A 'repo 105', as used by Lehman Brothers, is a variant on a standard sale and repurchase agreement, or repo. A repo can be treated in two ways by a firm. If assets are genuinely sold, with just a small chance of being bought back later, then a sale is booked, the assets are taken off the balance sheet and no liability to repurchase them is recorded.
If the seller plans to repurchase the assets, they stay on the balance sheet along with any 'sales proceeds' and a matching liability is recorded. In short, the deal is treated as a secured loan rather than a sale. In Lehman's case, repos that were in reality loans were treated as sales. That way it improved its balance sheet leverage ratios ahead of quarterly results.
• Watch Tim Bennett's video tutorial: What is a repo?