) noncash charge that must be added back in computing FCFF. In the case of intangible assets, there is a similar noncash charge, amortization expense, which must be added back. Other noncash charges vary from company to company.

After-tax interest expense must be added back to net income to arrive at FCFF. This step is required because interest expense net of the related tax savings was deducted in arriving at net income and because interest is a cash flow available to one of the company’s capital providers (i.e., the company’s creditors). In the United States and many other countries, interest is tax deductible (reduces taxes) for the company (borrower) and taxable for the recipient (lender). As we explain later, when we discount FCFF, we use an after-tax cost of capital. For consistency, we thus compute FCFF by using the after-tax interest paid.5

Similar to after-tax interest expense, if a company has preferred stock, dividends on that preferred stock are deducted in arriving at net income available to common shareholders. Because preferred stock dividends are also a cash flow available to one of the company’s capital providers, this item is added back to net income available to common shareholders in deriving FCFF.

Investments in fixed capital represent the outflows of cash to purchase fixed capital necessary to support the company’s current and future operations. These investments are capital expenditures for long-term assets, such as the property, plant, and equipment (PP&E) necessary to support the company’s operations. Necessary capital expenditures may also include intangible assets, such as trademarks. In the case of cash acquisition of another company instead of a direct acquisition of PP&E, the cash purchase amount can also be treated as a capital expenditure that reduces the company’s free cash flow (note that this treatment is conservative because it reduces FCFF). In the case of large acquisitions (and all noncash acquisitions), analysts must take care in evaluating the impact on future free cash flow. If a company receives cash in disposing of any of its fixed capital, the analyst must deduct this cash in calculating investment in fixed capital. For example, suppose we had a sale of equipment for $100,000. This cash inflow would reduce the company’s cash outflows for investments in fixed capital.

The company’s statement of cash flows is an excellent source of information on capital expenditures as well as on sales of fixed capital. Analysts should be aware that some companies acquire fixed capital without using cash—for example, through an exchange for stock or debt. Such acquisitions do not appear in a company’s statement of cash flows but, if material, must be disclosed in the footnotes. Although noncash exchanges do not affect historical FCFF, if the capital expenditures are necessary and may be made in cash in the future, the analyst should use this information in forecasting future FCFF.

The final point to cover is the important adjustment for net increases in working capital. This adjustment represents the net investment in current assets (such as accounts receivable) less current liabilities (such as accounts payable). Analysts can find this information by examining either the company’s balance sheet or its statement of cash flows.

Although working capital is often defined as current assets minus current liabilities, working capital for cash flow and valuation purposes is defined to exclude cash and short-term debt (which includes notes payable and the current portion of long-term debt). When finding the net increase in working capital for the purpose of calculating free cash flow, we define working capital to exclude cash and cash equivalents as well as notes payable and the current portion of long-term debt. Cash and cash equivalents are excluded because a change in cash is what we are trying to explain. Notes payable and the current portion of long-term debt are excluded because they are liabilities with explicit interest costs that make them financing items rather than operating items.

Estimating Free Cash Flow

Estimating FCFF or FCFE requires a complete understanding of the company and its financial statements. To provide a context for the estimation of FCFF and FCFE, we first use an extensive example to show the relationship between free cash flow and accounting measures of income.

For most of this section, we assume that the company has two sources of capital, debt and common stock. Once the concepts of FCFF and FCFE are understood for a company financed by using only debt and common stock, it is easy to incorporate preferred stock for the relatively small number of companies that actually use it.

FCFF Valuation Approach

The FCFF valuation approach estimates the value of the firm as the present value of future FCFF discounted at the weighted average cost of capital.

Because FCFF is the cash flow available to all suppliers of capital, using WACC to discount FCFF gives the total value of all of the firm’s capital.

The value of equity is the value of the firm minus the market value of its debt:

Equity value = Firm value – Market value of debt  

Dividing the total value of equity by the number of outstanding shares gives the value per share.

Free Cash Flow

Free cash flow is the amount of cash generated by a business that is available for distribution among its security holders. Security holders include debt holders, equity holders, preferred stock holders, and convertible security holders.

Specifically, free cash flow is used to pay dividends, make acquisitions, develop new products, invest in new property, plant and equipment, pay interest expenses, and reduce debt.

Types

There are two types of most commonly used free cash flow: free cash flow to the firm (FCFF) and free cash flow to equity (FCFE).

Free cash flow to the firm is the cash flow available to the company’s suppliers of capital after all operating expenses (including taxes) have been paid and necessary investments in working capital (e.g., inventory) and fixed capital (e.g., equipment) have been made. FCFF is the cash flow from operations minus capital expenditures. A company’s suppliers of capital include common stockholders, bondholders, and sometimes, preferred stockholders. The equations analysts use to calculate FCFF depend on the accounting information available.

Free cash flow to equity is the cash flow available to the company’s holders of common equity after all operating expenses, interest, and principal payments have been paid and necessary investments in working and fixed capital have been made. FCFE is the cash flow from operations minus capital expenditures minus payments to (and plus receipts from) debtholders.

When to Use

Free Cash Flow Analysis is one type of discounted cash flow analysis. Analysts like to use free cash flow as the return (either FCFF or FCFE) whenever one or more of the following conditions is present:

  • The company does not pay dividends.

  • The company pays dividends but the dividends paid differ significantly from the company’s capacity to pay dividends.

  • Free cash flows align with profitability within a reasonable forecast period with which the analyst is comfortable.

  • The investor takes a “control” perspective. With control comes discretion over the uses of free cash flow. If an investor can take control of the company (or expects another investor to do so), dividends may be changed substantially; for example, they may be set at a level approximating the company’s capacity to pay dividends. Such an investor can also apply free cash flows to uses such as servicing the debt incurred in an acquisition.

How to Use

The way in which free cash flow is related to a company’s net income, cash flow from operations, and measures such as EBITDA (earnings before interest, taxes, depreciation, and amortization) is important: The analyst must understand the relationship between a company’s reported accounting data and free cash flow in order to forecast free cash flow and its expected growth. Although a company reports cash flow from operations (CFO) on the statement of cash flows, CFO is not free cash flow. Net income and CFO data can be used, however, in determining a company’s free cash flow.

The advantage of FCFF and FCFE over other cash-flow concepts is that they can be used directly in a DCF framework to value the firm or to value equity. Other cash-flow- or earnings-related measures, such as CFO, net income, EBIT, and EBITDA, do not have this property because they either double-count or omit cash flows in some way. For example, EBIT and EBITDA are before-tax measures, and the cash flows available to investors (in the firm or in the equity of the firm) must be after tax. From the stockholders’ perspective, EBITDA and similar measures do not account for differing capital structures (the after-tax interest expenses or preferred dividends) or for the funds that bondholders supply to finance investments in operating assets. Moreover, these measures do not account for the reinvestment of cash flows that the company makes in capital assets and working capital to maintain or maximize the long-run value of the firm.

Using free cash flow in valuation is more challenging than using dividends because in forecasting free cash flow, the analyst must integrate the cash flows from the company’s operations with those from its investing and financing activities. Because FCFF is the after-tax cash flow going to all suppliers of capital to the firm, the value of the firm is estimated by discounting FCFF at the weighted average cost of capital (WACC). An estimate of the value of equity is then found by subtracting the value of debt from the estimated value of the firm. The value of equity can also be estimated directly by discounting FCFE at the required rate of return for equity (because FCFE is the cash flow going to common stockholders, the required rate of return on equity is the appropriate risk-adjusted rate for discounting FCFE).

The two free cash flow approaches, indirect and direct, for valuing equity should theoretically yield the same estimates if all inputs reflect identical assumptions. An analyst may prefer to use one approach rather than the other, however, because of the characteristics of the company being valued. For example, if the company’s capital structure is relatively stable, using FCFE to value equity is more direct and simpler than using FCFF. The FCFF model is often chosen, however, in two other cases:

  • A levered company with negative FCFE. In this case, working with FCFF to value the company’s equity might be easiest. The analyst would discount FCFF to find the present value of operating assets (adding the value of excess cash and marketable securities and of any other significant nonoperating assets1 to get total firm value) and then subtract the market value of debt to obtain an estimate of the intrinsic value of equity.

  • A levered company with a changing capital structure. First, if historical data are used to forecast free cash flow growth rates, FCFF growth might reflect fundamentals more clearly than does FCFE growth, which reflects fluctuating amounts of net borrowing. Second, in a forward-looking context, the required return on equity might be expected to be more sensitive to changes in financial leverage than changes in the WACC, making the use of a constant discount rate difficult to justify.

Macaulay Duration

The Macaulay duration is defined as the average time it takes to receive all the cash flows of a bond, weighted by the present value of each of the cash flows. It measures the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future. Essentially, it is the payment-weighted point in time at which an investor can expect to recoup his or her original investment.

The Macaulay duration is quoted in “years” and it is the only type of duration with this unit. Interest rates are assumed to be continuously compounded.

Given its relative ability to predict price changes based on changes in interest rates, duration allows for the effective comparison of bonds with different maturities and coupon rates. For example, a 5-year zero coupon bond may be more sensitive to interest rate changes than a 7-year bond with a 6% coupon. By comparing the bonds’ durations, you may be able to anticipate the degree of price change in each bond assuming a given change in interest rates.

Utilizing Duration

Duration can help predict the likely change in the price of a bond given a change in interest rates. As a general rule, for every 1% increase or decrease in interest rates, a bond’s price will change approximately 1% in the opposite direction for every year of duration. For example, if a bond has a duration of 5 years, and interest rates increase by 1%, the bond’s price will decline by approximately 5%. Conversely, if a bond has a duration of 5 years and interest rates fall by 1%, the bond’s price will increase by approximately 5%.

Formula

Example

For example, for a two-year bond with a $1000 face value and one coupon payment every six months of $50, the duration (calculated in years) is:

Rules of Duration

When thinking about duration, a few general rules apply. With everything else being equal:

  • The duration of any bond that pays a coupon will be less than its maturity, because some amount of coupon payments will be received before the maturity date.

  • The lower a bond’s coupon, the longer its duration, because proportionately less payment is received before final maturity. The higher a bond’s coupon, the shorter its duration, because proportionately more payment is received before final maturity.

  • Because zero coupon bonds make no coupon payments, a zero coupon bond’s duration will be equal to its maturity.

  • The longer a bond’s maturity, the longer its duration, because it takes more time to receive full payment. The shorter a bond’s maturity, the shorter its duration, because it takes less time to receive full payment.

Convexity

The duration measure indicates that regardless of whether interest rates increase or decrease, the approximate percentage price change is the same. However, while for small changes in yield the percentage price change will be the same for an increase or decrease in yield, for large changes in yield this is not true. This suggests that duration is only a good approximation of the percentage price change for small changes in yield.

For example, using a 5% 20-year bond selling to yield 4% with a duration of 13.09. For a 10 basis point change in yield, the estimate was accurate for both an increase or a decrease in yield. However, for a 200 basis point change in yield, the approximate percentage price change was off considerably.

The reason for this result is that duration is in fact a first (linear) approximation for a small change in yield. The approximation can be improved by using a second approximation. This approximation is referred to as “convexity.” The use of this term in the industry is unfortunate because the term convexity is also used to describe the shape or curvature of the price/yield relationship. The convexity measure of a security can be used to approximate the change in price that is not explained by duration.

Break-even Inflation Rate

The break-even inflation rate (BEI) is a market-based measure of expected inflation. It is the difference between the yield of a nominal bond and an inflation-linked bond of the same maturity.

BEI is comprised of two elements: expected inflation (\pi) and risk premium for uncertainty in inflation (\theta).

The fundamental difference between the pricing formula as applied to, for example, a three-month T-bill and its application to, for example, a default-free zero-coupon bond relates to their investment horizons. The relative certainty about the real payoff from a three month T-Bill and thus the relative certainty about the amount of consumption that the investor will be able to undertake with the payoff means that the investment in the T-Bill will be a good hedge against possible bad consumption outcomes. In other words, the payoff, in real terms, from a three month T-Bill is highly unlikely to fall if the investor loses his or her job during the T-Bill’s three month investment horizon. The low, probably zero, correlation between the T-Bill’s payoff with bad consumption outcomes will mean that the risk premium needed to tempt an investor to invest in the T-Bill will be close to zero.

However, it is unlikely that the same level of certainty would apply, for example, to a 20-year default-free conventional government bond. For such a bond, it would seem reasonable to assume that the risk premium would be higher than that related to a one- or three-month T-Bill. Note that the cash flow in Equation 10 is still certain, but only in nominal terms. Because investors will naturally have less confidence in their ability to form views about future inflation over 20 years relative to their abilities to form those views over three months, the greater uncertainty about the real value of the bond’s payoff will cause investors to demand a premium in compensation for this uncertainty, represented by πt,s.

The difference between the yield on, for example, a zero-coupon default-free nominal bond and on a zero-coupon default-free real bond of the same maturity is known as the break-even inflation (BEI) rate. It should be clear from the discussion earlier that this break-even inflation rate will incorporate the inflation expectations of investors over the investment horizon of the two bonds, θt,s, plus a risk premium that will be required by investors to compensate them predominantly for uncertainty about future inflation, πt,s. Although the evolution of real zero-coupon default-free yields over time should be driven mainly by the inter-temporal rate of substitution, the evolution of their nominal equivalents will, in addition, be driven by changing expectations about inflation and changing perceptions about the uncertainty of the future inflation environment. We can see this evolution by plotting the constant maturity zero-coupon break-even inflation rates over time.

Modigliani–Miller Theorem

The Modigliani–Miller theorem is a set of two propositions on corporate capital structure. It was first proposed by Franco Modigliani and Merton Miller in 1958.

Two Propositions (No Taxes)

Modigliani and Miller made some very serious assumptions. The most important two are that there are no taxes and no costs of financial distress. Additional assumptions will be discussed in the next section. The two propositions are still true when the no taxes assumption is relaxed.

Proposition I : the market value of any firm is independent of its capital structure.

This means a firm cannot change its total value just by splitting its cash flows into different streams: The firm’s value is determined by its real assets, not by how it is financed. Thus capital structure is irrelevant as long as the firm’s investment decisions are taken as given.

Firms can not create value simply by changing the company’s capital structure.

Proposition II: the cost of equity is a linear function of the company’s debt/equity ratio.

More specifically, expected return on equity = expected return on assets + (expected return on assets – expected return on debt) * debt-equity ratio.

The mathematical representation (which can be derived from the WACC formula) is:

r_E = r_0 + (r_0 - r_D)(D/E)

According to this proposition, as the company increases its use of debt financing, the cost of equity rises. We know from MM Proposition I that the value of the company is unchanged and the weighted average cost of capital remains constant if the company changes its capital structure. What Proposition II then means is that the cost of equity increases in such a manner as to exactly offset the increased use of cheaper debt in order to maintain a constant WACC.

The risk of the equity depends on two factors: the risk of the company’s operations (business risk) and the degree of financial leverage (financial risk). Business risk determines the cost of capital, whereas the capital structure determines financial risk.

The expected rate of return on the common stock of a levered firm increases in proportion to the debt–equity ratio (D/E), expressed in market values; the rate of increase depends on the spread between r_A, the expected rate of return on a portfolio of all the firm’s securities, and r_D, the expected return on the debt.

Note that r_E = r_A if the firm has no debt.

Assumptions

  • Expectations are homogeneous. This means investors agree on the expected cash flows from a given investment. This means that all investors have the same expectations with respect to the cash flows from an investment in bonds or stocks.

  • Bonds and shares of stock are traded in perfect capital markets. This means that there are no transactions costs, no taxes, no bankruptcy costs, and everyone has the same information. In a perfect capital market, any two investments with identical cash flow streams and risk must trade for the same price.

  • Investors can borrow and lend at the risk-free rate.

  • There are no agency costs. This means that managers always act to maximize shareholder wealth.

  • The financing decision and the investment decision are independent of each other. This means that operating income is unaffected by changes in the capital structure.

  • No costs of asymmetric information

  • debtholders have prior claim to assets and income relative to equityholders, the cost of debt is less than the cost of equity

Two Propositions (With Taxes)