The premium measured against the right reference price, then turned into the permanent cash flow the buyer must add to justify it.
A control premium is the offer price per share divided by the unaffected share price, minus one: 39.00 against an unaffected 30.00 is a 30.0 per cent premium, 180,000,000 on 20,000,000 shares. The useful second step converts that sum into the cash flow the buyer must add to justify it: at an 8.5 per cent WACC and 2.0 per cent growth, 11,700,000 a year after tax, or 15,600,000 before tax, every year, growing. That is 20.8 per cent of the target's EBITDA.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A percentage invites comparison with "typical" premiums, which settles nothing. A required cash flow can be set against a synergy plan line by line, and either the plan reaches it or it does not.
| Input | Value |
|---|---|
| Unaffected share price (before any rumour) | 30.00 |
| 30-day volume-weighted average price before announcement | 30.60 |
| Price the day before announcement (after a leak) | 33.00 |
| Offer price per share | 39.00 |
| Diluted shares | 20,000,000 |
| Net debt | 150,000,000 |
| EBITDA / revenue | 75,000,000 / 400,000,000 |
| WACC for the target's risk / perpetual growth / tax rate | 8.5% / 2.0% / 25% |
Step 1: choose the reference price. The premium is only meaningful against a price that does not already contain it. The same 39.00 offer measures three ways:
| Reference | Price | Premium |
|---|---|---|
| Unaffected price | 30.00 | 30.0% |
| 30-day VWAP | 30.60 | 27.5% |
| Day before announcement | 33.00 | 18.2% |
The day-before price has already run up 10.0 per cent on the leak. Measured from it, the premium looks like 120,000,000; the shareholders are actually being paid 180,000,000 over what the market thought the company was worth on its own.
Step 2: the premium in money and on enterprise value.
Premium = (39.00 − 30.00) × 20,000,000 = 180,000,000 = 30.0% of equity
On enterprise value: 930,000,000 / 750,000,000 − 1 = 24.0%, from 10.0x to 12.4x EBITDA
The premium is the same money either way; net debt, assumed at face, dilutes the percentage. Quote equity premiums against equity premiums and multiples against multiples.
Step 3: the cash flow the premium requires. Treat the premium as the price of a growing perpetuity of extra after-tax cash flow, and solve for the first year's amount.
After-tax cash flow = premium × (WACC − g) = 180,000,000 × 6.5% = 11,700,000
Pre-tax = 11,700,000 / (1 − 25%) = 15,600,000 = 20.8% of EBITDA = 3.90% of revenue
Excel: =Premium*(WACC-g)/(1-Tax), then divide by EBITDA and by revenue.
Paying 39.00 is a commitment to raise the target's EBITDA by about a fifth, permanently, from the first year, in synergies or improvements the target could not have achieved alone. Add 12,000,000 of transaction costs and the requirement is 16,640,000, 22.2 per cent. If the synergies only start in year three, the first payment has to be larger by 1.085 squared, or 1.1772: 18,364,710, 24.5 per cent of EBITDA.
Expressed as a share of revenue, 3.90 per cent, it can be checked against an integration plan: cost savings on procurement and overlap, revenue synergies with their own margin. If the plan, risked and net of the cost to achieve, does not reach it, the premium transfers value from the buyer's shareholders to the seller's. The net-of-cost test is worked in how to value synergies net of the cost to achieve them.
| Premium | Premium paid | From year one | % of EBITDA | From year three | % of EBITDA |
|---|---|---|---|---|---|
| 20% | 120,000,000 | 10,400,000 | 13.9% | 12,243,140 | 16.3% |
| 30% | 180,000,000 | 15,600,000 | 20.8% | 18,364,710 | 24.5% |
| 40% | 240,000,000 | 20,800,000 | 27.7% | 24,486,280 | 32.6% |
Each ten points of premium costs about 7 points of the target's EBITDA in permanent improvement. Two years of delay cost about as much as another five points of premium would.
Measure the premium against the unaffected price: 30.0 per cent, 180,000,000. Then turn it into the pre-tax cash flow it needs, 15,600,000 a year, 20.8 per cent of EBITDA, and test the synergy plan against that number. For the gap between a DCF and a transaction multiple, see why a DCF and a transaction multiple disagree. The free workbook for this book runs the same test on a full case, including the premium delayed and partly attributed to auction tension.
The price before rumours or leaks of the deal moved it, usually taken on a stated date before the first report. In the illustrative case it is 30.00, against 33.00 the day before announcement after a 10.0 per cent run-up. The 39.00 offer is a 30.0 per cent premium on the unaffected price but only 18.2 per cent on the leaked one.
They are the same gap seen from opposite ends. A 30.0 per cent premium on a minority price of 30.00 gives a control value of 39.00; seen from 39.00, the minority price is 23.1 per cent lower. Apply one or the other to the right reference value, never both, and never a premium to a value that already reflects control.
Convert it into the cash flow it requires: premium times WACC minus growth, grossed up for tax. A 180,000,000 premium at 6.5 per cent and 25 per cent tax needs 15,600,000 a year before tax, 20.8 per cent of EBITDA or 3.90 per cent of revenue, and then compare that with a risked synergy plan net of the cost to achieve it.
This article is one calculation from Business Valuation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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