# 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%