Paper LBO: Revenue grows by $10 every year and EBITDA margins are constant. Company is bought at 10x at 5x debt, sold at 10x in 5 years. There’s a 10% interest rate and a 40% tax rate. D&A is flat throughout at $15/year, and capex is equal to D&A. There are no transaction fees or changes in net working capital. Assume no debt is paid off until the end, cash is accumulated until the final debt repayment at year 5 when the company is sold. Revenue in year 0 is $100, and COGS is $50 while SG&A is $20. Round all numbers. What’s the IRR?

EBITDA in year 0 = revenue – COGS – SG&A = $100 – $50 – $20 = $30

Since the company is bought at 10x:
Enterprise value = EBITDA x entry multiple = $30 x 10 = $300

With debt of 5x, we borrow 5 x $30 = $150, so the other $150 is funded by equity.

Levered free cash flow in the first year is:
LFCF (yr 1)= Revenue x EBITDA margin % – D&A – interest – taxes + D&A – capex – changes in NWC= ($110 x 30% – 15) * (1-40%) + 15 -15 = $11

Since revenue is going up linearly at $10 per year and costs are either constant or constant as a % of revenue, we can just find the average levered free cash flow, which is just the average between year 1 and year 5 levered free cash flow.

LFCF (yr 5) = ($150 x 30% – 15) * (1-40%) + 15 -15 = $18

Average LFCF = ($11 + $18) / 2 = $15

Cash accumulated = $15 x 5 years = $75

Ending enterprise value = last year EBITDA x exit multiple = $150 x 30% x 10 = $450
Ending equity value = ending enterprise value – ending debt + ending cash = $450 – $150 + $75 = $375
Multiple of capital = ending equity investment / beginning equity investment = $375 / $150 = 2.5x
IRR = multiple of capital ^ ( 1/# of years) – 1 = 2.5 ^ (1/5) -1 = 20%