Free Cash Flow Valuation

READING 21

FREE CASH FLOW VALUATION

EXAM FOCUS

This topic review introduces the concept of free cash flow. The value of a firm's stock is calculated by forecasting free cash flow to the firm (FCFF) or free cash flow to equity (FCFE) and discounting these cash flows to the present at the appropriate required rate of return. Use FCFF or FCFE models when:

• the firm pays no dividends or pays out fewer dividends than its cash flow would suggest;
• free cash flow tracks profitability better than dividends;
• the analyst takes a corporate control perspective (for example, acquisition analysis).

Note the parallels between the free cash flow framework and the discounted dividend framework: the basic free cash flow model is analogous to the Gordon growth model. Memorise the formulas for FCFF and FCFE. Many analysts prefer free cash flow models to dividend discount models; this topic is frequently examined.

MODULE 21.1: FCF COMPUTATION

Warm-Up: Free Cash Flow

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Picture the firm as a cash processor. Cash flows in as revenue from selling products or providing services. Cash flows out as cash operating expenses (for example, salaries and taxes). Note that interest expense is a financing expense, not an operating expense, and thus is treated separately. The firm invests the remaining cash in working capital (inventory, receivables) and in long-term assets (property, plant, and equipment - PP&E). The cash that remains after operating expenses and investments is available to pay the firm's investors - bondholders and shareholders. That remaining pile of cash is called free cash flow to the firm (FCFF).

Formal definition: FCFF is the cash available to all of the firm's investors, including stockholders and bondholders, after the firm produces and sells its products and services, pays its cash operating expenses (including taxes), and makes required short- and long-term investments.

PROFESSOR'S NOTE

Taxes paid are included in operating cash expenses for FCFF, even though taxes are not part of operating income in accounting terms.

How is FCFF used? The firm first meets obligations to creditors (bondholders). It pays interest and repays or borrows debt. Interest payments reduce taxable income and so reduce taxes, which benefits shareholders. The residual after all obligations to other investors is free cash flow to equity (FCFE). FCFE is the cash available to common shareholders after funding capital expenditures, working capital needs, and debt financing requirements. The board of directors then decides whether to pay this out as dividends or retain it as cash.

PROFESSOR'S NOTE

Memorise the general definitions of FCFF and FCFE. You will be given many formulas; understanding the concepts allows reconstruction of formulas if forgotten under exam conditions.

LOS 21.a: Compare the free cash flow to the firm (FCFF) and free cash flow to equity (FCFE) approaches to valuation.

We use discounted cash flow (DCF) techniques: estimate expected future cash flows and discount them at the appropriate required return. Complications arise because there are two values to estimate (firm value and equity value), two cash flow definitions (FCFF and FCFE), and two discount rates (WACC and required return on equity). The key is to know which cash flows to discount at which rate to estimate which value.

Principles:

• Firm value = present value of expected future FCFF discounted at the weighted average cost of capital (WACC).
• Equity value = present value of expected future FCFE discounted at the required return on equity.

Note: Technically, "firm value" here means the value of operating assets (assets that generate FCFF). Add non-operating assets (excess cash, marketable securities, land held for investment) if provided.

Equity value alternative:

Equity value = firm value - market value of debt.

Memorise: always discount FCFF at WACC for firm value, and discount FCFE at required return on equity for equity value. A common error is mixing cash flow definitions and discount rates.

Choice between FCFF and FCFE: FCFE is suitable when capital structure is stable. If FCFE is negative or capital structure is volatile or leverage is high, use FCFF. You can always value equity indirectly by valuing the firm via FCFF and subtracting market value of debt.

Adjusted Present Value (APV): For volatile capital structure, APV is an alternative: discount unlevered cash flows at the unlevered cost of equity and add the net present value (NPV) of debt (value of interest tax shield less cost of financial distress).

LOS 21.b: Explain the ownership perspective implicit in the FCFE approach.

The FCFE ownership perspective is the control perspective: the acquirer (controller) can change dividend policy and distribution of cash. Dividend discount models represent the minority owner perspective, who cannot change dividend policy. If control has value, the FCFE and dividend discount valuations may differ.

Why analysts prefer FCFF/FCFE over dividends:

• Many firms pay little or no dividends.
• Dividends are discretionary and may not reflect long-run profitability.
• For acquisition targets, free cash flow is more appropriate as new owners will control distribution.
• Free cash flows may better reflect long-run profitability than dividends.

MODULE QUIZ 21.1

1. Chamber Group is analyzing the potential takeover of Outmenu, Inc. Chamber has gathered the following data on Outmenu. All figures are in millions of dollars.

The most appropriate model for valuing Outmenu is the:

A. free cash flow to equity model.

B. dividend discount H-model.

C. free cash flow to the firm model.

2. An analyst calculates firm value using a single-stage model on December 31, 2023, as:

Assuming there are no nonoperating assets on the balance sheet, the analyst has most likely:

A. correctly calculated firm value.

B. incorrectly calculated firm value. The weighted average cost of capital should be substituted for the required return on equity.

C. incorrectly calculated firm value. The weighted average cost of capital should be substituted for the required return on equity, and FCFE2023(1 + g) should be substituted for FCFE2024.

MODULE 21.2: FIXED CAPITAL AND WORKING CAPITAL

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LOS 21.c: Adjustments to compute FCFF and FCFE

FCFF and FCFE can be estimated starting from different financial statement items: net income (NI), EBIT, EBITDA, or cash flow from operations (CFO), by making appropriate adjustments. We present the commonly required formulas and the adjustments needed without full derivations so you can apply them reliably.

Calculating FCFF from net income

Starting from net income, the adjustments are:

• add back noncash charges (NCC) such as depreciation and amortisation;
• add back after-tax interest because interest is a financing cash flow: Int × (1 - tax rate) (we add after-tax interest back to net income when computing FCFF from NI);
• subtract fixed capital investment (FCInv) (capital expenditures less proceeds from sales of long-term assets);
• subtract working capital investment (WCInv) (change in non-cash working capital accounts).

The formula is:

FCFF = NI + NCC + [Int × (1 - tax rate)] - FCInv - WCInv

Noncash charges

Noncash charges reduce reported net income but do not use cash and therefore must be added back to obtain FCFF. Common items:

• Depreciation - usually the largest noncash charge.
• Amortisation of intangibles - treated like depreciation.
• Provisions for restructuring and other noncash losses - add back unless these provisions cover expected future cash outflows, in which case reduce future free cash flows accordingly.
• Gains or losses on sale of long-term assets - removed from net income and accounted for under fixed capital investment.
• Income from reversals of restructuring charge accruals and other noncash gains - subtract from net income when computing FCFF.
• Bond discount amortisation - add back; bond premium accretion - subtract.
• Deferred taxes - analyse carefully: if deferred tax liabilities are expected to continue to increase (not reverse), increases in deferred tax liabilities should be added back to net income; increases in deferred tax assets not expected to reverse should be subtracted.

Fixed capital investment

Fixed capital investment (FCInv) is the net cash spent on long-term fixed assets:

FCInv = capital expenditures - proceeds from sales of long-term assets

If no long-term assets were sold:

FCInv = ending net PP&E - beginning net PP&E + depreciation

If long-term assets were sold, determine capital expenditures and sale proceeds from cash flow from investing activities or vignette data. If not directly provided, use gain/loss on asset sales and PP&E figures:

FCInv = ending net PP&E - beginning net PP&E + depreciation - gain on sale

If there is a loss, add the loss instead of subtracting it.

Examples: Calculating FCInv

EXAMPLE: Calculating FCInv with no long-term asset sales

Airbrush, Inc., financial statements for 2023 include the following information:

There were no sales of PP&E during the year; depreciation expense was $300. Calculate Airbrush's FCInv for 2023.

Answer:

Use FCInv = ending net PP&E - beginning net PP&E + depreciation. (Specific numeric values from the original table would be used here; the formula is the same as change in gross PP&E.)

EXAMPLE: Calculating FCInv with long-term asset sales

Suppose Airbrush reports capital expenditures of $1,400, long-term asset sales of $600, and depreciation expense of $850. The long-term assets sold were fully depreciated. Calculate revised FCInv for 2023.

Answer:

FCInv = capital expenditures - proceeds from sale of long-term assets = 1,400 - 600 = 800

If assets sold were fully depreciated, the gain/loss adjustments are not needed beyond this calculation.

Working capital investment

Investment in net working capital is the change in working capital excluding cash, cash equivalents, notes payable, and the current portion of long-term debt. A reduction in working capital is a cash inflow (treated as a positive item to FCFF), so it appears with a plus sign when computing FCFF.

Interest expense

Interest expense is a financing cash flow. When computing FCFF from net income, add back interest expense after tax because paying interest reduces taxable income. The net effect on free cash flow is to add back interest × (1 - tax rate).

MODULE 21.3: VARIATIONS OF FORMULAE

Figure 21.2 (referenced): Calculating FCFF and FCFE Using the Statement of Cash Flows.

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Memorise several FCFF and FCFE formulas. The statement of cash flows is a useful framework: FCFF is operating cash flow left after working capital and fixed capital investment. Because interest is reported as an operating cash flow in the statement of cash flows but is conceptually financing, we adjust for after-tax interest to arrive at FCFF.

Key formulas

FCFF (from net income):

FCFF = NI + NCC + [Int × (1 - tax rate)] - FCInv - WCInv

FCFF (from EBIT):

FCFF = [EBIT × (1 - tax rate)] + Dep - FCInv - WCInv

Explanation: Starting from EBIT (before interest and taxes) we compute after-tax EBIT and add back depreciation because EBIT is before depreciation deduction for FCFF purposes; interest is not subtracted because EBIT is before interest.

FCFF (from EBITDA):

FCFF = [EBITDA × (1 - tax rate)] + (Dep × tax rate) - FCInv - WCInv

Explanation: EBITDA is before depreciation; the depreciation tax shield (Dep × tax rate) increases free cash flow.

FCFF (from CFO):

FCFF = CFO + [Int × (1 - tax rate)] - FCInv

Explanation: CFO (cash flow from operations) equals NI + NCC - WCInv; add back after-tax interest to reverse financing treatment and subtract fixed capital investment.

Which formula to memorise

At minimum, memorise the net income and CFO based formulas: the ones that start with NI and CFO. Given either an income statement or a cash flow statement you can calculate FCFF. You may be asked to use the EBIT or EBITDA variants as well.

Calculating FCFE

From FCFF:

FCFE = FCFF - [Int × (1 - tax rate)] + net borrowing

Explanation: FCFE adjusts FCFF for financing cash flows belonging to equity: subtract after-tax interest (which was added to get FCFF) and add net borrowing (new debt issued less debt repayments) since net borrowing increases cash available to equity holders.

From net income:

FCFE = NI + NCC - FCInv - WCInv + net borrowing

Note the differences from FCFF-from-NI: after-tax interest is not added back; net borrowing is added.

From CFO:

FCFE = CFO - FCInv + net borrowing

Free cash flow with preferred stock

If a firm has preferred stock, adjust FCFF and FCFE formulas accordingly. Treat preferred stock similarly to debt in FCFF computations (i.e., preferred dividends should be added back to FCFF if net income is reported net of preferred dividends), but remember that preferred dividends are not tax deductible.

Specifically:

• Add preferred dividends back to FCFF (assuming NI is net of preferred dividends).
• Revise WACC weights to include preferred stock and use the cost of preferred stock in WACC.
• Adjust net borrowing in FCFE to reflect net issuance/repurchase of preferred stock.

MODULE QUIZ 21.2, 21.3

Use the following information to answer Questions 1 through 3.

Meyer Henderson, CFA, is analyzing the financials of Roth Department Stores. He intends to use an FCFF model to value Roth's common stock. In the 2023 financial statements and footnotes he has identified the following items:

• Item #1: Roth reported depreciation and software amortisation of $23 million in 2023.
• Item #2: The deferred tax liability increased by $17 million in 2023.
• Item #3: Roth reported income of $6 million in 2023 from the reversal of previous restructuring charges related to store closings in 2022.
• Item #4: Net income totalled $173 million in 2023.
• Item #5: The net increase in noncash net working capital accounts was $47 million in 2023.
• Item #6: Net capital spending totalled $86 million in 2023.
• Item #7: Roth reported interest expense of $19 million.

Henderson estimated Roth's marginal tax rate to be 35%. He also expects Roth to be profitable for the foreseeable future, so he does not expect the deferred tax liability to reverse. As the base-year projection for his FCFF valuation, Henderson calculates FCFF for 2023 as:

1. In implementing the FCFF model to value Roth, did Henderson correctly treat Items #1 and #2?

A. Both items were treated correctly.

B. One item was treated correctly and the other incorrectly.

C. Neither item was treated correctly.

2. In implementing the FCFF model to value Roth, did Henderson correctly treat Items #3 and #4?

A. Both items were treated correctly.

B. One item was treated correctly and the other incorrectly.

C. Neither item was treated correctly.

3. In implementing the FCFF model to value Roth, did Henderson correctly treat Items #5 and #7?

A. Both items were treated correctly.

B. One item was treated correctly and the other incorrectly.

C. Neither item was treated correctly.

4. Imagine we are provided the following information for a firm:

Net income = $50. Working capital investment = $4. Beginning gross fixed assets = $90; ending gross fixed assets = $136. Beginning accumulated depreciation = $30; ending accumulated depreciation = $40. Depreciation expense = $27. Net borrowing = $0. In addition, a piece of equipment with an original book value of $19 was sold for $10. The equipment had a book value at the time of sale of $2. The gain was classified as unusual. Free cash flow to equity is closest to:

A. $6.

B. $10.

C. $18.

5. Suppose an analyst uses the statement of cash flows to calculate FCFF as CFO less FCInv, and FCFE as FCFF plus net borrowing. The firm has short- and long-term debt on its balance sheet. Has the analyst correctly stated, overstated, or understated FCFF and FCFE?

MODULE 21.4: EXAMPLE

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LOS 21.d: Calculate FCFF and FCFE.

Let's work through examples to verify formulas.

EXAMPLE: Calculating FCFF and FCFE

Anson Ford, CFA, analyses the financial statements of Sting's Delicatessen. He has a 20X6 income statement and balance sheet, as well as 20X7 income statement, balance sheet, and cash flow from operations forecasts. Assume no sales of long-term assets in 20X7. Calculate forecasted FCFF and FCFE for 20X7.

Sting's Income Statement

Sting's Balance Sheet

Sting's Cash Flow From Operations Forecast

Answer:

Fixed capital investment (FCInv) equals capital expenditures (no asset sales), which is equal to the change in net PP&E plus depreciation:

FCInv = ending net PP&E - beginning net PP&E + depreciation

Working capital investment (WCInv) is the change in working capital accounts excluding cash and short-term borrowings.

Given depreciation as the only noncash charge, compute FCFF from net income using:

FCFF = NI + NCC + [Int × (1 - tax rate)] - FCInv - WCInv

A short term: FCFF can be negative. Methods to value firms with negative FCFF are discussed later.

Net borrowing equals the change in long- and short-term debt: new debt issues less debt repayments.

EXAMPLE: Calculating FCFF and FCFE with other starting points

Calculate FCFF starting with EBIT, EBITDA, and CFO, and calculate FCFE starting with NI and CFO to confirm consistency with the formulas above.

EXAMPLE: Using the statement of cash flows

Reconstruct the cash flow framework from Figure 21.2 using actual numbers from the previous example to show the sources and uses of FCFF and FCFE. FCFF sources must equal FCFF uses, and FCFE sources must equal FCFE uses.

MODULE QUIZ 21.4

1. The adjustments to cash flow from operations necessary to obtain FCFF are:

A. add noncash charges, subtract fixed capital investment, and subtract working capital investment.

B. add after-tax interest expense and subtract fixed capital investment.

C. add net borrowing and subtract fixed capital investment.

MODULE 21.5: FCF - OTHER ASPECTS

LOS 21.e: Forecasting FCFF and FCFE

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Two common approaches to forecasting future FCFF and FCFE:

• Method 1 - Forecast total historic FCF and apply growth rates: Calculate historical free cash flow and apply a constant or staged growth rate (for example, FCFF grows at 8% for four years then 4% forever). This mirrors dividend discount single/multistage approaches. Note FCFF and FCFE growth rates usually differ.
• Method 2 - Forecast underlying components: Forecast sales, margins, capital expenditures (breakdown into maintenance and expansion capex), depreciation, and working capital changes and calculate FCFF/FCFE each year. This is more realistic but more data-intensive. Maintenance capex relates to current sales level; marginal capex supports growth.

When forecasting FCFE with Method 2, analysts often assume a target debt-to-asset ratio (DR) to determine debt financing of net new investment. For example, if DR = 40% and fixed capital investment = $60m, assume $24m financed with debt and $36m with equity. Under the target DR assumption, net borrowing can be expressed without explicit forecast of debt issuance/repayment:

FCFE = NI - [(1 - DR) × (FCInv - Dep)] - [(1 - DR) × WCInv]

LOS 21.f: Effects of financing decisions on FCF

Dividends, share repurchases, and share issues do not affect FCFF or FCFE because they are allocations of cash after free cash flow is determined. Changes in leverage do not affect FCFF and have only a minor effect on FCFE: a debt repayment reduces FCFE in the current year but may increase future FCFE by lowering interest expense.

Figure 21.3 (referenced): Effect of financing decisions on free cash flow.

LOS 21.g: FCFE vs Dividend Discount Models

The FCFE approach uses a control perspective (value is realised when new owners can change distributions). Dividend discount models take a minority perspective (value may not be realised until dividend policy reflects long-run profitability).

LOS 21.h: Net Income and EBITDA as proxies

Net income is a poor proxy for FCFE because:

• NI includes noncash charges that must be added back for FCFE.
• NI ignores cash flows not on the income statement such as fixed capital investment and working capital investment and net borrowings.

Formally:

FCFE = NI + NCC - FCInv - WCInv + net borrowing

EBITDA is a poor proxy for FCFF. From the formula:

FCFF = [EBITDA × (1 - tax rate)] + (Dep × tax rate) - FCInv - WCInv

EBITDA ignores cash taxes and effects of investments in working and fixed capital.

LOS 21.i: Sensitivity analysis in FCF valuations

Sensitivity analysis reveals how valuation outputs change with changes in model inputs. Some inputs (growth rates, discount rates, base year selection) can have large effects on value. Comprehensive sensitivity analysis helps assess the importance of forecasting errors. On exams you may be asked to interpret sensitivity analysis results or perform a few sensitivity calculations.

Two major sources of error:

• Estimating future growth in FCFF and FCFE (depends on sales growth, margins, life cycle, competitive strategy, industry profitability).
• Choice of base year for FCFF/FCFE forecasts - use a representative base year or forecasts will be biased.

LOS 21.j: Single-stage, two-stage, and three-stage models

Single-Stage FCFF Model

The single-stage model assumes FCFF grows at constant rate g forever and g < wacc.="" formula="" (analogous="" to="" gordon="">

Firm value = FCFF1 / (WACC - g) where FCFF1 is FCFF next year.

WACC is the market-value weighted average of the after-tax cost of debt and cost of equity:

WACC = wE × rE + wD × rD × (1 - tax rate)

Use target capital weights if provided; otherwise use market values.

Single-Stage FCFE Model

Analogous to the FCFF single-stage: use FCFE and the required return on equity (rE):

Equity value per share = FCFE1 / (rE - g)

Multistage models - variations

Multistage models differ by:

• Using FCFF or FCFE;
• Two-stage vs three-stage growth assumptions;
• Forecasting total free cash flow vs forecasting components of free cash flow.

Use a two-stage model for a short supernormal growth period followed by stable growth. Use a three-stage model when there are three distinct growth phases (growth → transition → maturity).

Model assumptions and firm characteristics

Choose the model that matches a firm's life cycle and the available forecasts. Forecast components when you can tie sales growth to capex, depreciation, and working capital needs; use terminal value after the first stage when growth settles to a long-run level.

Examples of two-stage models

Examples include:

• Two-stage FCFF: FCFF grows at 20% for four years, then 4% thereafter;
• Two-stage FCFE: FCFE declines from 20% to 4% over four years, then 4% forever;
• Two-stage FCFE forecasting components: sales grow at 20% for four years, net margin constant at 8%, FCInv = 60% of sales increase, WCInv = 25% of sales increase, debt ratio = 50%.

Terminal value

Common method: at the point when growth becomes stable, apply single-stage (constant growth) model to estimate terminal value. Another method is using valuation multiples (e.g., P/E) to estimate terminal value.

Examples of three-stage models

Examples include:

• Three-stage FCFE: FCFE grows 30% for 2 years, then 15% for 4 years, then 5% forever;
• Three-stage FCFF: FCFF grows 25% for 3 years, declines to 4% over next 5 years, then 4% forever;
• Three-stage FCFE forecasting components over three different stages.

LOS 21.k: Estimate company value using FCF models

We now demonstrate valuation calculations with single-stage, two-stage, and three-stage examples.

Single-Stage FCFF example

EXAMPLE: Knappa Valley Winery (KVW)

Given:

• Most recent FCFF (FCFF0) = $5,000,000;
• Target debt-to-equity ratio = 0.25;
• Market value of debt = $10,000,000;
• Shares outstanding = 2,000,000;
• Tax rate = 40%;
• Required return on equity = 16%;
• Before-tax cost of debt = 8%;
• Expected long-term FCFF growth rate g = 5%.

Solution (steps):

Since FCFF0 is given, compute FCFF1 = FCFF0 × (1 + g).

Compute WACC using target capital structure:

Target debt-to-equity = 0.25 implies for every $1 of debt there is $4 of equity → total capital = $5 → wD = 1/5 = 20% and wE = 4/5 = 80%.

WACC = wE × rE + wD × rD × (1 - tax rate).

Compute firm value = FCFF1 / (WACC - g).

Equity value = firm value - market value of debt.

Equity value per share = equity value / shares outstanding.

Note: WACC uses target weights even if actual current market weights differ.

Single-Stage FCFE example

EXAMPLE: Ridgeway Construction

Given:

• FCFE per share = C$2.50 (most recent, FCFE0);
• Target debt-to-equity ratio = 0.4;
• Market expected return = 9%; risk-free = 4%; beta = 1.5; equity risk premium = 5% (implied);
• Expected growth rate of FCFE = 4.5%.

Solution (steps):

Compute required return on equity using CAPM: r = rf + β × (market risk premium).

r = 0.04 + 1.50 × (0.09 - 0.04) = 0.115 = 11.5%.

Compute FCFE1 = FCFE0 × (1 + g).

Equity value per share = FCFE1 / (r - g).

Professor's note: If FCFE per share is given, compute value per share directly. If FCFE total is given, compute total equity value and divide by shares outstanding.

Two-Stage FCFF example

EXAMPLE: Prentice Paint Company

Given:

• Net profit margin = 20% on revenues of $20 million this year;
• Fixed capital investment = $2 million; depreciation = $3 million;
• Working capital investment = 7.5% of sales each year;
• Net income, FCInv, depreciation, interest, and sales expected to grow 10% per year for next 5 years; then 5% thereafter;
• Tax rate = 40%; shares outstanding = 1,000,000;
• Long-term debt with 12.5% interest trading at par value $32 million;
• WACC = 17% in high growth stage and 15% in stable stage.

Solution (outline of steps):

Calculate components of FCFF (per share) for years 0 through 5 using growth and component relationships.

Compute terminal value at Year 5 using FCFF in Year 6 and stable WACC (15%): terminal value = FCFF6 / (WACCstable - gstable).

Discount high-growth FCFFs and terminal value back to present using high-growth WACC (17%) for discounting those early cash flows.

Total firm value = PV(high-growth FCFFs) + PV(terminal value).

Equity value per share = (firm value - market value of debt) / shares outstanding.

The example demonstrates different WACC in stages and the resulting timeline for discounting.

Two-Stage FCFE example with declining growth in Stage 1

Consider a rival to Prentice Paint (Sioux Falls Decor) with similar revenues and forecasts. Sales growth and net margin are projected by year. Fixed capital investment net of depreciation is 30% of the dollar increase in sales; working capital is 7% of dollar increase in sales; debt finances 40% of investments; required return on equity is 12%; shares outstanding = 1 million. Compute FCFE for years 1 through 6 and terminal value in Year 5 with 5% stable growth, then discount at required return to find equity value.

Three-Stage FCFE example

EXAMPLE: Medina Classic Furniture, Inc.

Given:

• Most recent FCFE (FCFE0) = C$0.90 per share;
• High-growth (Stage 1): duration = 3 years, FCFE growth = 30% p.a., required return = 20%;
• Transitional (Stage 2): duration = 3 years, FCFE growth will decline by 9% per year down to stable growth; required return = 15%;
• Stable (Stage 3): FCFE growth = 3%, required return = 10%.

Task: Compute equity value using three-stage FCFE.

Solution (outline):

Project FCFE for each year through the end of Stage 2 (Year 6). Discount each FCFE using the appropriate sequence of discount rates (20% for Stage 1 cash flows, then 15% for transitional flows as of those years). Compute terminal value at Year 6 using FCFE7 and Stage 3 required return r3 = 10%:

Terminal value at Year 6 = FCFE7 / (r3 - g3)

Discount terminal value back to present using the appropriate sequence of discount factors reflecting the changing discount rates. The value of equity is the sum of PVs of FCFE1..FCFE6 and PV(terminal value).

Changing discount rates complicate calculations because standard financial calculators cannot directly apply varying discount rates in a single keystroke; discount in stages or use manual discount factors.

LOS 21.l: Terminal value methods

Two basic approaches to compute terminal value:

• Single-stage model: At the point cash flows stabilise, apply the constant growth model: TVn = FCFn+1 / (r - g).
• Multiple approach (valuation multiples): Use market multiples (e.g., trailing or leading P/E) applied to earnings at the terminal date: TVn = (trailing P/E) × (earnings in year n) or TVn = (leading P/E) × (forecasted earnings in year n+1).

EXAMPLE: P/E multiple

If EPS in five years (Year 5) = $2.10 and trailing industry median P/E = 35, terminal value in Year 5 = 35 × $2.10 = $73.50.

LOS 21.m: Overvalued, fairly valued, undervalued

Compare model price and market price:

• Market price > model price → stock is overvalued;
• Market price < model="" price="" →="" stock="" is="">undervalued;
• Market price = model price → stock is fairly valued.

MODULE QUIZ 21.5

1. The Gray Furniture Co. earned £3.50 per share last year. Investment in fixed capital was £2.00 per share, depreciation was £1.60, and investment in working capital was £0.50 per share. Gray is operating at its target debt-to-asset ratio of 40% (so 40% of annual investments financed by new borrowings). Shareholders require a return of 14%, expected growth = 4%. The value of Gray's stock is closest to:

A. £27.04.

B. £29.90.

C. £30.78.

Use the following information to answer Questions 2 through 4.

The Sanford Software Co. earned $20m EBIT on revenues of $60m last year. Investment in fixed capital = $12m; depreciation = $8m; working capital investment = $3m. Sanford expects EBIT, investments in fixed and working capital, depreciation, and sales to grow at 12% p.a. for the next five years. After five years, growth in sales, EBIT, and WCInv will decline to 4% p.a., and fixed capital investment and depreciation will offset each other. Tax rate = 40%. WACC = 11% during high growth and 8% during the stable stage. FCFF in Years 1-5 is shown in the table.

2. FCFF in Year 6 is closest to:

A. $14.14.

B. $16.49.

C. $18.26.

3. The terminal value in Year 5 is closest to:

A. $206.12.

B. $220.25.

C. $412.25.

4. The value of the firm using a FCFF model is closest to:

A. $149.04.

B. $265.17.

C. $270.35.

Use the following information to answer Questions 5 through 9.

An analyst following Barlow Energy compiled the following (data in hundreds of millions $):

• Bonds trading at par;
• Preferred share dividends: $14;
• Net income available to common: $125;
• Investment in working capital: $30;
• Investment in fixed capital: $100;
• Net new borrowing: $40;
• Depreciation: $50;
• Tax rate: 40%;
• Long-term growth rate of FCFF: 4%;
• Long-term growth rate of FCFE: 4%;
• WACC: 9.27%.

5. The current FCFF for Barlow Energy is closest to:

A. $36.

B. $62.

C. $86.

6. Total value of Barlow Energy using single-stage FCFF is closest to:

A. $894.40.

B. $1,631.88.

C. $1,697.15.

7. Value of equity using single-stage FCFF is closest to:

A. $897.15.

B. $1,097.15.

C. $1,497.15.

8. Current FCFE using the information is closest to:

A. $45.

B. $85.

C. $99.

9. Value of equity using single-stage model and current FCFE is closest to:

A. $468.

B. $850.

C. $884.

10. Which is the best estimate of cash flows available to the firm's investors before financing decisions?

A. EBITDA × (1 - tax rate).

B. EBITDA × (1 - tax rate) + (Dep × tax rate) - FCInv - WCInv.

C. EBITDA × (1 - tax rate) + (Dep × tax rate) - FCInv - WCInv + Int × (1 - tax rate).

Use the following information to answer Questions 11 and 12.

Rachel Keimmel, CFA, researches MWC Corporation (U.S. automobile parts). She expects:

• MWC's earnings and FCFE growth = 15% p.a. for 2 years, then stabilise at 8% p.a.;
• MWC maintains its current dividend payout ratio;
• Beta = 1.2; government bonds yield = 6.4%; market equity risk premium = 5.5%;
• Most recent dividend paid = $2.30;
• She also has the current cash flow statement.

11. The value of MWC common stock using two-stage DDM is closest to:

A. $56.33.

B. $61.55.

C. $65.88.

12. The value of MWC common stock using two-stage FCFE is closest to:

A. $55.09.

B. $59.10.

C. $68.24.

13. Hoffman Card Co. earned £1.50 per share last year. FCInv = £0.80 per share; depreciation = £0.30; WCInv = £0.20. Hoffman expects earnings to grow 15% p.a. for next five years; investments and WCInv grow at same rate. After five years, growth declines to stable 5% and FCInv and depreciation offset. Target debt ratio = 30%. Shareholders require return 17% during high growth and 10% during stable stage. FCFE in Year 6 and value per share closest to:

14. Suppose an analyst incorrectly: discounts FCFE at WACC in FCFE model and FCFF at required return on equity in FCFF model. The analyst would most likely:

A. overestimate equity value with FCFE model and underestimate firm value and equity value with FCFF model.

B. underestimate equity value with FCFE model and overestimate firm value and equity value with FCFF model.

C. underestimate equity value with FCFE model and underestimate firm value and equity value with FCFF model.

Use the following information to answer Questions 15 and 16.

At the end of 2023, Meyer Henderson prepared a 10-year forecast of FCFE and FCFF for Trammel Medical Supplies from 2024 to 2033. In early 2024 Trammel unexpectedly issued 15-year senior debt; proceeds will be used to repurchase common stock during 2024.

15. As a result of the unexpected debt issue, Henderson should most likely:

A. increase his FCFE forecast for 2024 and decrease FCFE for 2025-2033.

B. decrease his FCFE forecast for 2024 and increase FCFE for 2025-2033.

C. increase his FCFE forecast for 2024 and not change FCFE for 2025-2033.

16. As a result of the unexpected debt issue, Henderson should most likely:

A. increase his FCFF forecast for 2024 and decrease FCFF for 2025-2033.

B. decrease his FCFF forecast for 2024 and increase FCFF for 2025-2033.

C. not change his FCFF forecast for 2024 or for 2025-2033.

17. The Anderson Door Co. earned C$30m EBIT on revenues of C$80m last year. CAPEX = C$20m; depreciation = C$15m; additions to working capital = C$6m; WACC = 12.45%; tax rate = 40%; expected cash flow growth = 5%; market value of debt = C$25m. The value of the firm's equity is closest to:

A. C$73.70.

B. C$93.96.

C. C$98.70.

KEY CONCEPTS

LOS 21.a

Definitions:

• FCFF is cash available to all the firm's investors (stockholders and bondholders) after operating and investment activities.
• FCFE is cash available to common shareholders after funding capital requirements, working capital needs, and debt financing requirements.

Valuation rules:

• Firm value = PV(expected future FCFF discounted at WACC).
• Equity value = PV(expected future FCFE discounted at required return on equity).

Use FCFE when capital structure is stable; use FCFF for negative/volatile FCFE or significant debt.

LOS 21.b

Analysts prefer FCFF or FCFE when:

• The firm does not pay dividends;
• Dividends do not reflect long-run profitability;
• The analyst takes a control perspective.

Free cash flow models reflect a control perspective; dividend models reflect the minority shareholder perspective.

LOS 21.c, 21.d

You should be able to calculate FCFF and FCFE from the following starting points:

FCFF = NI + NCC + [Int × (1 - tax rate)] - FCInv - WCInv

FCFF = [EBIT × (1 - tax rate)] + Dep - FCInv - WCInv

FCFF = [EBITDA × (1 - tax rate)] + (Dep × tax rate) - FCInv - WCInv

FCFF = CFO + [Int × (1 - tax rate)] - FCInv

FCFE = FCFF - [Int × (1 - tax rate)] + net borrowing

FCFE = NI + NCC - FCInv - WCInv + net borrowing

FCFE = CFO - FCInv + net borrowing

LOS 21.e

Forecasting FCFE using target debt ratio (DR):

FCFE = NI - [(1 - DR) × (FCInv - Dep)] - [(1 - DR) × WCInv]

LOS 21.f

Dividends, repurchases, and share issues do not affect FCFF and FCFE; changes in leverage have minor effect on FCFE and no effect on FCFF.

LOS 21.g

FCFE takes a control perspective; dividend discount models use a minority shareholder perspective.

LOS 21.h

Net income is a poor proxy for FCFE because it excludes noncash charges and ignores investments and net borrowings:

FCFE = NI + NCC - FCInv - WCInv + net borrowing

EBITDA is a poor proxy for FCFF:

FCFF = EBITDA × (1 - tax rate) + (Dep × tax rate) - FCInv - WCInv

LOS 21.i

Sensitivity analysis assesses how valuation results vary with inputs; key sources of error are growth forecasts and choice of base year.

LOS 21.j, 21.k

Single-stage models suit stable firms; they assume constant growth g < required="" return.="" two-stage="" models="" suit="" firms="" with="" a="" temporary="" supernormal="" growth="" period="" and="" a="" long-term="" stable="" growth="" rate.="" three-stage="" models="" suit="" firms="" with="" growth,="" transition,="" and="" stable="" phases.="" forecast="" total="" fcff/fcfe="" or="" forecast="" components="" depending="" on="" available="" data="" and="" realism="">

LOS 21.l

Terminal value calculation approaches: single-stage constant growth model or valuation multiples (P/E, EV/EBITDA, etc.).

LOS 21.m

Compare market price with model price to classify stock as overvalued, undervalued, or fairly valued.

ANSWER KEY FOR MODULE QUIZZES

Module Quiz 21.1

1.

C Dividend discount models like the Gordon growth model and the dividend discount H-model are not appropriate because (1) dividends are not related to the firm's earnings stream and (2) this is a takeover situation where a free cash flow model is more appropriate. The FCFF model is preferred to the FCFE model because FCFE is negative and volatile and leverage is relatively high. (See LOS 21.a)

2.

A Although unusual, the analyst has correctly calculated firm value. The first term equals market value of equity on 31/12/2023; firm value equals market value of equity plus market value of debt. (See LOS 21.a)

Module Quiz 21.2, 21.3

For Questions 1-3: Items #1, #2, #4, #5, #6, and #7 were applied correctly. Item #3 (income from reversal of restructuring charges) was handled incorrectly - a noncash gain should be subtracted from net income when computing FCFF. Depreciation and software amortisation should be added back; after-tax interest added back; increases in deferred tax liabilities should be added back if not expected to reverse; net working capital and fixed capital investments subtracted. Correct FCFF calculation is consistent with the formula given above.

1.

A (See explanation above.)

2.

B (See explanation above.)

3.

A (See explanation above.)

4.

B Given: NI = $50; depreciation = $27; ending net PP&E = ending gross fixed assets - ending accumulated depreciation = $136 - $40 = $96; beginning net PP&E = $90 - $30 = $60; WCInv = $4; net borrowings = $0; gain on sale = $8 (since equipment sold for $10 with book value $2 → gain = 10 - 2 = 8).

Compute FCInv:

FCInv = ending net PP&E - beginning net PP&E + depreciation - gain on sale

FCInv = 96 - 60 + 27 - 8 = $55

Compute NCC (noncash charges) = depreciation - gain = 27 - 8 = $19

Compute FCFE:

FCFE = NI + NCC - FCInv - WCInv + net borrowings

FCFE = 50 + 19 - 55 - 4 + 0 = $10

(See Module 21.3, LOS 21.c)

5.

C If the analyst computes FCFF = CFO - FCInv and FCFE = FCFF + net borrowing, but the firm has interest expense on the income statement, the analyst has understated FCFF by omitting after-tax interest. The correct relationship is FCFF = CFO + Int × (1 - tax rate) - FCInv. However, FCFE computed as CFO - FCInv + net borrowing would be correct; so the analyst's FCFE may be correct while FCFF is understated. (Module 21.3, LOS 21.c)

Module Quiz 21.4

1.

B Free cash flow to the firm = cash flow from operations + after-tax interest expense [Int × (1 - tax rate)] - fixed capital investment. (LOS 21.d)

Module Quiz 21.5

1.

C (See LOS 21.e)

2.

B FCFF in Year 6 computed according to the table of FCFF for Years 0-6. (See LOS 21.c)

3.

C Terminal value as of Year 5 uses FCFF in Year 6 and WACC = 8% and stable growth = 4%: TV5 = FCFF6 / (WACCstable - g). (See LOS 21.k)

4.

C Value of the firm today is PV of forecasted FCFF discounted at WACC during high-growth stage of 11%: NPV calculation provided in text yields $270.35. (LOS 21.k)

5.

C With bonds trading at par, interest = $600 × 0.075 = $45. Add back preferred dividends to net income available to common to get FCFF. (LOS 21.c)

6.

C Value of the firm is PV of constantly growing FCFF using single-stage model: computation in text yields $1,697.15. (LOS 21.k)

7.

A Value of equity = firm value - market value of debt - preferred stock (if any). Given values yield $1,697.15 - $600 - $200 = $897.15. (LOS 21.k)

8.

B FCFF = 86 (computed earlier). (LOS 21.c)

9.

C Value of equity using FCFE approach computed in text. (LOS 21.k)

10.

B The best estimate of cash flows available to the firm's investors before financing decisions is:

FCFF = [EBITDA × (1 - tax rate)] + (Dep × tax rate) - FCInv - WCInv

11.

A Required return on equity via CAPM: r = 6.4% + 1.2 × 5.5% = 13%. Two-stage DDM calculation gives the current value of MWC common stock per the text. (LOS 21.k)

12.

B Two-stage FCFE approach yields the value indicated in the text. (LOS 21.d)

13.

A Table shows FCFE Years 0-6; terminal value Year 5 computed using Year 6 FCFE and discount with required return 10% in stable period. Present value discounted with short-term discount rate 17% yields the value per share in the text. (LOS 21.k)

14.

A Using WACC (too low) in the FCFE model overestimates equity value. Using required return on equity (too high if substituting for WACC) in FCFF model underestimates firm and equity value. (LOS 21.k)

15.

A Increased net borrowing in 2024 increases FCFE for 2024; in subsequent years higher interest expense will reduce future FCFE. (LOS 21.f)

16.

C FCFF is cash flow available to all investors before financing cash flows; changes in leverage do not affect FCFF in either current or future periods. (LOS 21.f)

17.

A See LOS 21.k for detailed calculation methodology and result.

End of answer key.