# Lehman Formula: Definition and Calculation Examples

## What Is the Lehman Formula?

The Lehman formula is a compensation formula developed by Lehman Brothers to determine the commission on investment banking or other business brokering services. Lehman Brothers developed the Lehman Formula, also known as the Lehman Scale Formula, in the 1960s while raising capital for corporate clients.

### Key Takeaways

• Lehman Brothers developed the Lehman formula to determine the commission an investment bank should receive for arranging client transactions. ​​​​​​
• Large investment banks work with corporations to raise capital, often through an initial public offering (IPO), a merger or acquisition, or through a spinoff.
• For their services, an investment bank can charge flat fees for each transaction, earn commissions based on the dollar amount of the transaction, or a combination of both.
• The Lehman formula structures the investment banking fee on a percentage of the transaction amount based on a set of tiered fees.

## Understanding the Lehman Formula

As a provider of global investment banking services, Lehman Brothers needed a way to clearly convey to its potential clients the fees they would charge for their services. The advantage of the Lehman formula is that it's easy to understand and easy for the client to quickly get a ballpark estimate on how much their transaction might cost them in fees. It's not uncommon for large investment banking firms to assist clients with transactions worth hundreds of millions or billions of dollars. The Lehman formula structures the investment banking fee on a percentage of the transaction amount with a set of tiered fees.

## How Investment Banks Earn Their Fees

Investment banks work with companies, governments, and agencies to raise money by issuing securities. An investment bank might help a company that has never issued stock to successfully complete its initial public offering (IPO). Other typical services that investment bankers provide include offering merger and acquisition (M&A) advice, developing reorganization strategies, or helping a company through a spinoff.

Investment banks make money in various ways. The can charge flat fees for each transaction, earn commissions based on the dollar amount of the transaction, or a combination of both. In the case of an IPO, an investment bank might provide underwriting services. The bank might buy stock in the IPO and then sell the shares to investors. The difference between what the bank purchased the IPO shares for and what they earn selling them to investors is the bank's profit.

Some investment banks that underwrite an IPO undertake the risk that they will not be able to sell the IPO shares for a higher price to investors, thus losing money on the trade.

## Examples of the Lehman Formula

The original structure of the Lehman Formula is a 5-4-3-2-1 ladder, as follows:

• 5% of the first $1 million involved in the transaction • 4% of the second$1 million
• 3% of the third $1 million • 2% of the fourth$1 million
• 1% of everything thereafter (above $4 million) Today and to keep up with inflation, investment bankers often seek some multiple of the original Lehman Formula, such as the double Lehman Formula. This structure is also more common in middle market transactions because of their complexity and longer close periods. • 10% of the first$1 million involved in the transaction
• 8% of the second $1 million • 6% of the third$1 million
• 4% of the fourth $1 million • 2% of everything thereafter (above$4 million)

## A Brief History of Lehman Brothers

Lehman Brothers was previously considered one of the major players in the global banking and financial services industries. However, on Sept. 15, 2008, the firm declared bankruptcy, largely due to its exposure to subprime mortgages. Lehman Brothers also had a reputation for short selling in the market.

A subprime mortgage is a type of mortgage that is normally issued by a lending institution to borrowers with relatively poor credit ratings. These borrowers will generally not receive conventional mortgages given their larger-than-average risk of default. Due to this risk, lenders will often charge higher interest rates on subprime mortgages.

Lenders began issuing NINJA loans—a step beyond subprime mortgages—to people with no income, no job, and no assets. Many issuers also required no down payment for these mortgages. When the housing market began to decline, many borrowers found their home values lower than the mortgage they owed. Interest rates associated with these loans (called "teaser rates”) were variable, meaning they started low and ballooned over time, making it very hard for borrowers to pay down the principal of the mortgage. These loan structures resulted in a domino effect of defaults.

The bankruptcy of Lehman Brothers was one of the largest bankruptcy filings in U.S. history. Although the stock market was in modest decline prior to these events, the Lehman bankruptcy, coupled with the prior collapse of Bear Stearns, significantly depressed the major U.S. indexes in late Sept. and early Oct. 2008. After the fall of Lehman Brothers, the public became more knowledgeable about the forthcoming credit crisis and the recession of the late 2000s.

Article Sources
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1. MergersCorp. "The Double Lehman Formula."

2. VentureFirst. "An Introduction to Success Fees and the Lehman Formula."

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