Background
The most significant complaint we hear from bankers regarding in-house and third party pricing models is that they don’t work well on small loans. Bankers get frustrated because no matter what rate assumption they put into their model, the loan never meets the bank’s ROE target levels. In this article, we’ll explain how loan profitability is calculated within a pricing model and how a properly calibrated system allows lenders to be competitive regardless of loan size.
Let’s first take a look at how pricing models calculate the profitability of loans. Below is a typical income statement.
An analysis of this income statement illustrates that the majority of line items have the same profitability impact for all loan sizes. In other words, these line items scale with loan size. This includes interest income, interest expense, fee income (in most cases), provision expense, and taxes. The only line item that has a different profitability impact for different loan sizes is the expense allocation. Most likely, it is this assumption that is causing the heartburn when analyzing small loans.
Expense Allocation
The best pricing model implementations generally include a detailed expense allocation study. In these studies, 100% of the institution’s non-interest expenses are distributed among its product lines. A percentage of each expense is allocated to loan, deposit, and treasury management products and further divided into origination, variable servicing, and fixed overhead categories.
After all expenses are allocated, an average cost per account can be calculated based on the number of accounts serviced within each product line. The following table shows an example of the average costs per account.
After the expense allocation study is complete, the results can be loaded into your pricing model for use on all new loan analyses going forward. By allocating expense on a “dollar per account” basis, you will see an inversely proportional relationship between loan size and the profitability impact of the expense assumptions. The following chart shows this relationship.
The smaller the loan, the larger the profitability impact of expenses. The larger the loan, the smaller the impact of expenses. This creates issues within a pricing model.
First of all, institutions typically apply a single numeric ROE target within their pricing models. It is impossible for a smaller loan to attain the same level of ROE as a larger loan assuming similar pricing and structure. This is due to the expenses allocated to each loan that negatively impact the smaller loan more than the larger loan. Therefore, we suggest using a matrix of ROE targets based on product type and loan size tranches. Your expense allocation study will give you vital insights into the current ROE levels of your existing portfolio by product line and account size. You should use this as the basis for creating your pricing model ROE target matrix. The following is an example target matrix.
In addition, institutions typically do not adjust the average cost per account data based on the effort it requires to originate and service loans of various sizes. If there are procedures in place to streamline the origination of smaller loans, then it makes sense to reduce the cost per account assumptions in your pricing model to reflect this. On the flip side, if there is a size threshold for loans to go through the full approval process, including full credit underwriting and loan committee review, it is then reasonable to increase the cost per account in your pricing model for larger loans.
There are alternatives to the cost per account allocation method. Some institutions decide to allocate either a portion or all of their expenses as a percentage of loan amount. By making this change, the expense allocation assumptions will have the same profitability impact on all loan sizes. The question you need to ask is whether a $1mm loan should get ten times the cost as a $100k loan. In a similar manner, some institutions opt to ignore cost allocations in their pricing model entirely. By doing this, the institution has decided to manage the profitability of their loans at the net interest margin level with small adjustments for fees and credit quality. Both of these methods generally force institutions to adjust their ROE targets higher to compensate for not fully allocating expenses.
Summary
If you have implemented a pricing model and are getting frustrated with the analysis on smaller loans, the first place to look is your expense allocation assumptions. Your model should allow you full control over these assumptions and it is vital to perform a fully allocated cost allocation study to ensure your model is properly calibrated. Once this is completed, you can adjust ROE targets based on loan size tranches to ensure smaller loans are being analyzed fairly, accurately, and competitively.
