A weighted conclusion of value is only as good as the basis of the numbers going into it. Strip the control premium out first, then choose the weights on purpose.
Put every method on the same level of value first, then weight them explicitly. On an illustrative company with a $72.0m DCF, $68.0m from trading comparables and $85.0m from precedent transactions, a simple average gives $75.0m, but the transaction value carries a control premium the other two do not. Removed at 25 per cent, it falls to $68.0m, and a 50/30/20 weighting gives $70.0m, not $75.0m. The order matters more than the weights.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Most valuation reports end with a football field and a single number. The single number is usually a weighted average of the methods, and the weights are usually chosen in a meeting. Two things decide whether that number means anything: whether the values being averaged answer the same question, and whether the weights reflect how much each method can be trusted.
| Method | Point value | Low | High | Level of value |
|---|---|---|---|---|
| DCF on the standalone forecast | 72.0 | 62.0 | 84.0 | Standalone |
| Trading comparables, median multiple | 68.0 | 63.0 | 74.0 | Minority, marketable |
| Precedent transactions, median multiple | 85.0 | 77.5 | 93.8 | Control |
| Control premium embedded in the deals | 25% | |||
| Judgement weights: DCF, trading, transactions | 50 / 30 / 20 |
A DCF on the company's own forecast, without buyer synergies, values the business as it stands; that is broadly the basis of a trading multiple. Precedent transactions price the purchase of control, often with synergies paid away to the seller. The 25 per cent premium is an assumption: it should come from the deals in the set where it can be observed, and the control premium article shows what such a premium must earn to be justified.
Transactions, standalone = 85.0 ÷ 1.25 = 68.0; range 77.5 ÷ 1.25 = 62.0 to 93.8 ÷ 1.25 = 75.0
Premium removed = 85.0 − 68.0 = 17.0
Raw equal average = (72.0 + 68.0 + 85.0) ÷ 3 = 75.0
Adjusted equal average = (72.0 + 68.0 + 68.0) ÷ 3 = 69.3
The raw average is 5.7 higher, or 8.2 per cent, purely because one input answers a different question. If the purpose of the valuation is a control transaction, the fix is the reverse: gross the standalone values up to control. What is never right is mixing the two.
The judgement weighting puts half on the DCF, because the forecast is the best information available about this company, and less on the multiples, because the peer and deal sets are small.
Weighted value = 50% × 72.0 + 30% × 68.0 + 20% × 68.0
= 36.0 + 20.4 + 13.6 = 70.0
Excel: =SUMPRODUCT(Weights,AdjustedValues)/SUM(Weights)
The same weights applied to the raw values would give 73.4. The weights are the visible judgement; the basis adjustment is the invisible one, and here it moves the answer by more.
An alternative to weights chosen in a meeting is to weight each method by how precise it is, measured by the width of its own range. Treat each range as roughly four standard deviations wide and weight by the inverse of the variance.
| Method | Adjusted value | Range width | Implied sd | Weight | Contribution |
|---|---|---|---|---|---|
| DCF | 72.0 | 22.0 | 5.50 | 12.7% | 9.16 |
| Trading comparables | 68.0 | 11.0 | 2.75 | 50.9% | 34.59 |
| Transactions, standalone | 68.0 | 13.0 | 3.25 | 36.4% | 24.76 |
| Weighted value | 100% | 68.5 |
Precision weighting gives 68.5, with half the weight on the trading comparables and only 13 per cent on the DCF, because a DCF's range across plausible discount rates and growth rates is wide. That does not make it the right answer; a narrow range on a poor peer set is precise and wrong. But when the judgement weights and the precision weights point in opposite directions, as here, the report should say why the judgement wins. The DCF sensitivity table is where the DCF's range comes from.
| Premium removed | Transactions, standalone | Equal weights | 50/30/20 weights |
|---|---|---|---|
| 15% | 73.9 | 71.3 | 71.2 |
| 20% | 70.8 | 70.3 | 70.6 |
| 25% | 68.0 | 69.3 | 70.0 |
| 30% | 65.4 | 68.5 | 69.5 |
| 35% | 63.0 | 67.7 | 69.0 |
Across a 15 to 35 per cent premium the weighted value stays between 69.0 and 71.2. The answer is far less sensitive to the size of the premium than to whether it is removed at all.
The common mistake is to average the three methods as they come out of the models. A transaction multiple, a trading multiple and a DCF are three answers to three slightly different questions; averaging them produces a number that answers none. The second mistake is to report the point estimate without the overlap: here the three adjusted ranges overlap between 63.0 and 74.0, and that band is the most defensible statement the analysis supports.
Adjust first, weight second, and write down the reason for each weight. On the illustrative figures the conclusion is about $70.0m on a standalone basis, and about $87.5m if the same weighted value is grossed up for a 25 per cent control premium, compared with the $75.0m a raw average would have suggested for neither. The free workbook for this case sets three methods on one set of facts so that the spread between them is computed rather than drawn, and the article on why a DCF and a transaction multiple disagree takes one of those gaps apart. Figures are illustrative, not a valuation of any company.
Only after they are on the same basis. Transaction multiples include a control premium and often synergies; trading multiples reflect minority, marketable prices. In the illustrative case, the $85.0m transaction value falls to $68.0m once a 25 per cent premium is removed, and only that figure can be averaged with the $68.0m from trading comparables and the $72.0m DCF.
There is no standard. Weights should reflect the quality of the inputs: a DCF on a reliable five-year forecast deserves more than one built on a hockey stick, and a peer set of three loosely comparable companies deserves little. A judgement weighting of 50/30/20 on the illustrative values gives $70.0m; weighting by the precision of each method's range gives $68.5m, with 51 per cent on trading comparables.
Show the football field with each method's range, the adjustments that put them on a common basis, the weights and the reason for each weight. In the illustrative case, the three adjusted ranges overlap between $63.0m and $74.0m, which is a more honest summary than the $70.0m point estimate on its own.
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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