Financial Modeling, 3rd Edition

1. 1Project free cash flow (FCF) for years 1–5 from the pro forma model. FCF is the cash generated by the core business, so it excludes financing flows. In the source example the FCFs are 176, 188, 201, 214, 228.
2. 2Set the discount rate to the firm's WACC, the weighted average of cost of equity and after-tax cost of debt. Weights are market values of equity (E) and debt (D): WACC = E/(E+D)·rE + D/(E+D)·rD·(1−Tc). The source example takes WACC as 20%.
3. 3Choose a long-term FCF growth rate separate from the 1–5 year sales growth. For a mature market, estimate it as real growth plus expected inflation (source: 2% real + 3% inflation = 5%). Use the sector's growth, not the firm's near-term growth.
4. 4Compute the year-5 terminal value with the growing-annuity model: TV = FCF5 × (1+g) / (WACC − g). Source: 228 × 1.05 / (0.20 − 0.05) = 1,598 (Excel =G58*(1+B55)/(B54-B55)).
5. 5Add the terminal value to the year-5 FCF in the same cell (228 + 1,598 = 1,826). Then discount the whole row: =NPV(WACC, year 1 to year 5 row). Source result: enterprise value = 1,231.
6. 6To reach equity value, add year-0 cash and marketable securities (80) to get asset value (1,311). Then subtract the firm's debt today (320). Source equity value = 991.
7. 7Re-run with different WACC and long-term growth values as a sensitivity check (Chapter 3.6 in the source). Terminal value carries most of the result, so the output is a range.

The source values a firm with a 20% WACC and 5% long-term FCF growth (2% real + 3% inflation). Projected FCFs for years 1–5 are 176, 188, 201, 214 and 228. Terminal value at year 5 is 228 × 1.05 / (0.20 − 0.05) = 1,598. The year-5 cash flow becomes 228 + 1,598 = 1,826. Applying =NPV(20%, 176, 188, 201, 214, 1826) gives an enterprise value of 1,231. Adding year-0 cash and marketable securities of 80 gives asset value of 1,311. Subtracting debt of 320 leaves equity value of 991. Enterprise value (1,231) is the operating-asset value before any capital-structure adjustment. Cash is added and debt subtracted only afterward to reach equity.

• If you need enterprise value, discount FCF at the WACC. If you need equity value, take enterprise value, add cash and marketable securities, and subtract debt.
• If the firm operates in a mature market, set long-term FCF growth to real growth plus inflation. Do not reuse the faster years 1–5 sales growth.
• If you will not project infinite cash flows, cut off the explicit forecast (here year 5) and substitute a terminal value for year 6 onward.
• If long-term growth approaches or exceeds the WACC, stop. The denominator (WACC − g) collapses and the terminal value becomes meaningless.
• If terminal value is most of the total (here 1,598 of a 1,826 final-year flow), run sensitivity analysis on WACC and g before presenting a single number.

• Subtracting debt or adding cash to the DCF result and still calling it enterprise value. The tell: the figure is 991 or 1,311 rather than 1,231.
• Using the near-term sales growth as the terminal growth rate. The tell: g is well above a realistic sector rate such as 5%, so the terminal value is inflated.
• Discounting FCF at the cost of equity, or using book-value weights in the WACC. The tell: the weights are not market values of E and D.
• Forgetting to include the terminal value in the year-5 cash flow before running NPV. The tell: the total of the final-year cell equals the FCF alone (228) instead of 1,826.
• Presenting one point estimate. The tell: no sensitivity table, although the source stresses that WACC calculation requires judgment, 'equal parts science and art'.

• ▸WACC: from market-value weights of equity and debt, rE, and after-tax rD (source example: 20%).
• ▸Long-term FCF growth g: real growth + inflation (source: 2% + 3% = 5%).
• ▸FCF years 1–5: projected free cash flows from the pro forma model.
• ▸Terminal value: FCF5 × (1+g) / (WACC − g).
• ▸Final-year cash flow: year-5 FCF + terminal value.
• ▸Enterprise value: =NPV(WACC, years 1–5 flows including terminal value).
• ▸Year-0 cash and marketable securities: add to enterprise value to get asset value.
• ▸Debt today: subtract from asset value.
• ▸Equity value: asset value − debt; then repeat for low and high WACC and g cases.

1. 1Build enterprise value first. Forecast free cash flow (FCF), the cash generated by the core business, and discount it at the WACC. The WACC is the weighted average of r_E and r_D(1−T_C), weighted by the market values of equity and debt. This gives the enterprise value, not the equity value.
2. 2Define the debt to subtract with one explicit policy. Total debt in the Kraft example is short-term borrowings, current portion of long-term debt, amounts due to the parent and affiliates, and long-term debt. Decide whether cash and cash equivalents (and marketable securities) are netted as 'negative debt'. Write the choice down, because the source calls it 'largely a judgment call'.
3. 3Compute net debt from the balance sheet. Sum the debt lines and subtract cash (Kraft: SUM of the four debt lines − cash). Use the same balance-sheet date as the valuation.
4. 4Bridge to equity value: enterprise value minus net debt gives the value that belongs to shareholders. If net debt is negative, as at Cascade, equity value exceeds enterprise value.
5. 5Check the equity value against the equity cash flows. Discount cash flows to equity at r_E (Gordon model or CAPM). Count the full equity payout, meaning dividends plus share repurchases (and net of shareholder paid-in capital), not dividends alone. The two routes should be close.
6. 6Resolve the circularity. The WACC weights use the market value of equity, but equity value is an output of the valuation. Start with the market weights, compute the equity value, compare it with the weights you assumed, and rerun if they differ materially.
7. 7Stress r_E before trusting the answer. Intel's cost of equity is 14.36% under classic CAPM and 16.29% under tax-adjusted CAPM. Value equity under each, and run the sensitivity analyses the source recommends, since WACC computation is 'equal parts science and art'.

Take Kraft's balance sheet at 31 Dec 2005. Short-term borrowings are 805m, current portion of long-term debt 1,268m, due to Altria and affiliates 652m, and long-term debt 8,475m. These sum to total debt of 11,200m. Cash is 316m, so net debt is 10,884m. The equity bridge is: Equity value = enterprise value (FCF discounted at Kraft's WACC) − 10,884m. If you do not net cash, the deduction is 11,200m, and the 316m difference moves equity value one-for-one. Cascade shows the opposite case at 31 Jan 2006. Total debt is 29.922m and cash is 35.493m, so debt net of cash is −5.571m. Netting marketable securities of 23.004m as well gives −28.575m. Equity value is then enterprise value plus 5.571m or 28.575m, depending on the policy chosen. The source does not give Kraft's or Cascade's enterprise values, so the example stops at the bridge.

• If the firm holds large cash and marketable securities (Cascade), then show equity value under both net-debt policies and state which one you use. Do not silently pick the more aggressive netting.
• If you cross-check with equity cash flows, then include repurchases as well as dividends. PPG's total equity payout grew 11.91%, far faster than its dividend, so a dividend-only check understates equity value.
• If the Gordon model is used for r_E, then confirm |g| < r_E before applying P0 = Div0(1+g)/(r_E−g). Otherwise the formula is invalid.
• If CAPM and tax-adjusted CAPM give different r_E (Intel: 14.36% vs 16.29%), then report equity value as a range rather than choosing one rate without a reason.
• If the equity value implied by your valuation differs materially from the market equity weight used in the WACC, then iterate the WACC until they are consistent.

• Reporting enterprise value as equity value. The tell: no debt deduction appears anywhere between the FCF discounting and the per-share number.
• Inconsistent debt treatment between the WACC and the bridge. The tell: cash is netted in the cost-of-debt calculation (Kraft's 5.50% net vs 5.73% gross interest cost) but not in the debt subtracted from enterprise value, or vice versa.
• Ignoring negative net debt. The tell: a firm like Cascade shows 'debt net of cash' below zero, yet the model subtracts a positive debt figure.
• Using dividends only as equity cash flows. The tell: the equity-cash-flow valuation comes in well below the FCF valuation for a firm that buys back stock, as PPG does.
• Treating one-point r_E or WACC estimates as exact. The tell: no sensitivity table, even though the cost of equity swings by about two points across CAPM variants.

• ▸Valuation date and balance-sheet date: use the same date for both.
• ▸PV of FCF at WACC (enterprise value): the discounted free cash flow from your model.
• ▸WACC used and its r_E, r_D, T_C inputs: record the rates and weights behind the discount rate.
• ▸Total debt: sum short-term borrowings, current portion of long-term debt, affiliate debt, and long-term debt.
• ▸Cash and cash equivalents: enter the balance-sheet figure.
• ▸Marketable securities (include / exclude): enter the amount and your netting decision.
• ▸Net debt (chosen policy): total debt minus the items you net.
• ▸Equity value = enterprise value − net debt: compute and compare under both policies.
• ▸Cross-check: PV of total equity payout (dividends + repurchases − paid-in capital) at r_E: note the gap to the bridge result.

1. 1Anchor the forecast window to the history. Benninga's PPG case analyzes ten years of statements (1991–2000) to set parameters for a five-year pro forma (2001–2005). Compute the historical ratios first, then write each forecast assumption as a cell that points to one of those ratios.
2. 2Put every assumption in its own labeled input cell. Financial models 'require a lot of assumptions' and 'everything is related to almost everything else', so a hard-coded number inside a formula cannot be audited or flexed.
3. 3Decide the depth of each item by materiality. Accelerated depreciation needs a schedule length (three, five or seven years), an assumed age for existing assets, and a separate schedule for each year's new assets. Model it only if the firm has large fixed assets and large annual additions, so that accelerated versus straight-line changes cash flow materially. Otherwise use straight-line depreciation plus deferred taxes, as Chapter 4 does.
4. 4Set the financing assumptions deliberately: debt as the balancing plug, or a target debt/equity ratio. State which one you use, because it drives interest and the capital structure.
5. 5Build the cost-of-capital inputs from market data. Cost of equity comes from the Security Market Line, which needs a market expected return E(rM) taken from one of three approaches. Cost of debt comes from the financial statements or from bond data. Combine them into the WACC.
6. 6When computing cost of debt from the statements, include all financial debt, short- and long-term, without distinguishing them (four items for Kraft). Treat cash and cash equivalents as negative debt. Keep the nonfinancial short-term assets and liabilities in the free cash flows.
7. 7Use the bond-return method (default probabilities, payoffs, Chapter 28) only if the firm has significant risky debt. Otherwise accept the simpler methods, whose errors are 'in many cases… not critical'. The promised return on debt is generally higher than the expected return, so do not treat the two as the same thing.
8. 8Finish with a sensitivity analysis. Cost of capital is 'part science and part art', so run the valuation across a range of WACC and operating assumptions rather than reporting one point estimate.

Benninga's accelerated-depreciation pro forma shows how a modeling choice becomes a set of explicit assumptions. He assumes all assets are depreciated on a five-year schedule and that the assets in place at date 0 are three years old. From those two inputs, cumulative depreciation on existing assets is 71 percent of initial value, so cell C82 × 2,674 = 1,904. The cumulative depreciation for years 1–5 is then summed across each vintage of assets using VLookup. Row 61 references the result, and row 60 gives fixed assets at cost. Each vintage needs its own schedule, which is why the author calls it 'a fairly big mess.' His rule is to do this only when the fixed-asset base is large and grows significantly, so the cash-flow gap versus straight-line is large. In the PPG chapter he instead models straight-line depreciation plus deferred taxes. The lesson: every extra assumption (schedule length, asset age, vintage) must earn its place by changing cash flow materially.

• If fixed assets are large and additions are significant, model accelerated depreciation by vintage. If not, use straight-line depreciation plus deferred taxes.
• If the firm has significant risky debt, estimate cost of debt from bond prices, default probabilities and payoffs. If not, use the simpler statement-based or yield-based methods.
• If you compute cost of debt from the statements, include every financial debt item (short- and long-term) and net cash against it. Leave operating short-term items in free cash flow.
• If you value a bank, do not copy a nonfinancial template. Include its financial items in working capital and the FCF, because its lending is financed by borrowing.
• If a cost-of-capital input is uncertain, spend little time perfecting it. Run a sensitivity table around it instead.

• Treating the WACC as a precise number. The tell: a single-point valuation with no sensitivity table, despite the text's warning that the estimate is part science, part art.
• Using the promised return on debt as the expected return. The tell: a cost of debt equal to the coupon or yield when default risk is material, which overstates the cost.
• Counting only long-term debt, or leaving cash out of net debt. The tell: debt items that differ from the full financial-debt list (Kraft's four items) and no cash netting.
• Applying the nonfinancial FCF definition to a bank. The tell: the bank's financial items are excluded from working capital and the FCF.
• Over-engineering minor assumptions, such as vintage-by-vintage accelerated depreciation for a firm with few asset additions. The tell: a sprawling depreciation block whose cash-flow effect versus straight-line is small.

• ▸Assumption name: the line item it drives (e.g., depreciation, debt, dividend).
• ▸Value and forecast years: the number used and the period covered (e.g., 2001–2005).
• ▸Historical basis: the ratio or trend from past statements (e.g., 1991–2000) that supports it.
• ▸Source type: historical analysis, strategic forecast, or market data.
• ▸Financing rule: debt as plug, or target debt/equity ratio (state which).
• ▸Cost of equity inputs: risk-free rate, beta, E(rM) and the approach used to get it.
• ▸Cost of debt method and debt items included: statement-based, bond-yield, or default-adjusted; list every financial debt item and the cash netted.
• ▸Materiality test: does the extra detail change cash flow materially versus the simpler method? Yes or no, with reason.
• ▸Sensitivity range: the low and high values to test and the valuation output tracked.

1. 1Fix the valuation date and pull the price on that date. The source works Kellogg at 30 May 2006 (P0 = $48.28) and Johnson & Johnson at 31 Dec 2005 (P0 = $61.07). Every input after this must be as of the same date.
2. 2Build the cost of equity in two independent ways so they can be compared: a Gordon-type estimate (rE = Div0×(1+g)/P0 + g) and a CAPM/security-market-line estimate (risk-free rate + beta × market risk premium). Keep the two columns side by side and do not blend them early.
3. 3For the Gordon leg, annualize the latest dividend (Kellogg: quarterly $0.278 × 4 = $1.112). Compute g over at least two windows (Kellogg: 1.90% over 5 years, 3.61% over 10 years) and run rE for each window (4.25% and 6.00%). The spread between windows is the uncertainty you must carry forward.
4. 4Extend the Gordon leg to all cash flows to equity: dividends plus share repurchases, minus stock issuance (including employee option exercises). Repurchases are around 50% of cash paid out by US corporations, so a dividend-only model misses much of the payout. Value total equity, not a per-share dividend. Expect to use annual data for repurchases and issuance, because they appear only in annual statements.
5. 5Estimate beta by regressing the stock's periodic returns on the market index's returns (r_it = a + b·r_SP,t) over a stated window, such as the 60 months used for the Dow-Jones 30 components, April 2002–April 2007. Use SLOPE and INTERCEPT, and record r-squared and the t-statistic of beta alongside the beta itself.
6. 6Fix the market premium by deciding how to compute E(rM). The source offers three approaches, one of which treats an index as a dividend-growth asset: dividend yield plus expected dividend growth. State which approach you chose and the risk-free rate paired with it.
7. 7Estimate the cost of debt (rD) separately, then apply the tax rate to get the after-tax cost. Set the capital structure weights from the market values of equity and debt, not book values, and combine into WACC. The source works this through three cases: Kraft, Tyson and Cascade.
8. 8Compare the Gordon and CAPM cost-of-equity results. If they disagree materially, investigate the input (growth window, beta window, premium) before choosing. The source devotes a section to when the models do not work.

Kellogg, 30 May 2006. The price is $48.28 and the quarterly dividend is $0.278, so annualized Div0 = 0.278 × 4 = $1.112. Dividend growth is 1.90% over the last 5 years and 3.61% over the last 10. Using rE = Div0×(1+g)/P0 + g, the 5-year growth gives 1.112 × 1.019 / 48.28 + 0.019 = 4.25%. The 10-year growth gives 1.112 × 1.0361 / 48.28 + 0.0361 = 6.00%. Same firm, same price, same date, yet the cost of equity moves by 175 basis points purely from the growth window, so you report a range and not a point. Johnson & Johnson (P0 = $61.07, annualized dividend $1.32) shows the second lesson. Using total cash flow to equity (dividends plus repurchases less issuance) with growth of 16.59%, rE is 19.54%, versus 18.75% on the 5-year-growth variant. The source notes that dividends are smooth, while repurchases and issuance carry the real variability. Here the totals barely change the answer, but the source warns that the opposite is often the case.

• If the firm repurchases or issues meaningful stock (J&J, Wachovia), then compute the Gordon cost of equity on total equity cash flows as well as per-share dividends, and compare the two.
• If the 5-year and 10-year growth rates give materially different rE (Kellogg: 4.25% vs 6.00%), then report both, test which window reflects expected future growth, and consider a pro forma model to forecast payout instead of extrapolating history.
• If a stock's regression r-squared is low (Boeing: beta 0.73, r-squared 0.14, t-beta 3.13), then treat its individual beta as noisy. Remember that beta is a far better risk measure for a diversified portfolio than for a single stock, and cross-check the CAPM result against the Gordon result.
• If a beta looks extreme (Alcoa 1.94, r-squared 0.56), then confirm that the t-statistic supports it (8.67) before it drives the CAPM cost of equity.
• If the Gordon and CAPM estimates disagree and neither input set is clearly wrong, then do not average them silently. Document the disagreement and test the WACC and valuation for sensitivity to both.

• Using dividends alone as the equity payout. The tell: the firm runs large buybacks or option-exercise issuance, and the dividend line is suspiciously smooth while total payout swings.
• Treating one growth window as the truth. The tell: changing 5 years to 10 years moves rE by several percentage points (Kellogg: 4.25% to 6.00%) and nobody reports the range.
• Mixing frequencies without noting it. The tell: annual repurchase and issuance figures are combined with quarterly dividends and daily-price betas, with no remark on the mismatch.
• Accepting a regression beta without its diagnostics. The tell: no r-squared or t-statistic is reported, and a low-fit stock like Boeing (r-squared 0.14) is plugged in as if exact.
• Pairing inconsistent inputs, such as a risk-free rate and market return from different dates or an E(rM) method not stated. The tell: the premium cannot be traced to a computation, and rE changes when someone re-derives it.

• ▸Firm and valuation date: name the firm and the date for price and data (e.g., Kellogg, 30 May 2006).
• ▸Current share price P0: enter the price on that date.
• ▸Annualized dividend Div0: latest periodic dividend times periods per year.
• ▸Growth rates g (two or more windows): record g for 5-year and 10-year (or other) windows and note the source series.
• ▸Total equity cash flow check: list dividends, repurchases and issuance by year, and the implied growth of the total.
• ▸Gordon rE per window: compute Div0×(1+g)/P0 + g for each g and show the range.
• ▸Beta regression: record the return window, frequency, index used, beta, r-squared and t-statistic of beta.
• ▸Risk-free rate and E(rM) method: state the rate, the chosen approach to the market return, and the resulting premium.
• ▸Cost of debt, tax rate, weights: enter rD, the tax rate, and market-value weights of equity and debt, then compute WACC and the gap between Gordon- and CAPM-based results.

1. 1List every driver in one assumptions block and make every projected line reference it. The source model uses: sales growth 10%, current assets/sales 15%, current liabilities/sales 8%, net fixed assets/sales 77%, COGS/sales 50%, depreciation rate 10%, interest on debt 10%, interest on cash and marketable securities 8%, tax rate 40%, dividend payout 40%. A hard-coded number inside a statement is an unlabeled assumption.
2. 2Project the income statement first, starting from sales (year 0 sales are 1,000, growing at the sales-growth rate). Run it through COGS, depreciation, interest paid on debt, interest earned on cash, and tax. Take net income and apply the payout ratio to get dividends.
3. 3Build the balance sheet from the same drivers. Set current assets, current liabilities and net fixed assets as percentages of sales. Roll retained earnings forward as prior retained earnings plus net income minus dividends.
4. 4Choose one balancing item and keep it fixed. The source treats cash and marketable securities as the plug, so cash equals total liabilities and equity minus all other assets. The alternative is debt as a plug (section 3.7). Never plug both.
5. 5Check that the statements agree. Build the consolidated statement of cash flows (operating, investing, financing) and confirm that its change in cash equals the change in cash on the projected balance sheet (line 75 in the source). If they differ, an interconnection is broken.
6. 6Derive free cash flow from the projected statements. Discount it at the WACC (20% in the source) and add a terminal value. The default is the Gordon form: year-5 FCF × (1 + long-term growth) / (WACC − growth).
7. 7Treat initial cash consistently. Either add year-0 cash to the enterprise value and subtract debt, or net it against debt as negative debt. Then decide on mid-year discounting: multiply the NPV by (1 + WACC)^0.5 if cash flows arrive evenly through the year.
8. 8Close the loop with a return on equity test. Take the equity value as the year-0 outflow, the projected dividends as inflows, and the year-5 equity value (terminal value + year-5 cash − year-5 debt) as the final inflow. Compute the IRR and judge whether it is plausible against the cost of equity.

Source model, 20% WACC, 5% long-term FCF growth. Projected FCFs for years 1–5 are 176, 188, 201, 214 and 228. Terminal value = year-5 FCF × 1.05 / (0.20 − 0.05), which the model shows as 1,598. Hand arithmetic on the rounded 228 gives about 1,596; the gap is rounding. Year 5 therefore carries 228 + 1,598 = 1,826. The NPV of the stream, scaled by (1.20)^0.5 for mid-year discounting, is an enterprise value of 1,348. Adding year-0 cash of 80 gives an asset value of 1,428, and subtracting debt of 320 gives an equity value of 1,108. Cross-check: the negative-debt method with end-of-year discounting gives an enterprise value of 1,295, net debt of (320 − 80) = 240, and equity of 1,055. The 53 gap between 1,108 and 1,055 equals 1,348 − 1,295, so the whole difference is the mid-year convention and the cash treatment is equivalent. For the ROE test, the equity cash flows are (1,108), 98, 108, 118, 129, 1,878. The final 1,878 is year-5 dividends of 141 plus anticipated equity value of 1,737. IRR gives an ROE of 18.29%, which the model can compare with the cost of equity.

• If the cash flow statement's change in cash does not equal the change in the balance sheet's cash plug, stop and fix the linkages before valuing anything.
• If you treat initial cash as surplus, add it to enterprise value and then subtract debt. If you treat it as negative debt, use net debt and do not also add the cash. Do either one, never both.
• If cash flows arrive through the year, apply the (1 + WACC)^0.5 mid-year adjustment. Compare end-year and mid-year results to see what the convention is worth (53 in the example) before presenting a single number.
• If a Gordon terminal value is too aggressive or too hard to defend, test the alternatives in the source: book value of debt plus equity, a market/book multiple, a P/E multiple, or an EBITDA multiple. A large spread between methods means the terminal assumption drives the answer.
• If the model's implied ROE (18.29% here) is far from the cost of equity you assumed, revisit the growth, margin and terminal assumptions before trusting the valuation.

• The statements are not truly interconnected: values are typed in rather than linked. The tell is that changing an assumption such as sales growth moves the income statement but leaves the balance sheet or cash flow check unchanged.
• Cash is plugged without a reconciliation check, so errors hide in the plug. The tell is that cash swings oddly or goes negative with no matching cash flow statement.
• Initial cash is double counted, added to enterprise value and also netted as negative debt. The tell is an equity value higher than the equity value from the other method.
• The terminal value is the bulk of the valuation and goes unquestioned. In the example, 1,598 of the year-5 total of 1,826 is terminal value, and the Gordon formula breaks down as long-term growth approaches the WACC.
• Costs are left out. The source exercise adds fixed SG&A of $200 per year, which the base model omits, so the model overstates profit. The tell is margins that look too good compared with the actual company.

• ▸Driver table: list each ratio (sales growth, current assets/sales, current liabilities/sales, net fixed assets/sales, COGS/sales, depreciation, interest rates, tax, payout) with its value and source.
• ▸Balancing item: name the plug (cash or debt) and confirm only one is used.
• ▸Cash reconciliation: record the change in cash from the cash flow statement, the change from the balance sheet, and their difference (must be 0).
• ▸FCF by year: list years 1–5 FCF with the formula used for each.
• ▸WACC and long-term growth: state both and confirm growth is below WACC.
• ▸Terminal value: record the method (Gordon or alternative), the inputs and the result, and its share of year-5 total value.
• ▸Cash treatment and timing: state surplus vs. negative debt, and end-year vs. mid-year discounting.
• ▸Equity bridge: enterprise value, plus cash, minus debt, equals equity value.
• ▸ROE test: list the equity cash flows, the IRR, and the comparison with the cost of equity.

1. 1Start from the projected financial statements (P&L and balance sheet) for every forecast year. FCF is cash available to all capital providers, so build it from the firm's operations, not from its financing.
2. 2Take profit after tax from the P&L as the starting row. In the source's pro forma it runs 200, 257, 323, 401, 493 for years 1–5.
3. 3Add back depreciation, a noncash charge (211, 233, 257, 284, 314). If the tax authorities see a different depreciation schedule than shareholders do, use the tax-basis figure, because it determines the taxes actually paid.
4. 4Adjust for working capital using the balance sheet changes. Subtract the increase in current assets and add the increase in current liabilities. These are the firm's nonfinancial short-term items, and the source says they belong inside FCF.
5. 5Subtract the increase in fixed assets at cost (capital expenditure). In the source model it equals depreciation each year (211, 233, 257, 284, 314), so depreciation generates no net cash.
6. 6Strip out financing. Add back after-tax interest on debt (54, 42, 30, 18, 6) and subtract after-tax interest earned on cash and marketable securities (0, 2, 6, 13, 24). Treat cash as negative debt, so its interest is a financing item.
7. 7If there are tax losses, rebuild the P&L as if the firm had no debt and no interest. Apply the loss carryforward to taxable income, then add the carryforward back to profit after tax as a noncash charge, as with depreciation.
8. 8Sum the rows and sanity-check. Year 2 gives 257 + 233 − 26 + 14 − 233 + 42 − 2 = 285. Discount the FCF stream at the WACC to obtain enterprise value.

The source's pro forma has a 40% tax rate, 10% interest on debt, 8% on cash, and sales growth of 15%. For year 2, profit after tax is 257. Add back depreciation of 233. Subtract the 26 increase in current assets and add the 14 increase in current liabilities. Subtract the 233 increase in fixed assets at cost, which cancels the depreciation add-back. Add back 42 of after-tax interest on debt and subtract 2 of after-tax interest on cash. The total is 257 + 233 − 26 + 14 − 233 + 42 − 2 = 285, which matches the model's year-2 FCF. The model's five-year FCF is 273, 285, 334, 391, 457, and in this version the firm cannot meet its debt repayments in years 1–4. The cash balance goes negative, which is equivalent to borrowing. FCF is unaffected by that financing problem because it is computed as if the firm had no debt.

• If the firm has interest expense or interest income, then add back after-tax interest on debt and subtract after-tax interest on cash. FCF must not depend on the capital structure.
• If the firm has a loss in a year, then recompute the no-debt P&L with the carryforward and add the carryforward back as a noncash charge. In the source's example, year-2 FCF is 310 (profit after tax of 210 plus a 100 carryforward add-back), not the levered profit after tax of 119.
• If the book and tax depreciation schedules differ, then use the tax schedule for cash. In the source's example, cash flow is 420, which is profit after tax of 120 plus tax-basis depreciation of 300, not 150 plus 250.
• If a line is a nonfinancial short-term asset or liability, then include it in FCF through working-capital changes. If it is financial debt or cash, then keep it out of FCF and treat it as part of financing.
• If the FCF is going to be discounted, then use the WACC as the rate. Because the WACC reflects the cost of both debt and equity, the result is enterprise value.

• Starting from profit after tax and leaving interest in. The tell: FCF changes when you change the debt level or the interest rate.
• Using book depreciation when the tax return uses accelerated depreciation. The tell: the cash flow does not reconcile to sales minus cash costs minus taxes actually paid (1,000 − 500 − 80 = 420 in the source's example).
• Treating a loss carryforward as a cash item or ignoring it. The tell: a year following losses shows taxes that look too high or too low relative to the loss history.
• Confusing a cash shortfall with negative FCF. The tell: the cash balance goes negative and you adjust FCF for debt repayments, when that cash balance is a financing outcome (borrowing) and not an operating one.
• Adding back depreciation but omitting the capex that replaces it. The tell: the fixed-asset-at-cost increase row is missing, so FCF is inflated by roughly the depreciation amount (211 in year 1 of the source model).

• ▸Year: label each column of the forecast (year 1 to N).
• ▸Profit after tax: take from the projected P&L.
• ▸Add back depreciation: use the tax-basis figure if book and tax schedules differ.
• ▸Change in current assets (subtract increases): take from the balance sheet, nonfinancial items only.
• ▸Change in current liabilities (add increases): take from the balance sheet, nonfinancial items only.
• ▸Increase in fixed assets at cost (subtract): capital expenditure for the year.
• ▸After-tax interest on debt (add back): interest × (1 − tax rate).
• ▸After-tax interest on cash and securities (subtract): interest income × (1 − tax rate).
• ▸Tax-loss carryforward add-back: enter only if the no-debt P&L has a carryforward, otherwise 0.
• ▸Free cash flow: sum the rows, then discount at the WACC for enterprise value.

1. 1Write the formula before you collect data: WACC = E/(E+D) × rE + D/(E+D) × rD × (1 − Tc). E and D are market values, not book values. Tc is the corporate tax rate. Only the debt term is tax-adjusted.
2. 2Fix the purpose first. Discounting the firm's free cash flows gives enterprise value. Using WACC as a hurdle rate is valid only for projects whose risk resembles the average risk of the firm's cash flows.
3. 3Estimate the cost of equity rE with at least two methods: the Gordon dividend model (adjusted for all cash flows to equity if payouts go beyond dividends), and CAPM or the security market line. Record both numbers side by side.
4. 4Estimate the cost of debt rD with at least one of the book's methods: (a) current interest payments divided by average debt; (b) a rating-adjusted yield curve, read at the firm's average debt maturity; (c) the expected return on the firm's bonds, which the book treats separately in Chapter 28.
5. 5If you use the yield-curve method, match the curve to the firm's rating and fit YTM against maturity. For Kraft the fit is the BBB curve from 11 Aug 2006: YTM = 0.0001·t³ − 0.0023·t² + 0.0152·t + 0.0221. Read it at the firm's average maturity (5 years for Kraft).
6. 6Measure E as share price times shares outstanding and D as the market value of debt. Compute the weights E/(E+D) and D/(E+D). Check whether the firm holds more cash than debt, as Cascade does, because that changes how you treat leverage.
7. 7Assemble WACC, then test it. Compare pre-tax rE with pre-tax rD, and compare the Gordon rE with the CAPM rE. Where they conflict, document the judgment call. The book says WACC estimation takes 'a considerable number of judgment calls' and makes no claim to scientific accuracy.
8. 8Run WACC through sensitivity analysis when you value the firm, since the rate rests on judgment. The PPG case in Chapter 4 does this in its valuation section.

The source's real worked piece is Kraft's cost of debt. Kraft's debt has an assumed average maturity of 5 years, and the BBB yield curve (Yahoo data, 11 Aug 2006) is fitted as YTM = 0.0001·t³ − 0.0023·t² + 0.0152·t + 0.0221, with R² = 0.8479. At t = 5 the terms are 0.0125 − 0.0575 + 0.0760 + 0.0221 = 0.0531, so the imputed pre-tax rD is 5.31%. In the WACC formula that debt term becomes D/(E+D) × 5.31% × (1 − Tc). The source flags that Kraft's equity side is the hard part: the Gordon rE and the CAPM rE diverge sharply. The question is whether shareholders judge risk by the market variability of the stock (CAPM) or hold the stock for its history of payouts (Gordon). The passages supplied do not give Kraft's equity numbers, so you cannot finish the calculation from them. Compute both rE values, carry both through the weighted formula, and report the resulting range rather than a single point.

• If you are discounting FCF for enterprise value, or evaluating a project with about average firm risk, use WACC. If a project's risk differs materially from the firm's average cash flows, do not use the firm WACC as its hurdle rate.
• If the Gordon rE and the CAPM rE diverge widely (the Kraft situation), decide which reflects shareholder expectations: payout history or market variability. Show both WACCs instead of silently choosing one.
• If pre-tax rE comes out below pre-tax rD (the Tyson situation), treat it as a warning sign. Re-examine the equity payout growth and its variability before accepting the result.
• If cash exceeds debt (the Cascade situation of negative leverage), do not apply the standard weights mechanically. Make the treatment of net debt an explicit, documented judgment.
• If debt interest divided by average debt and the yield-curve rate disagree, prefer the forward-looking measure. The text defines rD as the anticipated future cost of borrowing.

• Using book values for E and D. The tell: the weights do not match market capitalization and the market value of debt.
• Forgetting (1 − Tc) on debt, or applying it to the equity term. The tell: WACC sits too high, with after-tax rD no lower than pre-tax rD.
• Reading the yield curve at the wrong maturity or for the wrong rating. The tell: the curve's t is not the firm's average debt maturity (5 years for Kraft), or the curve is not rating-matched (BBB for Kraft).
• Accepting one rE method without a cross-check. The tell: Gordon and CAPM were never compared, so a Kraft-style divergence goes unnoticed.
• Treating WACC as a precise number. The tell: no sensitivity analysis, and a single-point valuation presented as scientific accuracy.

• ▸Purpose: enterprise-value discount rate for FCF, or hurdle rate for an average-risk project (state which).
• ▸Share price × shares outstanding = E (market value of equity).
• ▸Market value of debt = D, and whether cash exceeds debt (negative leverage: yes/no).
• ▸Weights: E/(E+D) and D/(E+D).
• ▸rE (Gordon): value from the dividend model, adjusted for all cash flows to equity if payouts exceed dividends.
• ▸rE (CAPM/SML): value from the security market line.
• ▸rD method used (interest ÷ average debt, rating-adjusted yield curve, or bond expected return) and the value.
• ▸Average debt maturity (years) and yield-curve fit, if the curve method is used.
• ▸Corporate tax rate Tc, and the resulting after-tax rD = rD × (1 − Tc).
• ▸WACC (low case with the lower rE and high case with the higher rE), plus notes on the judgment calls.