# Lehman Formula

The Lehman Formula, also known as the Lehman Scale, is a formula to define the compensation a bank should receive when handling a large underwriting or stock brokerage transfer transaction for a client. The formula usually applies to the entire value of the stock.[1]

## Formula

The Lehman formula is a formula used by investment banks for the raising of capital for a business, either in public offerings or private placements, and is normally payable by the vendor(s) of the business once the funds have cleared. It deals with amounts greater than a million dollars. Below this mark, brokerage services and investment banks usually offer a set of tiered fees, or set-rate trading prices (such as \$9.95 per trade).

Above a million dollars, the following is the Lehman Formula as originally described:

• 5% of the first \$1 million raised from investors
• 4% of the second \$1 million raised from investors
• 3% of the third \$1 million raised from investors
• 2% of the fourth \$1 million raised from investors
• 1% of everything above \$4 million raised from investors.

The Lehman Formula was widely used in the 1970s, 1980s and 1990s but no longer used. In recent years, due to inflation, a multiple of the formula is often used instead. For example, 5% of the first \$10 million, plus 4% of the next \$10 million is a common formula.[1]

## History

The formula was first developed in the early 1970s by the Lehman Brothers, for underwriting and capital raising services. Before this, the charge would vary wildly from institution to institution. In some cases, the charges exceeded 15%. The Lehman Brothers created a formula to apply to the dollars in terms of total capital of a transaction, rather than a larger share of equity dollars.[2]

## Usage

The Lehman Formula was only used when a large stock investment transaction is made with an investment bank or institutional broker. It is used in two different ways, either counting each million dollars of value separately, or all at one time.

### By million dollar amount method (MDA)

The MDA method is the original formula, and applies each percentage to its own bracket. For example, if an investor wished to sell \$3 million worth of stock, he would pay the broker he used a fee of 5%, or \$50,000, on the first million dollars of transaction value, 4% (40,000) of the second million, and 3% (30,000)of the third million, for a total fee of \$120,000. On an investment of \$50 million, the total fee would be \$600,000.

The MDA tends to generate the highest fees, and is usually used when the transaction is under 4 million, to generate the most money.[3]

### By total value amount (TVA)

The TVA basically applies the percentage fee that fits the highest dollar value. For example, if an investor wished to sell \$3 million worth of stock, he would pay the broker he used a fee of 3% of three million dollars, or \$90,000. On an investment of \$50 million, the total fee would be 1% of 50 million, or 500,000.

### By pertinent value amount (PVA)

The PVA works exactly like the TVA until the transaction exceeds 4 million. It then charges 2% of the first four million, and 1% of everything beyond that.[3]

## Variants due to inflation

One problem with the Lehman Formula is inflation. A five million dollar deal was significant when the formula was designed in the 1960s, but today it is small. However, rather than indexing the formula for inflation, most investment services ended up making adjustments to the formula to provide fee protection for the first few million dollars of transaction value.

### Double Percentage Lehman and Double Lehman

A typical variation, mostly used by mid market M&A specialists and business brokers, is the Double Percentage Lehman (not to be confused with the Double Lehman). Under this variation, the intermediary is compensated based on 10% of the first \$1 million of value, 9% of the next \$1 million of value, etc., however holding constant when the percentage reaches 3%. Basically, therefore, in common usage, "Lehman" now multiplies the percentages, rather than the amounts of cash, to strike a fair balance between client and adviser.

For example, if an investor wished to sell \$3 million worth of stock, he would pay the broker he used a fee of 10%, or \$100,000, on the first \$1 million of transaction value, 9% (\$90,000) of the second million, and 8% (\$80,000)of the third million, or \$270,000 in total. This compensates the intermediary fairly for work on smaller dollar values.

A related variant is the Double Lehman Formula, which omits the odd-numbered percents:

• 10% of the first \$1 million, plus
• 8% of the second \$1 million, plus
• 6% of the third \$1 million, plus
• 4% of the fourth \$1 million, plus
• 2% of everything above \$4 million.

### Other Variations

For larger transactions, it is common for bulk of the fee payments to be in the form of retainers and ongoing fees. The percentage numbers can also be highly variable. While Lehman and Double Lehman are in common use, sometimes they are tripled.[4]