The minority discount is the control premium read backwards, and it compounds with the marketability discount rather than adding to it.
The discount for lack of control is the control premium seen from the other side: DLOC = 1 − 1 / (1 + control premium). A 30 per cent control premium is therefore a 23.08 per cent discount for lack of control, not 30 per cent. Combined with a 25 per cent marketability discount, the two compound to 42.31 per cent, so a 20 per cent stake in a company worth 50,000,000 on a control basis is worth 5,769,231, not the 5,192,308 that adding the discounts gives.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A shareholder holds 20 per cent of a fictional private company. An income-approach valuation, built on cash flows a controlling owner could direct, puts the whole equity at 50,000,000 on a control, marketable basis. The stake carries no board seat and no veto, and there is no market for it. All inputs are illustrative.
| Input | Value |
|---|---|
| Equity value, control and marketable basis | 50,000,000 |
| Stake held | 20% |
| Control premium observed in comparable transactions | 30% |
| Discount for lack of marketability | 25% |
A control premium is measured upwards from the minority price: control value = minority value × (1 + CP). Going back down, the minority value is the control value divided by 1.30, so the discount is measured from the higher base.
DLOC = 1 − 1 / (1 + CP) = 1 − 1 / 1.30 = 1 − 0.7692 = 23.08%
Excel: =1-1/(1+CP)
The same arithmetic gives 16.67 per cent for a 20 per cent premium and 28.57 per cent for 40. The discount is always smaller than the premium it comes from.
Pro rata control value = 50,000,000 × 20% = 10,000,000
Marketable minority = 10,000,000 × (1 − 23.08%) = 7,692,308
Non-marketable minority = 7,692,308 × (1 − 25%) = 5,769,231
Combined discount = 1 − (1 − 23.08%) × (1 − 25%) = 42.31%
| Level | Whole company | 20% stake |
|---|---|---|
| Control, marketable | 50,000,000 | 10,000,000 |
| Minority, marketable | 38,461,538 | 7,692,308 |
| Minority, non-marketable | 28,846,154 | 5,769,231 |
The order matters for the logic, not the arithmetic: multiplication commutes, so either sequence gives 5,769,231. What matters is that each discount is applied to the level of value it was measured against. Marketability discounts are typically evidenced from restricted stock and pre-IPO studies, whose reference point is a freely traded minority share, so the DLOM belongs after the DLOC, on the marketable minority value.
The DLOC is only needed because the 50,000,000 was a control value. Valuation methods do not all land at the same level:
That last point is why many practitioners now argue that the control premium, and hence the DLOC, is mostly a statement about cash flows rather than a fixed percentage: a minority holder cannot capture the improvements a controlling owner could make, so either the cash flows are adjusted or the discount is, never both.
| Control premium | DLOC | DLOM 15% | DLOM 25% | DLOM 35% |
|---|---|---|---|---|
| 20% | 16.67% | 29.17% / 7,083,333 | 37.50% / 6,250,000 | 45.83% / 5,416,667 |
| 30% | 23.08% | 34.62% / 6,538,462 | 42.31% / 5,769,231 | 50.00% / 5,000,000 |
| 40% | 28.57% | 39.29% / 6,071,429 | 46.43% / 5,357,143 | 53.57% / 4,642,857 |
The marketability discount moves the answer more than the control premium does across these ranges, and it is also the harder of the two to evidence. The limits of that evidence are worked in whether a 30 per cent marketability discount can be evidenced.
Using the premium as the discount. Applying 30 per cent instead of 23.08 values the marketable minority stake at 7,000,000 instead of 7,692,308: 692,308 too low, 9.0 per cent.
Adding the discounts. 23.08 plus 25 is 48.08 per cent, which gives 5,192,308 against 5,769,231: 576,923 too low, 10.0 per cent. Discounts compound because each applies to what is left after the previous one.
Discounting twice for control. Taking a value from public company multiples, which is already minority, and then applying the DLOC anyway gives 4,437,870, 1,331,361 or 23.1 per cent below the defensible figure. This is the most expensive of the three and the most common in a dispute between shareholders, because it looks conservative.
The book converts a 26.8 per cent control premium into the perpetual after-tax cash flow it requires, in the free workbook for this case; the premium side of the same arithmetic is in how to calculate a control premium, and what it must earn.
DLOC = 1 - 1 / (1 + CP), where CP is the control premium. Because the premium is measured up from the minority value and the discount down from the control value, the discount is always smaller: a 20 per cent premium is a 16.67 per cent discount, 30 per cent is 23.08, and 40 per cent is 28.57.
No, they compound. Combined discount = 1 - (1 - DLOC) x (1 - DLOM). With a 23.08 per cent DLOC and a 25 per cent DLOM the combined discount is 42.31 per cent, not 48.08. On a 10,000,000 pro rata stake, adding them understates the value by 576,923, 10.0 per cent.
When the starting value is already a minority value. Guideline public company multiples come from minority trades, so they give a marketable minority value directly. Applying a 23.08 per cent DLOC on top double-counts the lack of control and, in the illustrative case, understates a 20 per cent stake by 1,331,361, 23.1 per cent.
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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