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July 11, 2023

Drafting mathematical formulas in asset-backed lending agreements is an art form. It requires an understanding of both the legal and financial aspects of such agreements. As discussed in other blog posts, calculations are becoming more complex to determine payments, covenants, and other financial considerations. Lawyers need to craft agreements that accurately reflect the business agreement between the investor and borrower. In this blog post, we will explore the various techniques used for drafting mathematical formulas in asset-backed lending agreements and discuss the importance of accurately reflecting these mathematical concepts.

****As a result of lawyers turning relatively simple formulas into long-winded paragraphs that completely obscure the formula in the language, misinterpretations, and errors are common. Typically the misinterpretation/error is based on the arithmetic order of precedence (otherwise known as BEDMAS). Most people wouldn't be able to calculate equations without putting them in their typical mathematical notation, so why not do this in the legal agreement? They'd likely find the simplified formula quicker to read and easier to understand, with fewer mistakes and less time required there is no reason not to include mathematical formulas. It's also important that when writing out mathematical formulas the business team thoroughly reviews the formulas to ensure they make sense. The equations should be black and white with no areas of grey for misinterpretation.

****At Cascade, we keep a library of legal definitions and covenants built on these definitions, the library is available for any party to use. When we onboard debt facilities, if a calculation is required, we first turn it into a mathematical formula broken down into easy-to-digest pieces. We've found that doing so eliminates all the guesswork out of how exactly the calculation is managed. Often times during the process it becomes clear that there is some level of grey in the legal formula that needs to be negotiated.

****To help illustrate why Cascade believes mathematical formulas should be used whenever a calculation is entered into a loan agreement here is an excerpt of a legal text that got the formula wrong.

**Borrowing Base** means with respect to any Advance Date, the product of (a) the Advance Rate (b) the sum of the Eligible Pool Balance and (c) Cash.

As a formula this means:

Advance Rate * Eligible Pool Balance * Cash

**Borrowing Base** means with respect to any Advance Date, the product of (a) the Advance Rate and (b) the sum of the Eligible Pool Balance *plus* Cash

As a formula this means:

$$Advance Rate * (Eligible Pool Balance + Cash)

In the legal text the Borrower will probably never have a borrowing base deficiency as as they are multiplying the Eligible Pool Balance by Cash - so as long as they have some cash on hand the Eligible Pool Balance will be enormously inflated.

This mistake was so outrageous both parties knew it had to be amended, but in other cases when a simple mistake in order of precedence, the parties could end up in litigation over what the interpretation should be - which no one wants to do.