LBO Model: Method

LBO Model: How It Works

What it does

In a leveraged buyout (LBO) a buyer, usually a private equity fund, buys a company with a small part of its own money (equity) and a large part of borrowed money (debt) that the company itself owes. While the buyer owns the company, the company's cash repays the debt; after a few years the company is sold. The page computes what the buyer earns on its equity and shows where the gain comes from. Every step is printed as formula, numbers put in, answer.

The method

Symbols. EBITDA is earnings before interest, tax, depreciation and amortisation, a rough measure of the cash the operations earn in a year; EBITDA₀ is its value now and EBITDA_t its value in year t. m_b and m_x are the purchase and exit multiples of EBITDA; x_d the debt as a multiple of EBITDA; i_d the interest rate; g_E the yearly growth of EBITDA; c_v the cash conversion, the share of EBITDA left after tax, capital spending and working capital; N the years held. Rates are used as decimals: 8 % is 0.08.

Purchase. Price P₀ = m_b EBITDA₀; debt D₀ = x_d EBITDA₀; equity Eq₀ = P₀ − D₀. With fees and a minimum cash balance (Advanced) the uses are U₀ = P₀ + fees + cash and Eq₀ = U₀ − D₀. Sources (debt and equity) always equal uses.

Each year t = 1 … N.

EBITDA_t = EBITDA_t−1 (1 + g_E)
I_t = i_d D_t−1   (interest on the debt owed at the start of the year)
CF_t = c_v EBITDA_t − I_t   (cash left to repay debt)
D_t = D_t−1 − CF_t   (once the debt is gone, the cash builds up in the company)

Exit. Enterprise value EV_x = m_x EBITDA_N; net debt ND_x = debt − cash at the end of year N; equity Eq_x = EV_x − ND_x.

Return. Money multiple MOIC = Eq_x / Eq₀ (multiple of invested capital). The internal rate of return is the constant yearly growth rate that turns the equity invested into the equity received: IRR = MOIC^1/N − 1 when there is one payment in and one payment out.

Value-creation bridge. The gain Eq_x − Eq₀ is split into three parts that add up exactly:

EBITDA growth = (EBITDA_N − EBITDA₀) m_b
Change in multiple = (m_x − m_b) EBITDA_N
Debt paydown = D₀ − ND_x = CF₁ + … + CF_N

The first two add up to EV_x − P₀, the rise in the value of the business. Growth is valued at the purchase multiple and the change in multiple is applied to the exit EBITDA; this is the usual convention, and another (growth at the exit multiple) would move part of the gain from one to the other.

Advanced mode. Revenue and margin: revenue R_t = EBITDA_t / margin; tax = rate × max(EBITDA − depreciation − interest, 0); CF_t = EBITDA_t − tax − capital spending − working-capital investment − interest, the working-capital investment being a percent of the rise in revenue. Two loans: senior debt takes the scheduled repayment and, with the cash sweep, all cash above the minimum balance; subordinated debt pays interest only and is repaid at the exit. Management pool: management is taken to hold a fixed share p_m of the equity from the purchase, so the buyer receives (1 − p_m) of every payment to the owners. Dividend recapitalisation: at the end of an entered year the company borrows new senior debt and pays it to the owners. The buyer then has two receipts at different dates and the IRR is the rate r that solves −Eq₀ + Σ receipts_t / (1 + r)^t = 0, found by Newton's method from the starting value MOIC^1/N − 1. The bridge gains two negative parts, the fees and management's share.

What it assumes

• EBITDA grows at one constant rate and the company is sold at the end of a whole year for a multiple of that year's EBITDA.
• Interest is charged on the opening balance of each year at a fixed rate. Cash held by the company earns nothing.
• In Simple mode one percentage stands for tax, capital spending and working capital, and it does not change when the interest bill changes; the tax saved by interest is computed only in the Advanced revenue form.
• All spare cash repays debt (Simple mode). No dividends are paid before the exit unless a recapitalisation is entered.
• Fees are paid at the purchase and are not spread over later years; no costs are charged at the exit or on the recapitalisation.
• The management pool is a plain share of the equity, not options with a purchase price.
• The return is that of the deal, before the private equity fund's own management fee and share of profits.

When it misleads

• The exit multiple drives the answer and nobody knows it. The exit-multiple table on the results page shows how far the IRR moves for one turn of multiple. A model that assumes a higher exit multiple than the purchase multiple shows a gain that owes nothing to the business.
• Leverage cuts both ways. The leverage table uses the same growth in every row, so more debt always looks better. With falling EBITDA the same debt can leave nothing for the equity; the page reports that case instead of a return.
• A smooth growth path hides the bad year. Real debt has covenants (limits on debt / EBITDA and interest cover) that can be broken in one weak year even when the five-year average is fine. The model has no covenants and no default.
• IRR rewards speed, MOIC rewards size. A dividend recapitalisation raises the IRR by returning money early while adding debt to the company. Neither number alone describes a deal.
• The bridge is an accounting split, not a cause. "Debt paydown" is the company's own cash, which depends on its growth and margins; the three parts are not independent.

Worked example

The default case is an illustrative company, not a real one. EBITDA 100, bought at 10 times: price 1,000. Debt 5 times EBITDA = 500 at 8 %, so the equity is 500. EBITDA grows 5 % a year, 60 % of it is left as cash, and the company is sold after 5 years at 11 times EBITDA.

Year 1: EBITDA = 100 × 1.05 = 105.00; interest = 0.08 × 500 = 40.00; cash for debt = 0.6 × 105 − 40 = 23.00; debt = 500 − 23 = 477.00. Year 2: EBITDA 110.25, interest 38.16, cash 27.99, debt 449.01. Continuing the same way the debt is 415.47, 375.78 and 329.27 at the end of years 3, 4 and 5.

Exit: EBITDA₅ = 100 × 1.05⁵ = 127.63; EV_x = 11 × 127.63 = 1,403.91; equity = 1,403.91 − 329.27 = 1,074.64.

Return: MOIC = 1,074.64 / 500 = 2.15; IRR = 2.149^1/5 − 1 = 16.54 % a year.

Bridge: growth (127.63 − 100) × 10 = 276.28; multiple (11 − 10) × 127.63 = 127.63; debt paydown 500 − 329.27 = 170.73; total 574.64 = 1,074.64 − 500.

A calculator for education and analysis, not investment advice.