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# Lehman Formula

The Lehman Formula is a formula to define the compensation a broker should receive when handling a large transaction for a client. The formula usually applies to the entire value of the transaction.The art of M&A financing and refinancing: a guide to sources and instruments for external growth. Alexandra Reed Lajoux, J. Fred (John Fred) Weston. McGraw-Hill Professional. ISBN 0070383030]

The formula

The Lehman Formula 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 million dollars involved in the transaction
*4% of the second million involved in the transaction
*3% of the third million involved in the transaction
*2% of the fourth million involved in the transaction
*1% of everything above 4 million dollars.

In recent years, due to inflation, the formula is often used as a multiple.

History

The formula was first developed in the early 1970s by the Lehman Brothers, for investment banking 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. Lehman Brothers: 1850-1984: a chronicle. Allan S Kaplan. New York: Lehman Brothers, 1985 OCLC: 36151691]

Since the creation, many brokers have informally adopted the same formula, since it is both fair and easy to use.

Usage

The Lehman Formula is only used when a large investment 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 dollars 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 dollars, 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.Financing Options. Edwin L. Miller, & Jeffrey P. Steele, Peter Barnes-Brown. Aspatore Press. ISBN 1596220112]

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 dollars 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 dollars, the total fee would be 1% of 50 million, or 500,000.

The TVA generates lower fees, and is used on transations over four million dollars, to entice high value investments to use their service. Also known as the Littlejohn formula when applied in a real estate context.

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.

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's small. However, rather than indexing the formula for inflation, most investment services ended up making adjustments to the formula to provide fee protection (and enhancement) for the first few million dollars of transaction value. Several other variants exist.

Double Lehman, dollar value

Some banks use a formula called the Double Lehman, on dollar value. Instead of 5% on the first \$1 million of value, the Double Lehman calls for 5% on the first \$2 million, 4% on the next \$2 million, and so forth. It doubles the values, and thus the name. For example, if an investor wished to sell 3 million dollars worth of stock, he would pay the broker he used a fee of 5%, or \$100,000, on the first 2-million dollars of transaction value, 4% (40,000) of the second 2-million (in this case, there is only \$1M left to calculate a commission on), and 3% of the third 2-million, for a total fee of \$140,000. [ cite book
last = Russell
first = Robb
series =
page = 115
year = 1997
doi =
isbn = 1558507027
]

Double Lehman, percentage

Yet another variation, mostly used by mid market M&A specialists and business brokers, is the Double Percentage Lehman. Under this variation, the intermediary is compensated based on 10% of the first \$1 million of value, 8% of the next \$1 million of value, down to 2% of the fifth \$1 million of value, and then 2% of value thereafter. Basically, it multiplies the percentages, rather than the amounts of cash. For example, if an investor wished to sell 3 million dollars worth of stock, he would pay the broker he used a fee of 10%, or \$100,000, on the first million dollars of transaction value, 8% (80,000) of the second million, and 6% (60,000)of the third million, for a total fee of \$240,000. On an investment of \$50 million dollars, the total fee would be \$1.2 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.The Watchdogs Didn't Bark: Enron and the Wall Street analysts. United States Congress U.S. G.P.O. ISBN 0160688639]

References

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