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Mergers and acquisitions - the arithmetic of deal math

LBO returns calculator

Entry multiple, leverage, growth, cash conversion and exit multiple in; sources and uses, the debt schedule, MOIC, IRR and the four-way value-creation bridge out. The four components sum exactly to the change in sponsor equity value. Every input is encoded in the URL.

Assumptions

Returns

Sources and uses at entry

Debt schedule and cash sweep

Cash interest is charged on the beginning-of-year debt balance. Free cash flow after interest is applied to debt at the sweep percentage; the unswept remainder accumulates as cash. Where free cash flow after interest is negative, cash is drawn first and the balance is added to debt.

Value-creation attribution

IRR against the exit multiple

Inverse solves

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The formulas

Sources and uses

Total uses must equal total sources. In a sponsor deal the equity cheque is the residual, which is why it moves whenever any other line moves.

EV_0 = x_entry * EBITDA_0 fees = fee% * EV_0 D_0 = turns * EBITDA_0 E_0 = EV_0 + fees - D_0

Fees are pure equity leakage: they buy no asset and never come back.

Debt schedule and the cash sweep

EBITDA_n = EBITDA_0 * (1 + g)^n uFCF_n = conv% * EBITDA_n interest_n = r_d * D_(n-1) paydown_n = sweep% * (uFCF_n - interest_n) D_n = D_(n-1) - paydown_n cash_n = cash_(n-1) + (uFCF_n - interest_n) - paydown_n

Interest is charged on the opening balance, so paydown accelerates over the hold even at constant EBITDA. Where a margin change is supplied, revenue is implied from the entry margin and EBITDA becomes Rev_0 * (1+g)^n * (m_0 + Δm * n/t), with the margin moving straight-line.

Exit value, MOIC and IRR

EV_t = x_exit * EBITDA_t E_t = EV_t - D_t + cash_t MOIC = E_t / E_0 IRR solves sum_j CF_j / (1 + IRR)^t_j = 0

IRR is solved numerically by bisection on the discount rate, not by annualising MOIC. With one outflow at t=0 and one inflow at t the two agree, and IRR = MOIC^(1/t) - 1; any interim cash flow breaks that identity while the numerical solve still holds.

Four-way value-creation attribution

E_t - E_0 = (EBITDA_t - EBITDA_0) * x_entry EBITDA growth + (x_exit - x_entry) * EBITDA_t multiple expansion + (D_0 - D_t + cash_t) net debt paydown - fees entry fees

The cross-term between growth and multiple change has to be assigned to one component or the other. The convention here values the multiple change on exit EBITDA, which assigns the cross-term to multiple expansion. Valuing growth at the exit multiple and the multiple change at entry EBITDA also ties and produces a different-looking split of the same total, so ask which convention a bridge uses before comparing two of them. The paydown bar is net of any cash build so that the four components sum to the equity change in every case, including a partial sweep.

Inverse solves

x_exit for a target IRR = [E_0 * (1 + IRR_target)^t + D_t - cash_t] / EBITDA_t EBITDA_t required at a constant multiple = [E_0 * (1 + IRR_target)^t + D_t] / x_entry g required = (EBITDA_t / EBITDA_0)^(1/t) - 1

Because the closing debt balance itself depends on the operating case, the exit-multiple solve and the growth solve are not independent. The growth figure above holds the debt schedule at the current case; the calculator also reports the growth rate found by re-running the schedule at each candidate growth rate, which is lower because faster growth generates more cash to sweep.

The base case, worked

Entry EBITDA 100.0, entry multiple 10.0x, fees 3.0 percent of enterprise value, debt 500.0 at 6.0 percent cash interest, unlevered free cash flow 60 percent of EBITDA, EBITDA growth 5.0 percent per year, a 100 percent cash sweep, a five-year hold, and a 10.0x exit. These are the defaults above.

YearBeginning debtEBITDAUnlevered FCFCash interestDebt paydownEnding debt
1500.00105.0063.0030.0033.00467.00
2467.00110.2566.1528.0238.13428.87
3428.87115.7669.4625.7343.73385.14
4385.14121.5572.9323.1149.82335.32
5335.32127.6376.5820.1256.46278.87
Cumulative-580.19348.11126.98221.13278.87
E_0 = 1,000.0 + 30.0 - 500.0 = 530.0 EBITDA_t = 100.0 * 1.05^5 = 127.6282 E_t = 10.0 * 127.6282 - 278.8655 = 997.4161 MOIC = 997.4161 / 530.0 = 1.8819x IRR = 13.4802% bridge = +276.2816 growth, 0.0 multiple, +221.1345 paydown, -30.0 fees = +467.4161 = 997.4161 - 530.0

URL parameters

Every parameter is optional; omitted parameters take the base-case default. Percentages are entered as numbers, so 6 means 6 percent. All computation happens in the browser and no request leaves the page.

ParameterMeaningDefault
ebitdaEntry EBITDA, in any consistent unit100
entryEntry EV/EBITDA multiple10
exitExit EV/EBITDA multiple, applied to exit-year EBITDA10
debtDebt at entry in turns of entry EBITDA5
rateCash interest rate, percent, on the opening balance6
growthCompound annual EBITDA growth, percent5
marginTotal change in EBITDA margin over the hold, percentage points, straight-line0
emarginEntry EBITDA margin, percent. Only used when margin is non-zero, to imply revenue20
convUnlevered free cash flow as a percent of EBITDA60
yearsHolding period in whole years5
feesTransaction and financing fees, percent of entry enterprise value3
sweepShare of free cash flow after interest applied to debt, percent100
targetTarget IRR, percent, for the inverse solves20

The base case:
https://m-a.wiki/calc/?ebitda=100&entry=10&exit=10&debt=5&rate=6&growth=5&conv=60&years=5&fees=3

Two turns of multiple expansion on the same operating case:
https://m-a.wiki/calc/?ebitda=100&entry=10&exit=12&debt=5&rate=6&growth=5&conv=60&years=5&fees=3

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Related: LBO returns math · accretion and dilution · accretion / dilution calculator · purchase price bridge · valuation cross-checks

A simplified model. It uses a single debt tranche at a flat rate, no mandatory amortisation, no revolver, no cash taxes modelled separately from the cash conversion assumption, no interest income on accumulated cash, no interim distributions, no management incentive plan dilution, and no transaction expenses at exit. It assumes entry cash of zero, so gross debt and net debt coincide at entry. Real structures are governed by the credit agreement, not by a formula.

Reference information only. Not legal, tax, or investment advice. Acquisition agreements, credit documents, and tax structures vary materially between transactions and jurisdictions; the mechanics described here are common patterns, not the terms of any particular deal. Worked examples use assumed inputs chosen to make the arithmetic verifiable, not to represent market levels. Consult counsel.

Text and data under CC BY 4.0. Reviewed 2026-08-27.