How To Use NPV for Loans and Get Our Free NPV Calculator

RELATIONSHIP PROFITABILITY
RELATIONSHIP PROFITABILITY

We were recently working to close a commercial loan when the lender officer paused the closing.  He did not want his bank to spend legal fees to clarify some tax-transfer issues (costs which the borrower also refused to cover).  The legal bill would be between $2 and $3k.  We asked the lending officer to calculate the legal costs versus the loan’s net present value (NPV) of income – the lender gave us a puzzled look.  We quickly calculated the lifetime income of the loan versus the legal fees for the lender, and the lender proceeded to close the loan within two days. In this article, we discuss the value of knowing the NPV for any investment and provide you with our NPV calculator in order to save you time.

 

Lifetime NPV of Income

We find it surprising that many banks still do not calculate a loan’s NPV of income, but it is a valuable measure to quantify for every credit.  Even if your bank uses a sophisticated risk-adjusted return on capital (RAROC) relationship profitability model, such as Loan Command (which is based on NPV), the lifetime NPV of income is another benchmark that every banker should consider. 

We created such a model, and you can download it HERE.

What is NPV

The lifetime NPV of income is the net present value of cash inflows for the expected life of a loan, netting out direct and indirect costs (including credit charge, but not cost of capital).  The lifetime NPV of income for the loan discussed above is calculated at $49k.  Therefore, covering approximately $3k of legal costs made sense for the lender (even if the borrower should have paid for this cost directly). 

The lifetime NPV of income is calculated as NIM plus fees earned, minus COF, minus credit charge (expected loss), minus maintenance cost, minus upfront acquisition costs.  This calculation can demonstrate insight that ROE and ROA measures do not. For example, the ROE on a loan can be 20%, but if the NPV of income is only $1k, then the bank spending $3k in legal costs creates a highly unprofitable loan.  The lifetime NPV is important because it measures the total profit to the bank after all charges (except capital costs) for the life of the loan.  However, the measure is even more profound because it also highlights the essential variables that make lending profitable and those variables that can easily make loans unprofitable.

What Drives Loan Profitability

We used our model to run scenarios with NPV of income as the output variable testing various input variables to identify key drivers in profitability.  The results are exciting and maybe surprising to some.

 First, we looked at how loan size determines the NPV of income.  The relationship is shown in the graph below. 

Net Present Value

 

Most commercial banks cannot book positive NPV loans under $500k in size (unless the sourcing and underwriting are automated or highly optimized).  The reason for this relationship is that most banks have a high cost of loan acquisition – the direct and indirect acquisition costs are related to lending activity, underwriting activity, branch costs, and executive and corporate costs.  The average community bank’s costs of acquiring a new commercial loan are about $9k (but can range from $5k to $25k depending on the complexity and size of the credit and competition).  Our modeling demonstrates that size matters when measuring lifetime NPV of income.

Second, we looked at loan yield and NPV of income.  The relationship is shown in the graph below.

Net Present value of a loan

 

There is a linear relationship between yield and NPV of income.  However, we all know that banks are not free to set the loan rate where they choose, as borrowers have other options.  The biggest detractor from a higher yield on loans is the credit charge -  if borrowers are willing to pay more for the credit, it is because credit quality is inferior (probability of default is higher, or loss-given default is higher).  When adjusted for credit charge, higher-yielding loans are less profitable for the bank than lower-yielding loans.  The graph below shows the reality of loan yield adjusted for credit charges in a competitive loan market.

Net present value of a loan

 

The graph shows that because the market is relatively efficient in pricing credit risk, higher-yielding loans, on average, actually result in lower NPV of income because of the credit charge.  Every banker will point to an anomaly arguing against this case, but in the long run and through credit cycles, this relationship holds.

Third, we looked at loan terms and NPV of income.  The relationship is shown in the graph below.

Net present value of a loan

 

This is the most surprising discovery for some bankers.  Most lenders and underwriters have been conditioned to prefer shorter loan maturities (for some good and some not so good reasons).  Bankers correctly prefer relationship customers versus transaction customers; it is not surprising then that the term of the relationship dictates the NPV of income.  Longer credits commitments generate more NPV of income for the following reasons: 

  • More earning over a longer number of years (captured in the graph above);.
  • More cross-sell opportunities;
  • More growth with the customer (upsell opportunities);
  • Less need for banks to spend the upfront costs that are required to replace existing customers.

Conclusion

If your bank uses a sophisticated RAROC model, be sure to pay attention to the lifetime NPV of income as it will reveal details about the loan that the ROE or ROA may not.  If your bank does not use a RAROC model yet, be sure to inquire about our low-cost Loan Command model, or at least make sure to quantify lifetime NPV of income – our calculator is a good starting point.