Modeling II: DCF, Comps, LBO & M&A

Phase 3 · Week 34 · ~20 hours

Where it sits. Ninth module of the valuation phase, and the one where the machinery you have been building for eight modules finally becomes equipment. Last week left you with a fully-linked three-statement model: assumptions feeding schedules feeding statements, a revolver that catches shortfalls, checks that light up when anything breaks. That model forecasts what the business will do. Now come the tabs that say what it is worth, and what different kinds of buyers would pay for it. A DCF tab turns the FCFF and terminal-value theory into live cells, with a two-way sensitivity table. A comps tab is the multiples theory as a working peer table, and the football field assembles every lens into one picture. A complete mini-LBO works out what a leveraged financial buyer could pay, via sources & uses, a debt waterfall, IRR and MOIC. Then M&A accretion/dilution: what a corporate acquirer's EPS math will claim, and why that claim is not value. You will never be an investment banker running these models at 2 a.m., and you don't need to be. But a public-market analyst who cannot do PE math on a target, or check an announced deal's EPS arithmetic against its economics, is blind in two directions the market watches constantly. Next week takes the finished stack into special situations and the phase capstone; Phase 8's Day-2 model is a compressed version of what you build this week. The week also finalizes the phase's reusable artifact: the valuation workflow. Print it and keep it beside every valuation you ever run.

Budget 8h for the core content, 2h for worked examples and 4h for the practice set. The mini-project (the model-suite build + audit) takes 4h, and flashcards plus the mastery check 2h.

In the app, the week powers the Intrinsic Valuation branch's build layer. The valuation sandbox grows a full DCF grid: your assumptions in, per-share value and sensitivity matrix out, with the feedback engine flagging indefensible inputs. The comps builder has you assemble a peer table and catch the normalization traps, and the LBO waterfall stepper drives the debt schedule year by year so you watch the sweep and revolver logic fire. Accretion/dilution drills give you a deal's terms and race the clock to the EPS impact, then ask the follow-up: did it create value? Last, the model-suite audit case feeds your finished workbook through the §4.12 checklist. Badge earned here: "Built the stack."

Learning objectives

By the end of the week you can:

1. Build a DCF tab on top of a linked three-statement model: an FCFF build pulled row-by-row from the model (FCFF = NOPAT + D&A − capex − ΔNWC), a WACC block, discount factors, and PV of the explicit window: every cell a formula, no hardcodes.
2. Compute terminal value both ways, a Gordon perpetuity with a reinvestment-consistent numerator (FCFF_T+1 = NOPAT_T+1 × (1 − g/ROIC_T)) and an exit multiple, then reconcile them: back the implied exit multiple out of the perpetuity and the implied perpetual growth out of the multiple.
3. Run the EV → equity bridge with every bridge item (debt, leases, cash and non-operating assets, minority interest, preferred, options via the treasury-stock method), land on per-share value, and compare it to price without flinching.
4. Build a live two-way sensitivity table (WACC × terminal growth) with Excel/Sheets data tables: correct input-cell wiring, same-sheet rule, recalculation settings. Read it as a range, not 25 point estimates.
5. Construct a comps tab: peer selection, clean EV assembly, forward and trailing multiples, medians. Then apply peer multiples to your company with the M3.06 normalization discipline intact.
6. Assemble a football field from the 52-week range, trading comps, precedent transactions, the DCF band, and a reverse-DCF marker, then describe its construction (helper columns, stacked bars, invisible base series, price line) well enough to build it in any spreadsheet.
7. Explain and compute how leverage torques equity returns: run a complete 5-year mini-LBO: sources & uses, a debt waterfall (term loan with mandatory amortization + full cash sweep, revolver for shortfalls), exit value, equity IRR and MOIC. Then decompose the return into EBITDA growth, multiple change, and debt paydown.
8. Run M&A accretion/dilution for all-stock, all-cash, and mixed consideration, including foregone interest and new intangible amortization. State the two quick rules and their limits, and demonstrate numerically why EPS accretion is not value creation (conservation of value, M3.07).

Prerequisites & connections

Builds on. M3.08 is the chassis. Everything here bolts onto the three-statement model you built there, so its Assumptions / Model / checks architecture comes along, and so do its revolver and its no-hardcodes rule. M3.04 supplies the FCFF definition and forecast drivers, and M3.05 the terminal-value law (g capped, numerator rebuilt for reinvestment) plus the reverse-DCF habit. M3.03 supplies the WACC you'll now wire into cells. This phase's illustrative hurdles are ~12% INR for India and ~8 to 9% USD for the US, as of mid-2026, so verify them against your own M3.03 builds. M3.06 supplies the multiples grammar: EV construction, driver-justified multiples, normalization before comparison. M3.07 supplies the conservation-of-value lens that lets you see through EPS accretion, plus the M&A decision framework, where value created = PV of synergies − premium. M3.01's IRR machinery comes back as the LBO scorecard, trap included. IRR ignores scale and duration, so MOIC rides alongside it.

Feeds forward. M3.10 uses the finished suite on special situations, and the phase capstone requires it: a three-way valuation of one Indian and one US company, presented on a football field, with a memo. Phase 8's 2 to 3 day deep dive carries a compressed version, the "3-statement-lite → base/bull/bear → reverse DCF" of Day 2. The valuation workflow artifact you finalize this week becomes a permanent pre-flight for every valuation after it. Sector models (Phase 5) are these tabs re-skinned with sector drivers. The M&A lens returns in M8.04 when you grade acquisitive managements, and a serial acquirer touting "EPS accretion" there is an M3.07 exam question wearing a suit.

One engine, four gauges. You can read the same forecast as intrinsic value (DCF), as the market's opinion (comps), as a leveraged buyer's bid (LBO), and as a corporate buyer's EPS story (accretion/dilution). If you can compute all four, you'll know which one is lying.

Core teaching content

4.1 The finished machine: workbook architecture

Open last week's workbook. You have at least three layers. Assumptions holds the blue inputs, the only cells a user touches. Model holds the linked IS/BS/CFS with its supporting schedules. Checks holds the balance check and the cash-flow tie-out, plus the revolver logic. Five tabs go on top of that:

Three rules carry over from last week, and none of them bends.

1. No hardcodes in formula rows. If a number isn't computed, it goes in a blue input cell with a label and a source.
2. One direction of flow, from Assumptions to Model to the valuation tabs. A valuation tab never writes back into the model.
3. Every tab ends in a check. On the DCF tab, that's TV as % of EV and the implied exit multiple. On the LBO tab, it's sources = uses and debt ≥ 0 every year. On the comps tab, any peer whose EV build is missing a component gets flagged.

Your worked build for the whole week is Sundar Foods Ltd, a synthetic Indian packaged-snacks company with deliberately clean numbers, in ₹ crore throughout. Your own model is built on a different company, so your row numbers will differ. Re-point the references. You're here to learn the architecture, and the numbers are just scaffolding.

4.3 The WACC block

It's a ten-row tab, and every input carries a label with its source and pull-date. Think of it as the whole cost-of-capital build squeezed into cells:

These are the phase's standing illustrative INR numbers, Rf 7% and India ERP 7%, as of mid-2026. Verify both. You're learning the method here, and the values expire. Now the layout enforces three habits from the cost-of-capital work. Currency matches, so INR flows take an INR rate and the whole tab is in INR. Weights are market values, and book weights don't come into it. And the beta is built bottom-up from peers, so document the peer set in a cell note. Your DCF tab reads =WACC!C12. One WACC with one home, so there's no "12% here, 11.5% there" drift.

4.4 Terminal value, both ways: and the reconciliation

Way 1: the Gordon perpetuity, done lawfully. Both terminal-value laws now become cells: the growth cap and the reinvestment-consistent numerator. Take terminal growth g ⟦5.0%⟧ and terminal ROIC ⟦20%⟧. That ROIC is a deliberate fade from the ~67% incremental returns the forecast implies, because competition arrives:

NOPAT_T+1 = NOPAT_FY5 × (1+g)            = 434.7 × 1.05  = 456.4
Terminal reinvestment rate = g / ROIC_T   = 5% / 20%      = 25%
FCFF_T+1  = NOPAT_T+1 × (1 − g/ROIC_T)   = 456.4 × 0.75  = 342.3
TV        = FCFF_T+1 / (WACC − g)        = 342.3 / 0.07  = 4,889.9

Where does the cap on that 5.0% come from? From the terminal-value rule, and the rule is about your own stack, whatever the headlines say. Terminal g may not exceed the risk-free rate you used to build this WACC, in the same currency, taken from the same place. Row 3 of the WACC block above is the raw 7.0% ten-year G-sec, so the cap on this tab is 7.0%, and the 5.0% input is comfortably inside it. Build the same company on the credit-cleaned INR stack from the cost-of-capital work instead. There the risk-free rate is 4.5% once the 2.0-point sovereign default spread comes out, so the cap is 4.5%. Rate and cap move down together, as the rule intends. What you may not do is take the cleaned rate for the denominator and the raw one for the cap.

And none of these numbers is India's current nominal GDP growth of roughly 10 to 11 percent. That figure describes the India of today, so it belongs in the explicit window. Your terminal year describes a mature economy a decade or more out.

In cell form: =G7*(1+$C$17)*(1-$C$17/$C$18)/($C$4-$C$17), where G7 is FY5 NOPAT, C17 is g, C18 is terminal ROIC, C4 is WACC. Compare what the naive version would have done. FCFF_FY5 × (1+g)/(WACC−g) = 382.8 × 1.05/0.07 = 5,741.8, 17.4% too high. FY5's FCFF rides on a 12% reinvestment rate, and that can't fund 5% growth forever at any sane ROIC. More real-world DCFs die in this one cell than anywhere else. With the formula above, the mistake is impossible, because growth gets paid for inside the numerator.

Way 2: the exit multiple. TV = exit multiple × terminal-year EBITDA. Use 9.0×, today's peer median from the comps tab, on FY5 EBITDA of 724.4 (579.5 + 144.9). That gives TV = 6,519.9.

Then reconcile the two, and always run it in both directions:

• From the perpetuity to an implied multiple. 4,889.9 / 724.4 = 6.75× EV/EBITDA, while today's peers trade at ~9×. Is 6.75× sensible for Sundar five years out, in steady state? Yes. A maturing company should exit below today's growth-company multiple, so 6.75× hangs together. If your implied exit multiple is higher than today's, you're smuggling optimism in through g or ROIC_T.
• From the multiple to an implied growth rate. What perpetual g makes the Gordon TV equal 6,519.9? Solve 434.7 × (1+g) × (1 − g/0.20) / (0.12 − g) = 6,519.9 by iterating, or with Goal Seek on the TV cell. You get g ≈ 7.5%, above this stack's 7.0% cap. So the peer median multiple has growth faster than the economy, forever, built into it. Either peers are pricing a longer high-growth runway than perpetuity math allows, which is fine if you say so, or the market is being generous. Either way, you now know what the disagreement is about. Use the perpetuity as the primary and report the multiple as the cross-check.

Build a diagnostics row into the tab as well. TV % of EV = 2,774.7 / 3,808.6 = 72.9%, which is normal for a growing company, where 60 to 80% is typical. Above ~85%, your explicit window is decoration. Extend the forecast, or admit the valuation is one assumption in a trench coat.

4.7 The comps tab

You already have the theory of multiples. This tab puts it to work. Left to right, the columns run in this order: identifiers, raw market data, the EV build, operating metrics, multiples, drivers. Each peer gets one row, your company gets one shaded row, and a stats block goes below.

Step 1: the peer set (5–8 names). Match economic exposure first: the customer, the product economics, the capital intensity. Similar scale comes second, and the same listing geography is a distant third. Write a one-line justification for each peer in a comments column. A comps table without documented peer logic is a random-number generator with borders.

Step 2: the EV build, per peer. Start with Mkt cap = price × diluted shares, using the treasury-stock method from the bridge. Then build EV = mkt cap + total debt + leases (one convention for every row) + minority interest + preferred − cash & liquid investments. Every element comes from the latest balance sheet, and every price is as of one common date, stamped on the tab. In cells that's =F5+G5+H5+I5-J5, filled down.

Step 3: metrics and multiples. Forward FY1E figures are the default basis, with trailing as backup. There are two exceptions. With no analyst coverage, fall back to trailing numbers. When the cycle turns, use normalized trailing numbers. Calendarize if fiscal years differ by a quarter or more. Indian March year-ends against US December ones is the usual case. Weight the quarters or state the mismatch. You've already built a last-twelve-months figure and a stub period from published quarters, working the arithmetic end to end. Keep that lesson open the first few times you do this. For multiples, use EV/EBITDA = K5/L5, EV/EBIT and P/E = C5/M5, and for the stats row, =MEDIAN(N5:N9). Use the median, because one 30× peer wrecks a mean. If you must average P/Es, use a harmonic mean.

Sundar's peer table holds five synthetic mid-cap Indian packaged-foods peers. They're regional players, in ₹ cr, with forward-year estimates:

Scan the drivers before you trust the median. Vindhya's 10.0× comes with the best growth (15%) and near-best ROCE. That premium is earned, so don't treat it as an anomaly. Malabar's 8.1× belongs to the slowest grower with the weakest ROCE, which makes it cheap for a reason. The set hangs together, so the median is usable.

A real Indian large-cap set of Britannia, Nestlé India and HUL trades far richer. Their premium multiples reflect the scarcity-float-flows regime from the multiples work, roughly 45 to 60× P/E for the leaders as of mid-2026 (check on screener.in). We use a saner mid-cap set so the arithmetic teaches and doesn't distract.

Step 4: apply to your company. Sundar's FY1E EBITDA = 504.0 and PAT = 307.5, which is EPS of ₹12.3 on 25 cr shares. Note that PAT includes ~₹28 cr of interest income on the cash pile.

• EV/EBITDA at median ± 1 turn (8.0× / 9.0× / 10.0×): EV = 4,032 / 4,536 / 5,040 → equity (EV − 250 + 400 − 30) = 4,152 / 4,656 / 5,160 → ₹166 / ₹186 / ₹206 per share.
• P/E at 15–18×: ₹185–221.

Notice that P/E comes out higher than EV/EBITDA. That's no mistake. P/E is putting a 17× multiple on Sundar's interest income, while EV/EBITDA correctly strips the cash out of the numerator and its income out of the denominator. When a company holds net cash, P/E flatters it. When it carries heavy debt, P/E punishes it. So the gap between the two comps rows tells you something about the balance sheet.

4.12 What this toolkit means for a public-market analyst

All of this serves the five questions. Here's what each tool does for them:

• Your DCF tab answers question 5, what is it worth?, and its live cells, which you can shock, keep it straight. Your deliverable is never cell C28. It's the sensitivity box plus a sentence naming the driver the disagreement turns on.
• The comps tab gives you the market's answer, organized. Its best use is locating your variant view. If you're at ₹157 and the peer-implied value is ₹186, the comps tab tells you the debate is one turn of EBITDA. Then the reverse DCF converts that turn into a growth claim you can research.
• A football field is how you communicate. It's the one-slide answer to "so what's it worth?" that survives contact with a portfolio manager. It keeps you in check, too. A field whose bars don't overlap anywhere is a finding in itself. Your lenses disagree, so find out why before anyone sees the chart.
• An LBO gives you the floor bid. Solve for the price at which a sponsor clears ~20% IRR on conservative operating assumptions. For Orion as a public company, exit equity 907.6 ÷ 1.2⁵ = entry equity 364.7, so max TEV = 364.7 + 400 − 24 = 740.7, or ~7.4× EBITDA. If Orion's stock trades at 6.5×, there's a natural private bidder ~14% above the market, and that's downside protection you can compute. Run this "PE-math radar" on any underleveraged, stable-FCF small/mid-cap in your coverage. It flags leverage risk in reverse too, because any 4×-levered listco is an LBO whether it admits it or not.
• Accretion/dilution is your deal-reaction tool. Within an hour of any announcement in your coverage, you can produce the EPS math the sell-side will print and the value verdict it hides, which is premium against synergies. Mauboussin's To Buy or Not to Buy checklist formalizes this. It's also a management-quality lens. A CEO who says "accretive" when the deal fails premium-vs-synergies has told you which metric they manage.

The model-suite audit checklist is the gate. Your finished workbook passes when every hard check holds:

Common mistakes & how experts think differently

Worked examples

Worked example 1: the stress case: when the revolver earns its keep

Take Orion Packaging again, but in year 2 a customer bankruptcy and destocking hit. EBITDA prints $60m against the $112.4 plan, then recovers to $90m in year 3. Walk the waterfall through the trough. Y1 runs as in the base case, so the term loan ends at 367.8 and the revolver at 0.

In year 2, EBITDA prints 60.0. Interest = 8.5% × 367.8 = 31.3. EBT = 60.0 − 25.0 (D&A) − 31.3 = 3.7. Tax at 25% is 0.9, so NI = 2.8. CFADS = 2.8 + 25.0 − 25.0 − 0 = 2.8, with no NWC build in a down year. Mandatory amortization due is 20.0. That leaves a shortfall of 20.0 − 2.8 = 17.2, drawn on the revolver. By year-end the term loan is at 367.8 − 20.0 = 347.8, and the revolver at 17.2.

The mandatory payment is contractual. Miss it and you're in default, and the revolver is the buffer that turns a liquidity crisis into an interest expense. Check the headroom. Drawing 17.2 of a $50 commitment is survivable. An EBITDA print of ~$48 or lower would have used up CFADS and revolver capacity within two such years. That number is the deal's stall speed, and computing it is the downside work sponsors and distressed-debt analysts do.

Year 3 recovers to EBITDA of 90.0. Interest = 8.5% × 347.8 + 8.0% × 17.2 = 29.6 + 1.4 = 30.9. EBT = 90.0 − 25.0 − 30.9 = 34.1, tax is 8.5, and NI = 25.5. CFADS = 25.5 too. Now run the waterfall in order. Mandatory takes 20.0, which leaves 5.5. That 5.5 goes to repaying the revolver first, so the revolver falls to 11.7, and there's nothing left for the term-loan sweep. By year-end the TL is at 327.8 and the revolver at 11.7.

Notice the ordering. Revolver balances get repaid before any optional term-loan sweep, because the revolver is the emergency line. You clear the credit card before you prepay the mortgage. Now look at what the trough cost. Two years of sweeps, ~$46m of planned paydown, never happened. So every later year carries more interest, which compounds into less paydown, and the base case's flywheel spins in reverse. If exit still happens in year 5 at 8.0× on a recovered EBITDA path, equity survives, but the MOIC sags. Leverage turns a temporary operating problem into a permanent returns haircut. So entry leverage is sized against trough EBITDA, and plan EBITDA doesn't come into it.

Worked example 2: accretion/dilution, full dress: mixed consideration with all refinements

Acquirer A (NI $1,000m, 500m shares, price $40) buys T (NI $300m) for $4,500m, paid 50% in stock and 50% in cash. Of the cash, 60% is funded by new debt at 6% pre-tax and 40% comes from balance-sheet cash yielding 4% pre-tax. Tax is 25%. Purchase accounting creates $1,200m of intangibles amortized over 10 years, and expected pre-tax cost synergies are $80m/yr. Compute year-1 pro-forma EPS both as reported and as "cash EPS," and give the value verdict if synergies are worth their capitalized after-tax value at 10%.

Start with the consideration plumbing. On the stock leg of 2,250, new shares = 2,250/40 = 56.25m. Another 2,250 is the cash leg, split into 1,350 of debt and 900 of balance-sheet cash.

Next come the income adjustments, all after tax at 25%:

• new-debt interest = 1,350 × 6% × 0.75 = 60.8
• foregone cash yield = 900 × 4% × 0.75 = 27.0
• synergies = 80 × 0.75 = +60.0
• intangible amortization = 1,200/10 × 0.75 = 90.0

Reported pro-forma NI = 1,000 + 300 + 60.0 − 60.8 − 27.0 − 90.0 = 1,182.2 over 556.25m shares. That's EPS of $2.13, +6.3% accretive against $2.00 standalone. "Cash EPS" adds back the deal amortization: (1,182.2 + 90.0)/556.25 = $2.29, or +14.4%, and that's the number the deal deck will feature. It's the same deal, with an 8-point headline gap and zero difference in cash flow. Now you know which lever produced the press release.

Now the value verdict. Assume T's unaffected value was $3,600m, so the premium is $900m. Synergies are worth $60m/yr after tax ÷ 10% = $600m PV, and that's before integration costs, so be meaner in practice. Premium 900 > synergies 600, so A's holders are ~$300m worse off despite +6.3% reported and +14.4% "cash" accretion. Both EPS numbers were true, and neither was the answer. Here's a verdict template you'll reuse for good: "Accretive +6% reported / +14% cash. Value-negative ~$300m unless synergies come in ≥ $900m PV (≈ $120m/yr pre-tax vs guided $80m). Watch the synergy bridge in the first four quarterly calls."

Worked example 3: the LBO floor under a public stock, end to end

Orion Packaging is now listed: EBITDA $100m, net debt $150m, 40m shares, stock at $16.25. A sponsor would underwrite 4.0× term-loan leverage at 8.5%, fees of $24m, the base operating case from the full LBO, exit at the entry multiple in year 5, a 20% IRR hurdle. What can they pay per share, and what does it mean for the stock?

Step 1: current pricing. Market cap = 40 × 16.25 = 650, and EV = 650 + 150 = 800. So the stock trades at 8.0× EBITDA, the same as the full LBO's entry multiple. That's convenient, and it's deliberate.

Step 2: what equity cheque clears the hurdle? In the full LBO, an 8.0× entry gives year-5 exit equity of 907.6. On the debt side that figure doesn't depend on the entry price. Whatever the sponsor pays, the term loan is sized off EBITDA at 400. So the debt schedule and exit equity stay put. Only the entry cheque moves, and a higher offer price flows rupee-for-rupee into required equity. Max entry equity = 907.6 / 1.20⁵ = 907.6 / 2.488 = 364.7.

Step 3: max price. Max TEV = equity 364.7 + term loan 400 − fees 24 = 740.7, or 7.41× EBITDA. Equity value to public holders = 740.7 − 150 net debt = 590.7, which is $14.77/share, 9% below the market. So at $16.25 there's no PE bid underneath this stock at a 20% hurdle. That puts the LBO floor at ~$14.75. Put another way, a sponsor stretching to pay today's price + 25% premium would underwrite to only ~9% IRR, which you can compute the same way, backwards.

Now flip the growth dial. Suppose a sponsor believed in 9% EBITDA growth instead of 6%. Year-5 EBITDA = 153.9 and exit equity ≥ 8 × 153.9 − 163 ≈ 1,068, holding the base debt schedule. That's conservative, since faster growth sweeps more debt. Max equity cheque = 429, so max TEV = 805, which works out to ~$16.4/share. That makes today's price a 20%-IRR bid under the bull operating case. In a precise sense, the stock is priced at the sponsor bull case. A toy model and ten minutes just gave you a real piece of market intelligence. Public-market analysts keep an LBO tab for this. They aren't doing deals. They want to know where the deal math puts the net under the tightrope.

Worked example 4: a full DCF, model to per-share, then run it backwards (Sarita Diagnostics, synthetic, ₹)

Sarita Diagnostics Ltd (synthetic) is an asset-light Indian diagnostic-labs chain, in ₹ cr. Your linked model hands the DCF tab FY0 revenue of 900, with revenue growth fading from 15% to 13%, 12%, 10% and 9%. EBIT margin is 20%, D&A is 5% of revenue, and capex fades from 8.0% to 6.0% of revenue. ΔNWC = 12% of incremental revenue, and tax is 25%. Use the phase's standing INR hurdle, WACC 12.0%, as built in your WACC tab. Terminal g is 5.0% and terminal ROIC 18%. Bridge items are borrowings of 380, cash & investments of 210 and minority interest of 40, with 20 cr diluted shares. Value the equity per share against a ₹112 market price, then invert the model. What perpetual growth is ₹112 paying for?

Step 1: the FCFF build. Pull the drivers and compute it row by row.

Step 2: discount at 12%.

Σ PV of the explicit window = ₹538.9 cr.

Step 3: the lawful terminal value. Growth has to be paid for, so rebuild the numerator instead of growing FY5's FCFF:

NOPAT_T+1 = 235.6 × 1.05                    = 247.4
Terminal reinvestment rate = g/ROIC_T = 5%/18% = 27.8%
FCFF_T+1  = 247.4 × (1 − 0.278)              = 178.7
TV        = 178.7 / (0.12 − 0.05)            = 2,552.2

Cross-check the multiple this implies. FY5 EBITDA = 314.1 + 78.5 = 392.6, so the implied exit EV/EBITDA = 2,552.2 / 392.6 = 6.5×. That's comfortably below the ~9× today's mid-cap peers trade at, which is what a maturing company should exit at. Done naively, FCFF₅ × (1+g)/(WACC − g) = 204.3 × 1.05 / 0.07 = 3,064.8, which overstates TV by 20.1% and makes it the most expensive cell in the model.

Step 4: enterprise value to per share.

TV is 1,448.2 / 1,987.1 = 72.9% of EV. That's normal for a grower, so the explicit window is doing real work.

Step 5: run it backwards (the reverse DCF). ₹88.9 on your 5%-growth assumptions is 20% below the ₹112 price, so the market is buying more growth than you modeled. How much more? Hold WACC (12%), terminal ROIC (18%), the explicit-window PV (538.9) and FY5 NOPAT (235.6) fixed, and solve for the terminal g that makes value per share = ₹112. You get g ≈ 7.7%. That's above your 5%, and it's above the 7.0% cap the terminal-value rule sets on this stack, which is the 7.0% G-sec risk-free rate in row 3 of the WACC block. So ₹112 is paying for "faster-than-the-economy forever," well beyond "5% forever," and lawful perpetuity math won't allow that.

Then reconcile, because that's the reason for the whole exercise. Either the market is underwriting a longer explicit high-growth runway than your five years, or it's simply generous. If it's the first, you've got a research task: extend the window and re-price. Either way, you've turned a vague "looks expensive" into a testable claim about growth duration. That's question 5 made quantitative, and it's the statement the reverse-DCF marker puts on a football field.

Worked example 5: the complete mini-LBO, sources to IRR, and the exit multiple you don't get to assume (Cascade Filtration, synthetic, $)

Cascade Filtration Inc (synthetic) is a US industrial-filtration maker, in $m. LTM EBITDA is $120, growing 6%/yr. D&A is $30, capex $32 and ΔNWC $4/yr, all flat. Tax is 25%. A sponsor buys at 8.0× LTM EBITDA, cash-free/debt-free. Funding comes from a Term Loan B at 4.5× EBITDA (8.5% on the beginning balance, 5%/yr mandatory amortization), a $60 revolver (8%, undrawn at close), fees of 3% of TEV, and sponsor equity as the plug. It's a five-year hold with a 100% cash sweep, exiting at the entry multiple. Compute sources & uses, the debt waterfall, exit equity, MOIC and IRR, and the value-creation bridge. Then show what happens to the return if the exit multiple lands one turn either side of entry.

Step 1: sources & uses.

Entry leverage is 4.5×, and the equity cheque of 448.8 is ~47% of enterprise value. Build the live check Sources − Uses = 0.

Step 2: the debt waterfall (base case). CFADS = NI + D&A − capex − ΔNWC. Priority runs interest first, then mandatory amortization, then the revolver, then a 100% sweep of whatever remains. Interest is charged on the beginning balance, which kills the circularity.

CFADS clears the $27 mandatory in every year, and the tightest is Y1's 32.5. So, unlike the stress case in Worked example 1, the revolver never draws. Here it's pure insurance. Watch the flywheel turn. Each sweep cuts next year's interest, which lifts CFADS, which sweeps more.

Step 3: exit and returns. Exit at the entry 8.0× on Y5 EBITDA:

Exit EV      = 8.0 × 160.6                  = 1,284.7
Exit equity  = 1,284.7 − 290.9 (ending TL)  =   993.8
MOIC = 993.8 / 448.8                        =  2.21×
IRR  = 2.21^(1/5) − 1                       =  17.2%

Step 4: the value-creation bridge. It ties to the dollar:

Operating growth (324.7) and deleveraging (249.1) each did roughly half the work. From the multiple, the sponsor underwrote zero.

Step 5: the lever the sponsor doesn't control. Hold the business and the debt schedule fixed, and move only the exit multiple:

One turn of exit multiple is worth ~3.5 to 4 IRR points here, on an asset whose Y5 EBITDA and ending debt are identical across all three columns. So the flat-multiple rule from the LBO section underwrites the flat (8.0×) row and treats the +1-turn column as luck, never a plan. A serious memo shows the −1-turn column as the realistic downside. A pitch that leans on multiple expansion to clear its hurdle is renting the market's mood and calling it skill.

Practice set

Use a spreadsheet where a problem names one. Otherwise a calculator and paper will do. Problems ramp from guided to independent to timed.

P1 (guided: FCFF build). From a model extract: EBIT ₹240 cr, tax rate 25%, D&A ₹60 cr, capex ₹90 cr, working capital rose ₹25 cr. Compute FCFF.

Solution. NOPAT = 240 × 0.75 = 180. FCFF = 180 + 60 − 90 − 25 = ₹125 cr. Interest never appears, because FCFF is pre-financing. An NWC increase is a cash use, so it's subtracted.

P2 (guided: discounting). FCFF of 125, 140, 160 over years 1 to 3, with WACC at 11%. Compute each discount factor and the PV of the window.

Solution. Discount factors are 1/1.11 = 0.9009, 1/1.11² = 0.8116 and 1/1.11³ = 0.7312. PVs come to 125 × 0.9009 = 112.6, 140 × 0.8116 = 113.6 and 160 × 0.7312 = 117.0. Σ = ₹343.2 cr. As a check, =NPV(11%, {125,140,160}) returns the same, with flows assumed at year-ends.

P3 (guided: lawful terminal value). Final-year NOPAT is ₹500 cr, terminal g 4.5%, terminal ROIC 18% and WACC 11%. Compute TV, and the error a naive analyst makes by using final-year FCFF of ₹420 cr.

Solution. NOPAT_T+1 = 500 × 1.045 = 522.5. Reinvestment rate = 4.5/18 = 25%, so FCFF_T+1 = 522.5 × 0.75 = 391.9. TV = 391.9/(0.11 − 0.045) = ₹6,028.8 cr. The naive version gives 420 × 1.045/0.065 = 6,752.3, which is 12% too high. That forecast-year reinvestment rate supported faster growth, and it got carried into a slower-growth perpetuity for free.

P4 (independent: implied growth from an exit multiple). An analyst sets TV = 10× terminal EBITDA = ₹8,000 cr. Terminal-year NOPAT is ₹540 cr, terminal ROIC 15% and WACC 10.5%. What perpetual growth does the multiple imply, and does it pass a 7% Indian nominal-GDP cap?

Solution. Solve 540(1+g)(1 − g/0.15)/(0.105 − g) = 8,000 by iteration. At g = 5% you get 6,873, at g = 6% you get 7,632, and at g = 6.5% you get 8,148, so g ≈ 6.4%. It passes a 7% Indian nominal cap, barely. For a mature company, though, that's aggressive. Without saying so, the multiple is claiming near-economy growth forever, plus 15% ROIC on all of it. Report it, then decide.

P5 (independent: the full bridge). EV is ₹12,000 cr. Borrowings are 2,400, and lease liabilities 600, since FCFF was built lease-capitalized with rent excluded. Cash & investments are 900. Minority interest is 350 and preferred is 150. There are 100 cr basic shares, plus 8 cr employee options struck at ₹50, with the stock at ₹90. Value per share?

Solution. Equity = 12,000 − 2,400 − 600 + 900 − 350 − 150 = ₹9,400 cr. TSM dilution is 8 × (1 − 50/90) = 3.56 cr new shares, which makes 103.56 cr diluted. Per share = 9,400/103.56 = ₹90.8. Leases are subtracted because the flows excluded rent, so they go on one side of the boundary and never both. Skip any bridge item and you're wrong by that item.

P6 (independent: data-table forensics). A colleague's sensitivity table has three problems. (a) The corner cell contains 157.1 typed as a constant. (b) The row input cell points at WACC, though g runs across the row. (c) WACC is on another worksheet. Which of these breaks the table, and how does each failure look?

Solution. All three do. (a) The table computes but never updates with the model, so it goes stale without warning. Test the center cell against the live base case. (b) Excel shocks the wrong variable on each axis, and the grid fills with plausible-looking transposed values. Since the base-case cell still matches, this is the most dangerous error. (c) Excel rejects the reference, or you mirror it wrongly. Inputs must be on the table's own sheet, so fix it with a local input cell the WACC tab reads from.

P7 (independent: comps application). Peers trade at EV/EBITDA 7.9×, 8.4×, 8.8×, 9.6×. Your company has FY1E EBITDA of ₹240 cr, net debt of ₹480 cr and 60 cr shares. Apply the median ± 0.5 turns.

Solution. Median = (8.4 + 8.8)/2 = 8.6×. At 8.1× / 8.6× / 9.1×, EV = 1,944 / 2,064 / 2,184, so equity = 1,464 / 1,584 / 1,704, which is ₹24.4 / ₹26.4 / ₹28.4 per share. That's a range, and you should report it as one. Before you use it, confirm the peer table was normalized: one lease convention, one-offs removed, common basis.

P8 (independent: toy LBO with attribution). Buy at 6.0× on EBITDA of ₹50 cr, for TEV of 300, funded with 55% debt (165) and equity of 135. Exit in year 4 at 6.0× on EBITDA of ₹65 cr, with debt paid down to ₹80 cr. What are the MOIC, the IRR and the value-creation bridge?

Solution. Exit EV = 390, and exit equity = 390 − 80 = 310. MOIC = 310/135 = 2.30×, and IRR = 2.30^(1/4) − 1 = 23.1%. In the bridge, EBITDA growth is (65 − 50) × 6 = +90. Multiple expansion is 0, and paydown is 165 − 80 = +85. The total, +175, equals 310 − 135, so it ties. Roughly half the gain is deleveraging, and that half was rented.

P9 (independent: one year of waterfall, both directions). Your term loan begins at ₹200 cr, with mandatory amort of ₹15 cr/yr and 9% interest on the beginning balance. Your revolver starts at 0 and costs 10% when drawn. Year 1 CFADS = ₹12 cr, and year 2 CFADS = ₹22 cr. Trace both years.

Solution. In Y1, CFADS of 12 is below the mandatory 15, so you draw 3 on the revolver. That leaves the TL at 185 and the revolver at 3. In Y2, the mandatory 15 goes first and leaves 7. Then you repay the revolver's 3, which leaves 4. That 4 is swept into the TL. So the TL ends at 185 − 15 − 4 = 166, and the revolver at 0. Priority is contractual: interest, then mandatory, then revolver, then sweep. For the record, interest is 18.0 in Y1 and 0.09 × 185 + 0.10 × 3 = 16.95 in Y2, already inside CFADS through net income.

P10 (independent: all-stock A/D). Acquirer: NI $500m, 200m shares (EPS 2.50), price $60 (P/E 24×). Target: NI $120m, bought at P/E 16× all-stock. Pro-forma EPS, accretion %, and the breakeven paid P/E?

Solution. Consideration = 120 × 16 = 1,920, so new shares = 1,920/60 = 32m. EPS = (500 + 120)/232 = 620/232 = $2.67, +6.9% accretive. Breakeven paid P/E is the acquirer's own 24×. Pay more than your own multiple and the same math turns dilutive. None of this says the deal is good. That takes premium against synergies.

P11 (independent: cash deal, and the value hurdle). An acquirer has NI of $500m and 200m shares. It buys a target with NI of $90m for $1,500m cash, all funded with new debt at 7% pre-tax, and tax is 30%. (a) EPS impact. (b) If the target's standalone value was $1,200m, what annual after-tax synergies (capitalized at 9%) make the deal value-neutral?

Solution. (a) After-tax debt cost = 7% × 0.70 = 4.9%, so interest = 1,500 × 4.9% = 73.5. ΔNI = 90 − 73.5 = +16.5, and EPS = 516.5/200 = $2.58, +3.3% accretive. (b) Premium = 1,500 − 1,200 = 300, so the required synergy PV ≥ 300 and the after-tax run-rate ≥ 300 × 9% = $27m/yr, or ≈ $38.6m pre-tax at 30% tax. An "accretive" deal that can't clear $27m of real synergies is a wealth transfer wearing a press release.

P12 (timed: 12 minutes, the analyst drill). A US mid-cap: EBITDA $60m, net debt $110m, 20m shares, stock $14.00. Sponsor math: debt available 4.2× at blended 9%, fees $10m, credible operating case gives year-5 exit equity of $600m at a flat exit multiple, hurdle 22.5%. (a) Current EV/EBITDA. (b) Max sponsor TEV and per-share bid. (c) One-sentence verdict for your PM.

Solution. (a) Mkt cap 280 + net debt 110 = EV 390, or 6.5×. (b) Max entry equity = 600/1.225⁵ = 600/2.759 = 217.5, and debt = 4.2 × 60 = 252. So max TEV = 217.5 + 252 − 10 = 459.5 ≈ 7.7×, and equity to holders = 459.5 − 110 = 349.5/20 = $17.5/share. (c) "A sponsor clearing 22.5% can pay ~$17.5, 25% above market, so there's a live financial-buyer floor under this stock. Downside here is somebody else's entry point." One insight makes the drill fast. Because the debt quantum is EBITDA-sized, the sponsor's price flexes only through the equity cheque.

P13 (guided: build the WACC). India, INR. Risk-free is 7.0%, levered beta 0.90, and the equity risk premium, including country risk, 7.0%. Pre-tax cost of debt is 9.0%, tax is 25%, and target weights are 80% equity / 20% debt. Compute the cost of equity, the after-tax cost of debt, and the WACC.

Solution. Cost of equity (CAPM) = 7.0 + 0.90 × 7.0 = 13.30%. After-tax cost of debt = 9.0 × (1 − 0.25) = 6.75%. WACC = 0.80 × 13.30 + 0.20 × 6.75 = 10.64 + 1.35 = 11.99% ≈ 12.0%. Watch for two traps. One is failing to tax-affect the debt cost. Using 9.0% pushes WACC to ~12.6% and throws away the tax shield. Another is using book weights instead of market or target weights. Keep one WACC in one home, and have the DCF tab read this single cell.

P14 (guided: the mid-year convention). A US-target DCF puts enterprise value at $1,000m under year-end discounting at WACC 9.0%. (a) By what factor and to what value does the mid-year convention raise EV? (b) Why must the same convention hit the terminal value as well as the explicit window?

Solution. (a) Mid-year shifts every flow half a year earlier, so multiply year-end EV by (1 + WACC)^0.5 = 1.09^0.5 = 1.0440. EV becomes $1,044.0m, a +4.40% uplift. (b) The terminal value is usually the largest single piece, at 60 to 80% of EV. Discount the explicit window at t − 0.5 while leaving the TV at year-end. You've mixed conventions and understated the biggest number without noticing. Pick one convention, apply it everywhere, disclose it. Never let a 4 to 6% convention choice masquerade as 4 to 6% of insight.

P15 (independent: reverse DCF, solve for the implied growth). A listed Indian company (₹ cr). Your lawful DCF gives Σ PV of the explicit FY1 to FY5 FCFF = 640 and FY5 NOPAT = 300. WACC is 11.0%, terminal ROIC 16.0% and the year-5 discount factor 0.5935. Net debt is 500, with 25 cr shares. Its stock trades at ₹120. What perpetual growth is the price implying, and how do you read it against the ~7% Indian nominal-GDP cap?

Solution. Write value per share as a function of g. EV(g) = 640 + [300(1+g)(1 − g/0.16)/(0.11 − g)] × 0.5935, equity = EV − 500, and you divide by 25. Set it equal to ₹120 and iterate, or use Goal Seek. At g = 7.0% you get ≈ ₹113, and at g = 7.5% ≈ ₹122, so g ≈ 7.4%. That's above the ~7% nominal-GDP cap. So ₹120 is pricing in faster-than-the-economy growth forever, beyond "steady 7% forever," and perpetuity math forbids that. To reconcile, either the market is underwriting a longer high-growth runway than your five-year window models, or it's simply optimistic. If it's the first, extend the explicit forecast, then re-price. Either way the disagreement now has a name and you can research it, and that's what a reverse DCF is for.

P16 (independent: the swap ratio, and the accretion trap; India ₹). Ganga Consumer Ltd (synthetic, NI ₹800 cr, 40 cr shares, price ₹500, P/E 25×) acquires Yamuna Foods Ltd (synthetic, NI ₹150 cr, 30 cr shares, price ₹100, P/E 20×) in an all-stock scheme of arrangement at a 20% premium. (a) Offer price, swap ratio, and new shares issued. (b) Pro-forma EPS and accretion/dilution. (c) With expected after-tax cost synergies of ₹45 cr/yr (capitalized at 10%), is the deal value-creating? Reconcile with (b).

Solution. (a) Offer = 100 × 1.20 = ₹120/target share. Swap ratio = 120 ÷ 500 = 0.24, or 6 Ganga shares per 25 Yamuna shares, and new shares = 30 × 0.24 = 7.2 cr. (b) Pro-forma EPS = (800 + 150)/(40 + 7.2) = 950/47.2 = ₹20.13 against Ganga's standalone ₹20.00, so it's +0.6% accretive. That fits the quick rule, since the paid P/E = 120/5 = 24× < the acquirer's 25×. (c) Premium = 30 × (120 − 100) = ₹600 cr, and synergy PV = 45 ÷ 0.10 = ₹450 cr. Premium 600 > synergies 450, so the deal is value-negative by ~₹150 cr. It raises EPS and destroys value at the same time. Accretion measures multiple blending, while value is premium against synergies. India's wrapper of scheme and swap ratio changes the plumbing and leaves the arithmetic alone.

P17 (independent: the amortization sign flip; US $). Acquirer A (NI $800m, 400m shares, EPS $2.00, price $36, P/E 18×) buys target T (NI $120m) all-stock at a paid P/E of 15×. Purchase accounting writes up $900m of intangibles amortized over 9 years, and tax is 25%. Compute (a) new shares and pre-amortization pro-forma EPS, (b) reported (GAAP) EPS after the new amortization, and (c) "cash EPS." What's the one true statement about the deal's cash flows?

Solution. Consideration = 120 × 15 = $1,800m, so new shares = 1,800/36 = 50m. (a) Pre-amortization EPS = (800 + 120)/(400 + 50) = 920/450 = $2.044, +2.2% accretive, since the acquirer's P/E of 18× > the paid 15×. (b) New amortization = 900/9 = $100m pre-tax, or $75m after tax, so reported EPS = (920 − 75)/450 = 845/450 = $1.878, −6.1% dilutive. (c) "Cash EPS" adds the amortization back: 920/450 = $2.044, +2.2%. Here's the one true statement: not a single cash flow changed between (a), (b) and (c). Whether the headline is positive or negative is an accounting-and-definition artifact, and that's why deal decks feature "cash EPS." All three leave the value question, premium against synergies, untouched.

P18 (timed: 15 minutes, DCF to per-share; US $). A US mid-cap, in $m. Forecast FCFF for Y1 to Y5 = 80, 90, 100, 108, 115, with WACC at 9.0%. For the terminal value, FY5 NOPAT is $130, terminal ROIC 14% and perpetual g 4.0% (the US nominal cap). Net debt is $250 and there are 60m shares. Its stock is at $28.00. Compute Σ PV of the window, the lawful terminal value, EV, equity value, value per share, TV % of EV, and give a one-line verdict.

Solution. At 9%, the DFs are 0.9174, 0.8417, 0.7722, 0.7084, 0.6499, which give PVs of 73.4, 75.8, 77.2, 76.5, 74.7 and Σ = $377.6m. For the TV, FCFF_T+1 = 130 × 1.04 × (1 − 0.04/0.14) = 135.2 × 0.7143 = 96.6, so TV = 96.6/(0.09 − 0.04) = $1,931.4m. PV of TV = 1,931.4 × 0.6499 = $1,255.3m, which makes TV 76.9% of EV, inside the normal 60 to 80%. EV = 377.6 + 1,255.3 = $1,632.9m. Equity = 1,632.9 − 250 = $1,382.9m, and per share = 1,382.9/60 = $23.05 against $28.00, a (17.7%) downside. Verdict: "~$23 on lawful assumptions vs a $28 price. This stock prices growth or returns above my terminal inputs, and the debate is in the terminal block and not in the explicit window." Watch the speed trap. Growing FCFF₅ mechanically for the TV, 115 × 1.04/0.05 = 2,392, overstates TV ~24% and flips the verdict to "cheap."

Applied mini-project: bolt the full stack onto your M3.08 model

Give the task 4 hours. Take the real company you modeled last week. Sundar stays out of this one. Build the five tabs onto that workbook and produce a one-page output.

1. Pull the raw material: the latest annual report or 10-K, from EDGAR for the US and from BSE/NSE or screener.in exports for India. Add the current price and share count with date and source stamped on them. Then add 5 to 7 peers' market data.
2. Build the DCF tab. Pull FCFF from your model, and source the WACC block's inputs from Damodaran's current ERP/CRP pages. Use this January's numbers, never a stale screenshot. Add a lawful TV both ways with the reconciliation row, then the full bridge, then a live 2-way data table.
3. Build the comps tab: your peer table with documented peer logic, one lease convention, medians, applied band.
4. Draw the football field: all bars labeled, price line dated, a one-sentence field verdict written on the tab.
5. Work out the LBO floor the way the worked example on a listed Orion does it. That means sponsor math on your company at a 20% hurdle. Even if the company is a terrible LBO candidate, the reason why is the finding. Maybe leverage is already high, maybe FCF is too volatile, or, in India, maybe it's the financing plumbing.
6. Run a deal reaction. Assume your company acquires its nearest listed peer at a 25% premium. Half the price is paid in stock and half in debt-funded cash. Compute year-1 accretion/dilution and the synergies required for value neutrality.
7. Audit your workbook against the model-suite checklist and fix every hard-check failure. Then write the one-page output with the valuation workflow's template: range, drivers, what's priced in, verdict.

Scoring rubric (0 = missing/wrong · 1 = present with gaps · 2 = clean and defensible):

Pass: ≥16/20, with no zeros. File the one-pager in your knowledge system, because you'll reuse this exact stack in the phase capstone on two companies.

Case Lab: run case XL-3.3 in the app's Cases tab: a guided build of the full valuation stack, meaning a DCF with a lawful terminal value, comps, an LBO floor and an accretion/dilution reaction, on one synthetic target. The feedback engine plants three traps for you to catch: a free-growth terminal value, a data table with its row/column inputs reversed, and a deal that is EPS-accretive yet value-destructive.

Reading & resources

• Rosenbaum & Pearl, Investment Banking: Valuation, LBOs, and M&A. Ch. 1 (Comparable Companies), Ch. 3 (DCF), Ch. 4–5 (LBO fundamentals & analysis), Ch. 6–7 (M&A). The standard mechanical reference; read for process, keep M3.05's valuation skepticism on. [Paid] [Intermediate]
• Aswath Damodaran, NYU spreadsheet library (pages.stern.nyu.edu/~adamodar → Spreadsheets): fcffsimpleginzu.xls (his full FCFF DCF; audit it against your tab), lbovaluation.xls. Free, forever, and the best way to check your architecture against a master's. [Free] [Intermediate]
• Damodaran, "Acquirers Anonymous" session (his corporate-finance/valuation class lectures on M&A, YouTube). The evidence on why most acquisitions destroy acquirer value. [Free] [Intermediate]
• McKinsey (Koller, Goedhart, Wessels), Valuation (8e). The chapters on Frameworks for Valuation, Forecasting Performance, Estimating Continuing Value, and Moving from Enterprise Value to Value per Share (chs. 10–16 in recent editions). The institutional gold standard on the DCF-to-per-share pipeline. [Paid] [Advanced]
• Mauboussin & Callahan, "To Buy or Not to Buy: A Checklist for Assessing Mergers & Acquisitions" (free PDF, 2017). The premium-vs-synergies test from the M&A section, as a full checklist, with base rates on deal outcomes. [Free] [Intermediate]
• A Simple Model (asimplemodel.com). Free video series building a 3-statement model into an LBO, cell by cell; the best free LBO-mechanics resource. Macabacus (macabacus.com) for free DCF/LBO/merger-model templates and Excel technique. [Free] [Beginner→Intermediate]
• Wall Street Prep & Breaking Into Wall Street free guides. Searchable articles on data tables, TSM dilution, debt schedules, accretion/dilution; use as a mechanics reference when a formula fights you. [Free] [Beginner]
• Zerodha Varsity, Financial Modelling module (zerodha.com/varsity). The India-flavored build (Schedule III statements into a model). [Free] [Beginner]
• Primary documents (the permanently underrated resource): any US merger proxy (DEF 14A) or S-4 on EDGAR contains the bankers' fairness opinion: real comps tables, real DCFs, real LBO analyses with disclosed assumptions (pull Microsoft–Activision's proxy, or Pioneer's S-4 from the ExxonMobil deal, and audit their football fields). India: NCLT scheme documents + registered-valuer reports + fairness opinions filed with BSE/NSE (pull HUL–GSK CH 2020): free masterclasses in these very tools. [Free] [Intermediate]
• Burrough & Helyar, Barbarians at the Gate. RJR Nabisco; the culture and stakes of LBOs in one narrative. [Paid] [Beginner]
• Pignataro, Leveraged Buyouts: A Practical Guide: if you want a second, slower walkthrough of full LBO construction. [Paid] [Intermediate]
• Going deeper: Rappaport & Mauboussin, Expectations Investing (revised edition; free companion tools at expectationsinvesting.com) [Paid] [Intermediate]. Builds the reverse DCF of Worked example 4 into a full method: read the price as the market's expectations, solve for the growth it embeds, then test that single claim instead of manufacturing a point forecast.
• Going deeper: Michael Mauboussin & Dan Callahan, "Return on Invested Capital" and "The Base Rate Book" (Counterpoint Global / Morgan Stanley, free PDFs) [Free] [Intermediate]. Sharpen the terminal-value engine with them. They show why ROIC and reinvestment drive continuing value and the discount rate doesn't, plus empirical base rates to sanity-check the growth-and-fade assumptions your TV and LBO exit lean on.

The Modern Analyst's Addendum

Everything above teaches this skill from first principles, by hand, and that is how you learn it, and the mastery check still tests it that way. This addendum shows how a working analyst amplifies the same skill today. It adds; it never replaces. (R1/R10)

AI-Augment this skill

{
  "skill": "The DCF tab from FCFF build to per-share bridge, the WACC block, terminal value both ways with the reconciliation, the two-way sensitivity table, comps and the football field, the full LBO from sources-and-uses through the debt waterfall to MOIC, IRR and the value-creation bridge, the LBO floor under a public stock, and accretion/dilution in every consideration mix",
  "use": "The three machines in this module fail in different places, and a tool is useful in exactly one of them. (1) DEAL FORENSICS, which is where the leverage is: a US merger proxy reproduces the bankers' own DCF, comps, precedent and sometimes LBO analyses, and an Indian scheme of arrangement carries a registered-valuer report and a fairness opinion with the swap-ratio workings. Ask for those tables extracted into a structured form with the discount rate, terminal growth, exit multiple and share count each analysis used, and you have a professional's assumption set to argue with rather than a headline to repeat. (2) DEBT-TERM EXTRACTION: the credit agreement or the 10-K debt footnote carries the pricing grid, the mandatory amortization, the excess-cash-flow sweep percentage and the covenants, every one of which is a formula in the waterfall, and all of which are tedious to find and easy to mis-read. (3) SYNERGY-CLAIM PARSING: pull every synergy figure a company has guided across its calls, with the date and the phasing, so the premium-versus-synergies inequality is underwritten against what management actually promised rather than against the deck's headline. (4) The deal-reaction first draft: within an hour of an announcement, the EPS math is mechanical and a tool can lay out the consideration plumbing while you do the value verdict.",
  "tools": ["Chat assistants: Claude, ChatGPT for pulling the bankers' assumption sets out of a fairness opinion, laying out consideration plumbing on announcement day, and stress-questioning a synergy bridge", "Document/PDF AI: for DEFM14A and S-4 merger proxies, NCLT scheme documents and registered-valuer reports, credit agreements and 10-K debt footnotes with their amortization and sweep terms", "Coding assistants: for the debt waterfall as an ordered priority list with its balance caps asserted, the exit-multiple and operating-case surfaces, and the multiplicative return bridge below"],
  "prompt": "From this merger proxy (or scheme of arrangement), extract every valuation analysis the financial adviser performed into one table: the method, the discount-rate range, the terminal growth or exit multiple, the comparable companies or precedent transactions used, the resulting per-share value range, and the page it appears on. Separately, list every synergy figure disclosed anywhere in the document with its phasing and whether it is described as cost or revenue, and every integration or restructuring cost disclosed against it. Do not value anything, do not tell me whether the price is fair, and do not summarise the fairness opinion's conclusion.",
  "verify": "Two verifications. First, the arithmetic must survive its own checks before anything else happens: sources equal uses, no debt balance negative in any year, the revolver drawn only when cash flow available for debt service falls short of mandatory amortization, interest computed on the stated balance convention, and the value-creation bridge tying to exit equity exactly. A waterfall that does not tie is not a model, and a tool will happily produce one that computes. Second, and this is what the Quant lens is about: never accept a returns attribution, whether from a tool, a pitch deck or your own spreadsheet, without asking which convention produced it, because the standard rupee bridge has an interaction term that the author gets to assign, and the assignment moves the 'operating improvement' line by a fifth. Same for accretion: the closed forms below mean you can check any accretion claim in ten seconds, and the claim is almost always true and almost never relevant. Pull the base rates on deal outcomes and synergy delivery from the sources M3.07 names rather than from a chat window (Guardrail 1-5).",
  "diy": "The gate is unaided: you build an FCFF forecast and discount it, construct a lawful terminal value and reconcile it to an implied exit multiple, walk enterprise value to a per-share number through the full bridge, run a five-year debt waterfall in priority order by hand, compute MOIC and IRR and tie the value-creation bridge to the last dollar, solve the LBO floor under a listed stock, and compute accretion in all three consideration mixes with the amortization refinement. Nothing in this callout is admissible in that room."
}

Modern Data Analysis

By hand first. You built Sarita's FCFF row by row to a ₹88.9 share and inverted it to the 7.7% the market demanded. You ran Orion's and Cascade's waterfalls year by year in priority order, tied both value-creation bridges to the dollar, solved the LBO floor at $14.77, and computed accretion in four consideration mixes, including the amortization refinement that flips the headline. Keep all of it, the waterfall most of all. Its ordering is the credit agreement, and you can't read a covenant you've never enforced by hand. What code adds is narrow. Both machines here produce a single headline that hides a choice, and code is how you make the choice visible.

Today's workflow. Three objects, and the third is the one nobody builds.

• waterfall(deal, case) holds the priority order as an explicit list, the balance caps as assertions instead of MIN functions you hope are right, and the year loop as a loop. The full LBO's check list becomes five assert statements. Worked example 1's stress case stops being a scenario you typed and becomes a search: what is the lowest EBITDA path this capital structure survives? Worked example 1 calls that number the "stall speed" and estimates it at about $48m. A solver returns it.
• returns_bridge(deal), and in particular the multiplicative bridge, because the additive one has a free parameter, as you'll see below.
• accretion(n, k) holds the closed forms, so you can answer an announcement from two ratios instead of a rebuilt model.

Tools & sources (IN + US). Use numpy for the waterfall and the surfaces, scipy.optimize.brentq for the LBO floor, the stall speed and the reverse-DCF solve, pandas for the deal-comparison table, and matplotlib for the football field and the exit-multiple sensitivity. For India, start with the NCLT scheme of arrangement documents filed on BSE and NSE. Their registered-valuer reports and fairness opinions contain full comps tables, DCFs and the swap-ratio derivation. Then use the SEBI letters of offer at sebi.gov.in for open-offer pricing under the 2011 Takeover Regulations, and the annual report's borrowings note for facility structure and MCLR/EBLR-linked pricing. RBI's External Commercial Borrowings framework explains how acquisition debt actually reaches an Indian target, given the restriction on domestic bank financing of share acquisitions. For the EBITDA base a leverage multiple is struck against, use screener.in. EDGAR's DEFM14A and S-4 filings carry the bankers' own DCF, comps, precedent and LBO analyses for US deals. Then come the 8-K for terms on announcement day, the 10-K debt footnote and the credit agreement for amortization, sweep percentages and covenant levels, and FRED for the cost of the debt that sizes every deal (SOFR for the floating base, BAMLH0A0HYM2 for the high-yield spread, DGS10 for the rate regime).

# The LBO bridge without an interaction fudge — R3, recomputed in-session on §4.10's Orion deal.
import numpy as np
E0, E1, m0, m1 = 100.0, 133.8226, 8.0, 8.0        # entry/exit EBITDA and multiple
EV0, EV1, D0, D1, fees = m0 * E0, m1 * E1, 400.0, 163.0, 24.0
eq0, eq1 = EV0 + fees - D0, EV1 - D1               # 424.0 -> 907.6
f = dict(growth   = E1 / E0,                       # 1.33823
         multiple = m1 / m0,                       # 1.00000
         delever  = (1 - D1 / EV1) / (1 - D0 / EV0),   # 1.69549
         fees     = (1 - D0 / EV0) / (eq0 / EV0))      # 0.94340
assert abs(np.prod(list(f.values())) - eq1 / eq0) < 1e-9    # MOIC factorises EXACTLY
print(f"MOIC {eq1/eq0:.4f}   IRR {(eq1/eq0)**0.2-1:.2%}")   # MOIC 2.1405   IRR 16.44%
for k, v in f.items():
    print(f"{k:9s} x{v:.5f}  {np.log(v)/np.log(eq1/eq0):+6.1%} of log-MOIC  {v**(1/5)-1:+7.2%} of IRR")
#   growth   x1.33823  +38.3% of log-MOIC   +6.00% of IRR   <- exactly the EBITDA growth rate
#   delever  x1.69549  +69.4% of log-MOIC  +11.14% of IRR
#   fees     x0.94340   -7.7% of log-MOIC   -1.16% of IRR

Verify. Prove the machines against the worked figures above before anything else. Orion's sources and uses come out at 800 / 24 / 400 / 424, with the schedule reproducing 106.0 · 112.4 · 119.1 · 126.2 · 133.8 of EBITDA, interest of 34.0 · 31.3 · 27.9 · 24.0 · 19.3, CFADS of 32.2 · 39.1 · 46.6 · 55.0 · 64.1 and sweeps of 12.2 · 19.1 · 26.6 · 35.0 · 44.1. Its term loan closes at 163.0, exit equity at 907.6, MOIC at 2.1406 and IRR at 16.44%. Its bridge ties at 424 + 270.6 + 237.0 − 24.0, and the all-equity comparison comes out at MOIC 1.7111 and IRR 12.73%. For Cascade, equity is 448.8, CFADS 32.5 · 40.3 · 48.9 · 58.5 · 69.0, the term loan closes at 290.9, exit equity is 993.8, MOIC 2.2143 and IRR 17.23%, and the exit-multiple ladder reads 13.17% · 17.23% · 20.80%. For the floor, max entry equity is 364.7 and max TEV 740.7 = 7.407×, or $14.769 per share, and the bull-case version comes to $16.379. That's what lets Worked example 3 say the stock is priced at the sponsor bull case. For Sarita, FCFF runs 108.0 · 130.0 · 153.4 · 178.8 · 204.3 with an explicit-window PV of 538.9. Terminal value is 2,552.2 against a naive 3,064.8 that overstates by 20.08%. Enterprise value is 1,987.1, equity 1,777.1 and value ₹88.85 per share, with terminal value at 72.88% of enterprise value and the reverse-DCF solve at 7.683%. For accretion, all-stock gives +6.122%, all-cash +9.750%, mixed +7.753% and cash-on-hand +16.500%, with amortization −3.061%. And the conservation check puts A's holders at 81.633% of $24,200m = $19,755m, which is $244.9m poorer. Before anyone compares bridges, state one convention. A rupee bridge attributes the interaction term by construction, and the Quant lens measures what that costs.

Quantitative lens

The full LBO's value-creation bridge ties to the dollar, and the accretion math is exact. Both are correct. Both also hide a decision that the presenter makes and the reader never sees, and in each case that decision is worth more than most of the analysis around it. Every figure below comes from running the engine above on the Orion and Cascade deals and the accretion pair worked earlier. They're properties of those deals. They don't measure any market.

An additive bridge has a free parameter, and it's in the line that says "luck". Take Cascade exiting one turn up, at 9.0×. Exit equity is 1,154.4, a gain of 705.6 on the 448.8 cheque. Now split it. The full LBO's convention prices EBITDA growth at the entry multiple and multiple expansion on exit EBITDA, which gives growth of 324.7 (46.0%) and expansion of 160.6 (22.8%). Its mirror image is just as defensible. Price growth at the exit multiple and expansion on entry EBITDA, and you get growth of 365.3 (51.8%) and expansion of 120.0 (17.0%). They differ by the cross term, ΔEBITDA × ΔMultiple = 40.6, which belongs to neither lever and has to be assigned to one. So "how much of this came from multiple expansion" is 120.0 or 160.6, a 33.8% swing, and every rupee of the swing goes to the line that separates skill from a rising market. A symmetric split, half the cross term each, gives 345.0 and 140.3, and it's the fair default. Which convention wins matters less than this: a bridge quoted without its convention isn't a measurement.

A multiplicative bridge has no such freedom, and it decomposes the IRR exactly. MOIC factorises without residue: MOIC = (EBITDA growth) × (multiple change) × (deleveraging) × (fee drag), where deleveraging is (1 − D₁/EV₁)/(1 − D₀/EV₀) and the fee drag is (1 − D₀/EV₀)/(equity₀/EV₀). Logs are additive, so each factor's share of log-MOIC is its share of the compound return, and each factor's fifth root is its contribution to the annual IRR. On Orion, growth is ×1.33823, multiple ×1.00000, deleveraging ×1.69549 and fees ×0.94340, multiplying to MOIC 2.1405 to nine decimals. In IRR points that's +6.00 / +0.00 / +11.14 / −1.16, compounding to 16.44%. Cascade at a flat exit gives +6.00 / 0 / +12.07 / −1.32 = 17.23%. Cascade exiting a turn up gives +6.00 / +2.38 / +12.79 / −1.32 = 20.80%.

Now read the first column of all three. In every one of them, the EBITDA-growth contribution to the equity IRR is exactly 6.00%. These deals didn't land there by coincidence. The growth factor is (1+g)^T, so its annualised contribution is ((1+g)^T)^(1/T) − 1 = g, identically, for any horizon and any capital structure. Operating improvement contributes exactly its own EBITDA growth rate to the equity IRR. No more, ever. Everything above that line is the multiple and the balance sheet.

That puts a number on the earlier advice to ask which lever did it. A sponsor reporting a 20.8% IRR on a business that grew EBITDA 6% a year is reporting 6 points of operating improvement, 2.4 points of a multiple they didn't control, and 12.8 points of rented balance sheet. By the rupee bridge, growth did 46 to 52% of the work. By the return bridge, it did 30.8%. Both are arithmetically correct, but only one of them is denominated in the thing the sponsor is paid on.

Of all the levers, the ones the sponsor controls are the smaller ones. Shock Cascade one lever at a time. Half a turn off the entry multiple is worth +1.51 IRR points, and half a turn on is −1.20. A full percentage point of annual EBITDA growth, sustained for five years, is worth +1.81 / −1.86. Half a turn of exit multiple, the one thing nobody controls, is worth +1.84 / −1.96, the largest single half-turn on the board. Half a turn of entry leverage is +1.41 / −1.08. So the exit multiple, which the LBO section rightly tells you to underwrite at flat and treat as luck, has a bigger grip on the answer than a percentage point of operating improvement sustained for half a decade. That's the case for the flat-multiple rule, made as a sensitivity instead of as advice.

Accretion has a closed form, and the closed form is the indictment. For an all-stock deal, write n = NI_target/NI_acquirer and k = P/E paid ÷ P/E of the acquirer. Then

accretion = n(1 − k) / (1 + nk)

and nothing else enters. Synergies don't, the target's standalone multiple doesn't, the premium as such doesn't, and value doesn't either. For the base pair from the accretion section, n = 0.30 and k = 0.75, giving +6.122%, the same +6.1%, from two ratios. This form also bounds the metric. As n grows without limit the accretion tends to 1/k − 1, so no all-stock deal struck at k = 0.75 can ever accrete more than 33.3%, however large the target. For cash it's simpler still, accretion = n(1 − r_after-tax × P/E paid). It gives +9.750% at a 4.5% after-tax funding cost and +16.500% at the 3% cash-on-hand rate, the same figures as before, from one multiplication.

That makes the hurdle visible, and it's lying on the floor. A cash deal accretes if and only if P/E paid < 1/r_after-tax. That's 22.2× at a 4.5% after-tax cost of debt, and 33.3× when the deal is funded from cash earning 3%. With no synergies, a deal is value-neutral when the target's earnings yield on the price paid clears the acquirer's cost of capital, around 9%, which is 11.1×. So there's an 11.1-turn band of P/E, or 22.2 turns when the cash pile pays for it, in which a deal is reported as accretive while it destroys value. Earlier you saw that the hurdle buried in the EPS math is the cost of funds, while value is judged against the cost of capital. That band is the gap, measured in turns.

The all-stock case between A and T from earlier shows the same picture. It tracks A's holders, with zero synergies, as the paid multiple walks from the target's unaffected 12× up to A's own 20×:

Read the middle row carefully. A 50% premium with no synergies at all still prints as +2.4% accretive while it transfers $1.4bn of A's holders' money to T's. Now notice what the table doesn't say. Accretion isn't random noise here. It falls monotonically as the premium rises, so within an all-stock deal at fixed size it really is correlated with value. The direction is fine, and the defect is the origin. Accretion crosses zero at a 66.7% premium, and value crosses zero at 0%. So the metric points the right way and puts its zero in the wrong place by two-thirds of the target's market capitalisation. That's a more precise and more damning statement than "accretion is meaningless."

These tools have real limits. A multiplicative bridge is exact arithmetic on a realised deal. It explains where a return came from and forecasts nothing, and the identity that growth contributes exactly g depends on holding EBITDA growth constant. A lumpy path with the same terminal EBITDA gives the same factor and a different lived experience. A path that grows late and not early sweeps less debt and produces a different deleveraging factor entirely. Nor is the deleveraging factor free money. It's compensation for taking the first-loss seat, and the reverse gear you saw in the toy LBO is the price.

Those IRR sensitivities are one-at-a-time on Cascade's specific structure, and they transfer to no other deal. A business with weaker cash conversion has a smaller deleveraging factor and a larger sensitivity to the exit multiple, so the boring cash-generative target is the archetype. Every LBO figure here assumes the sponsor's operating case happens. On whether it will, the whole apparatus is silent, and the base rates that would tell you belong to the M&A evidence you met earlier, outside this arithmetic.

Accretion's closed forms are exact for the simple cases and drop what the refinements add: deal amortization, foregone interest on cash, phased synergies, and any change in the share count between announcement and close. Use them for the ten-second check and the full machine for the memo. In the value-destruction column, the assumption is zero synergies and a market that prices the combination at the sum of standalone values plus synergies. That's a modelling convention. It isn't an observation about announcement-day prices.

Deepest of all, none of this says whether a deal should happen. It says the number the headline quotes and the number the owners care about are different numbers, that the gap is computable, and that the person who computes it in the first hour is the one worth listening to in the fourth quarter.

Do it in code: build the waterfall with its priority order explicit and its balance caps asserted, and solve for the stall speed instead of guessing a stress case. Report the multiplicative bridge alongside the rupee one, state which convention the rupee one used, and answer any accretion claim from n and k before rebuilding a model. See G1/AA1.03, G2/QD2.03 and G1/QM1.01.

Where this goes next: galaxy cross-links

• G1 · AA1.03 Performance Attribution & GIPS. The interaction term is not an LBO curiosity: arithmetic versus geometric attribution, and what to do with the cross-product, is the oldest argument in performance measurement, and its answers transfer directly to the value-creation bridge.
• G2 · QD2.03 Performance Attribution in Code. Building a compound-return decomposition that ties exactly, with the residual either eliminated by construction or reported rather than quietly assigned.
• G1 · QM1.01 Probability, Distributions & Estimation. Logs, geometric versus arithmetic means, and why a return that compounds must be decomposed multiplicatively if the shares are to mean what they appear to mean.
• G2 · CS2.06 Software Engineering & AI-Assisted Development. The debt waterfall as an ordered priority list with balance caps as assertions, so a sweep formula can never drive a balance negative and a stress case is a test rather than a typed column.
• G3 · CN6.01 Deal Rationale & Synergies. The premium-versus-synergies inequality at full depth: where synergy estimates come from, how they are phased and tracked after close, and what integration actually costs.

Teach it back & journal

Feynman prompt. Explain to a smart 15-year-old why buying a small apartment with 20% down and renting it out is a leveraged buyout. Walk her through it. The rent that pays the loan's EMI is the cash sweep. The loan shrinking while the flat's price stays flat is deleveraging. You get richer without the flat getting better. The flat's price rising is EBITDA growth and multiple expansion tangled together. Then ask what happens to her money if prices fall 20% the year she must sell, and leave the bank's money out of it. Then write the one-page explainer: "One engine, four gauges: how the same forecast tells an owner, the market, a leveraged buyer, and a CEO's press release four different stories, and which gauge to trust when." No formulas allowed on the page. If a step needs one, you haven't finished understanding it.

Journal prompt. Open your finished model suite and answer in writing: Which tab do I secretly trust most, and is that trust earned or comfortable? Most learners privately trust the comps tab because it feels external, despite having just spent eight modules learning that it's merely the market's DCF with the assumptions hidden. Then record the moment this week when a check caught a real error of yours: the sign flip, the dead data table, the negative debt balance. That catch is the argument for all the checks and the audit. Write down what it would have cost you in a live memo, and which line of the model-suite audit caught it. If nothing caught you, write down which check you'd delete first, and why that's the one you must keep.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.