Private Equity puzzles, solved step by step

EBITDA rises from 96 to 117.1, a 22% increase, and the margin from 12% to 14.6%. Costs are 800 less 96, which is 704. A 3% cut saves 21.1, and with revenue fixed every rupee of it reaches EBITDA. Because costs are about 7.3 times EBITDA, a small cost change is a large profit change: 3% times 7.33 is 22%.

Why does a 3% cost cut grow EBITDA by 22%?

A family earning Rs 1 lakh a month and spending Rs 88,000 saves Rs 12,000. Trim spending by 3%, about Rs 2,640, and savings jump to about Rs 14,640, up 22%. Profit is the thin slice left after costs, so any change to the large cost base is magnified when measured against the small profit. The magnifier is the ratio of costs to EBITDA, here 704 over 96, about 7.3.

How does an operating partner use this, and where does it break?

Multiply by the exit multiple to see what it is worth. At 8x EBITDA, 21.1 of lasting savings adds about 169 of enterprise value, which is why cost programmes sit at the centre of so many buyout plans. The thinner the margin, the bigger the magnifier: at a 5% margin costs are 19 times EBITDA and a 3% cut lifts EBITDA by 57%.

Say the limitations. Not all of 704 can be cut: raw materials may be fixed by contract and wages by law, so the 3% often has to come from a much smaller part of the base. Cuts that hurt service can cost revenue later. And the same magnifier works in reverse: a 3% cost overrun would take 22% off EBITDA.

Levered free cash flow is 92.5. EBITDA is 250. Take off D&A of 40 and interest of 60 to get pre-tax profit of 150, tax of 37.5 and net income of 112.5. Add back the 40 of D&A because it is not cash, then subtract capex of 50 and the 10 of working capital the growth absorbs. What remains, 92.5, is cash the owners could take out.

Why does depreciation come off and then go back on?

Think of a delivery van bought last year. Each year the accounts charge a slice of its cost as depreciation, but no money leaves the business that year: the van was paid for already. Depreciation reduces taxable profit, which saves real tax, but it is not a cash payment, so it is subtracted to work out tax and then added back to reach cash. The cash cost of assets enters through capex instead, here 50, which is more than the 40 of depreciation because the business is growing.

What makes it levered, and why does a buyout investor want that version?

Levered means after interest: the lenders have been paid. Levered free cash flow is the cash left for the equity holders after the lenders, the taxman and the business's own reinvestment, which is exactly the cash that repays debt in a buyout. Check it a second way from EBITDA: 250 less 60 less 37.5 less 50 less 10 is 92.5. The limit worth saying: working capital is modelled here as 10% of growth, and a real business can swing by far more in a single year.

Contribution rises about 6.9%. On a price of 100 with variable cost of 60, each unit contributes 40. A 5% price rise adds 5 straight to that margin, making 45, a 12.5% rise. Selling 95 units at 45 gives 4,275 against 4,000 before. Volume would have to fall 11.1% before the price rise stopped paying.

Why does a 5% price rise beat a 5% volume loss?

A tea stall sells a cup for Rs 20 that costs Rs 12 to make, keeping Rs 8. Raise the price by Rs 1 and the stall keeps Rs 9: a 5% price rise is a 12.5% rise in what it earns per cup. A price increase falls entirely on the margin because variable cost does not change, so the lower the margin, the bigger the percentage boost. Here the margin is 40% of price, so a 5% price rise lifts contribution per unit by 5 divided by 40, 12.5%.

What would an operating partner check before raising prices?

The arithmetic says volume could fall 11.1% before this price rise lost money, so the real question is how customers respond. A business whose customers cannot easily switch can usually hold more than 89% of volume after a 5% rise; one in a crowded market with lookalike products may lose far more. Operating teams test price on one region or product line first. Revenue here actually falls 0.25%, which is why a revenue-only dashboard would wrongly call the move a failure.

The team needs 150 of new revenue at a 40% margin, and about 171 at 35%. A fixed cost is paid for out of contribution, and each rupee of revenue brings only 40 paise of it: 60 divided by 0.40 is 150. If the team wins sales by discounting and the margin falls to 35%, the hurdle rises to 60 divided by 0.35, about 171. Breakeven revenue moves from 750 to 900.

Why is the answer not simply 60?

A shop hires a helper for Rs 6,000 a month. If every Rs 100 of sales costs Rs 60 in stock, the helper must bring in Rs 15,000 of extra sales, not Rs 6,000, because only Rs 40 of each Rs 100 is left to pay wages. New fixed costs are paid out of contribution, so the revenue needed is the cost divided by the contribution margin. At 40%, 60 of cost needs 150 of revenue.

What would an operating partner ask before approving the hire?

Breakeven is the floor, not the case for the hire: the team should bring in well above 150 within a reasonable ramp, at a margin close to the existing 40%. Sales teams often win volume with discounts, which is exactly what drops the margin to 35% and lifts the hurdle to 171. The partner would also ask how long the ramp takes, because a team that needs a year to sell anything costs 60 before it earns a rupee.