FASB’s CECL standard allows institutions to calculate their allowance for credit losses as either “the difference between the amortized cost basis and the present value of the expected cash flows” (ASC 326-20-30-4) or “expected credit losses of the amortized cost basis” (ASC 326-20-30-5). The first approach is commonly called the discounted cash flow or “DCF approach” and the second approach the “non-DCF approach.” In the second approach, the allowance equals the undiscounted sum of the amortized cost basis projected not to be collected. For the purposes of this post, we will equate amortized cost with unpaid principal balance.

A popular misconception – even among savvy professionals – is that a DCF-based allowance is always lower than a non-DCF allowance given the same performance forecast. In fact, a DCF allowance is sometimes higher and sometimes lower than a non-DCF allowance, depending upon the remaining life of the instrument, the modeled recovery rate, the effective interest rate (EIR), and the time from default until recovery (liquidation lag). Below we will compare DCF and non-DCF allowances while systematically varying these key differentiators.

Our DCF allowances reflect cash inflows that follow the SIFMA standard formulas. We systematically vary time to maturity, recovery rate, liquidation lag and EIR to show their impact on DCF vs. non-DCF allowances (see Table 1 for definitions of these variables). We hold default rate and voluntary prepayment rate constant at reasonable levels across the forecast horizon. See Table 2 for all loan features and behavioral assumptions held constant throughout this exercise.

For clarity, we reiterate that the DCF allowances we will compare to non-DCF allowances reflect amortized cost minus discounted cash inflows, per ASC 326-20-30-4. A third approach, which is unsound and therefore excluded, is the discounting of accounting losses. This approach will understate expected credit losses by using the interest rate to discount principal losses while ignoring lost interest itself.

Table 1 – Key Drivers of DCF vs. Non-DCF Allowance Differences (Systematically Varied Below)

 Variable Definitions and Notes Months to Maturity Months from reporting date until last scheduled payment Effective Interest Rate (EIR) The rate of return implicit in the financial asset. Per CECL, this is the rate used to discount expected cash flows when using the DCF approach and, by rule, is calculated using the asset’s contractual or prepay-adjusted cash flows. In this exercise, we set unpaid principal balance equal to amortized cost, so the EIR is the same assuming either contractual or prepay-adjusted cash flows and matches the instrument’s note rate. Liquidation Lag (Months) Months between first missed payment and receipt of recovery proceeds Recovery Rate Net cash inflow at liquidation, divided by the principal balance of the loan at the time it went into default. Note that 100% recovery will not include recovery of unpaid interest.

Table 2 – Loan Features and Behavioral Assumptions Held Constant

 Book Value on Reporting Date Par (Amortized Cost = Unpaid Principal Balance) Performance Status on Reporting Date Current Amortization Type Level pay, fully amortizing, zero balloon Conditional Default Rate (Annualized) 0.50% Conditional Voluntary Prepayment Rate (Annualized) 10.00%

Figure 1 compares DCF versus non-DCF allowances. It is organized into nine tables, covering the landscape of loan characteristics that drive DCF vs. non-DCF allowance differences. The cells of the tables show DCF allowance minus Non-DCF allowance in basis points. Thus, positive values mean that the DCF allowance is greater.

• Tables A, B and C show loans with 100% recovery rates. For such loans, ultimate recovery proceeds match exposure at default. Under the non-DCF approach, as long as recovery proceeds eventually cover principal balance at the time of default, allowance will be zero. Accordingly, the non-DCF allo­wance is 0 in every cell of tables A, B and C. Longer liquidation lags, however, diminish present value and thus increase DCF allowances. The greater the discount rate (the EIR), the deeper the hit to present value. Thus, the DCF allowance increases as we move from the top-left to the bottom-right of tables A, B and C. Note that even when liquidation lag is 0, 100% recovery still excludes the final month’s interest, and a DCF allowance (which reflects total cash flows) will accordingly reflect a small hit. Tables A, B and C differ in one respect – the life of the loan. Longer lives translate to greater total defaulted dollars, greater amounts exposed to the liquidation lags, and greater DCF allowances.
• Tables G, H and I show loans with 0% recovery rates. While 0% recovery rates may be rare, it is instructive to understand the zero-recovery case to sharpen our intuitions around the comparison between DCF and non-DCF allowances. With zero recovery proceeds, the loans produce only monthly (or periodic) payments until default. Liquidation lag, therefore, is irrelevant. As long as the EIR is positive and there are defaults in payment periods besides the first, the present value of a periodic cash flow stream (using EIR as the discount rate) will exceed cumulative principal collected. Book value minus the present value of the periodic cash flow stream, therefore, will be less than than the cumulative principal not collected, and thus DCF allowance will be lower. Appendix A explains why this is the case. As Tables G, H and I show, the advantage (if we may be permitted to characterize a lower allowance as an advantage) of the DCF approach on 0% recovery loans is greater with greater discount rates and greater loan terms.
• Tables D, E and F show a more complex (and more realistic) scenario where the recovery rate is 75% (loss-given-default rate is 25%). Note that each cell in Table D falls in between the corresponding values from Table A and Table G; each cell in Table E falls in between the corresponding values from Table B and Table H; and each cell in Table F falls in between the corresponding values from Table C and Table I. In general, we can see that long liquidation lags will hurt present values, driving DCF allowances above non-DCF allowances. Short (zero) liquidation lags allow the DCF advantage from the periodic cash flow stream (described above in the comments about Tables G, H and I) to prevail, but the size of the effect is much smaller than with 0% recovery rates because allowances in general are much lower. With moderate liquidation lags (12 months), the two approaches are nearly equivalent. Here the difference is made by the loan term, where shorter loans limit the periodic cash flow stream that advantages the DCF allowances, and longer loans magnify the impact of the periodic cash flow stream to the advantage of the DCF approach.

Figure 1 – DCF Allowance Relative to Non-DCF Allowance (difference in basis points) Conclusion

• Longer liquidation lags will increase DCF allowances relative to non-DCF allowances as long as recovery rate is greater than 0%.
• Greater EIRs will magnify the difference (in either direction) between DCF and non-DCF allowances.
• At extremely high recovery rates, DCF allowances will always exceed non-DCF allowances; at extremely low recovery rates, DCF allowances will always be lower than non-DCF allowances. At moderate recovery rates, other factors (loan term and liquidation lag) make the difference as to whether DCF or non-DCF allowance is higher.
• Longer loan terms both a) increase allowance in general, by exposing balances to default over a longer time horizon; and b) magnify the significance of the periodic cash flow stream relative to the liquidation lag, which advantages DCF allowances.
• Where recovery rates are extremely high (and so non-DCF allowances are held low or to zero) the increase to defaults from longer loan terms will drive DCF allowances further above non-DCF allowances.
• Where recovery rates are moderate or low, the increase to loan term will lower DCF allowances relative to non-DCF allowances.

Note that we have not specified the asset class of our hypothetical instrument in this exercise. Asset class by itself does not influence the comparison between DCF and non-DCF allowances. However, asset class (for example, a 30-year mortgage secured by a primary residence, versus a five-year term loan secured by business equipment) does influence the variables (loan term, recovery rate, liquidation lag, and effective interest rate) that drive DCF vs. non-DCF allowance differences. Knowledge of an institution’s asset mix would enable us to determine how DCF vs. non-DCF allowances will compare for that portfolio.

Appendix A:

The present value of a periodic cash flow stream, as discounted per CECL at the Effective Interest Rate (EIR), will always exceed cumulative principal collected when the following conditions are met: recovery rate is 0%, EIR is positive, and there are defaults in payment periods other than the first.

To understand why this is the case, note that the difference between the present value of cash flows and cumulative principal collected has two components: cumulative interest collected, which accrues to the present value of cash flows but not cumulative principal collected, and the cumulative dollar impact of discounting future cash flows, which lowers present value but does not touch cumulative principal collected. The present value of cash flows will exceed cumulative principal collected when the interest impact exceeds the discounting impact. The interest impact is always greater in the early months of a loan forecast because interest makes up a large share of total payment and value lost to discounting is minimal. As the loan ages, the interest share diminishes and the discount impact grows. In the pristine case, where book value equals unpaid principal balance and defaults are zero, the discount effect will finally catch up to the interest effect with the final payment. The present value of the total cash flow stream will thus equal the cumulative principal collected and equal the beginning unpaid principal balance. If there are any defaults in periods later than the first, however, the discount effect can never fully catch up to the interest effect. Table 3 provides one such example.

Table 3 – Cash Flow, Principal Losses, Present Value and Allowance under 0% Recovery

Loan Features and Assumptions:

• Reporting-date amortized cost and unpaid principal balance = \$10,000
• 5-year, annual-pay, fully amortizing loan
• Fixed note rate (and effective interest rate) of 4%
• 10% conditional voluntary prepayment rate, 0.50% conditional default rate, 0% recovery rate DCF allowance = \$10,000 − \$9,872 = \$128

Non-DCF allowance = Sum of Principal Losses = \$134

We make the following important notes:

• First-period defaults effectively make the loan a smaller-balance loan and will not cause a difference between the DCF allowance and non-DCF allowance; only defaults subsequent to the first period will drive a difference between the two approaches.
• Interest-only loans will exacerbate the advantage of DCF allowances relative to non-DCF allowances.
• For floating-rate instruments, a projected change in coupon rate (based on the known level of the underlying index as of the reporting date) does not change the fact that DCF allowance will be lower than non-DCF allowance if the conditions of 0% recovery rate, positive EIR, and presence of non-first-period defaults are met.

Finally, the discounting approach under CECL is different from that used in finance to assess the fundamental value of a loan. A loan’s fundamental value can be determined by discounting its expected cash flows at a market-observed rate of return (i.e., the rate that links recent market prices on similar-risk instruments to the expected cash flows on those instruments.) As we have noted in other blogs, CECL’s DCF method does not produce the fundamental value of a loan.

 We see just one case in Figure 1 that appears to be an exception to this rule, as we compare the lower-right corner of Table D to the lower-right corner of Table E. What happens between these two cells is that the DCF allowance grows from 36.8 basis points in Table D to 58.9 basis points in Table E (a 60% increase in ratio terms), while the non-DCF allowance grows from 28.4 basis points in Table D to 50.1 basis points in Table E (a 77% increase in ratio terms). Because the allowances rise in general, the subtractive difference between them increases, but we see more rapid growth of the non-DCF allowance as we continue moving from the lower-right corner of Table E to the same corner of Table F. 