# LO 35.7: Define and calculate the delinquency ratio, default ratio, monthly

LO 35.7: Define and calculate the delinquency ratio, default ratio, monthly payment rate (M PR), debt service coverage ratio (D SC R ), the weighted average coupon CWAC), the weighted average m aturity fWAM), and the weighted average life fWAL) for relevant securitized structures.
As described previously, the delinquency ratio, default ratio, and monthly payment rate (MPR) serve as triggers to signal early amortization of the receivables pool for an ABS.
Example: Delinquency ratio, default ratio, monthly payment rate
Suppose an ABS has a total outstanding balance of credit card receivables of $57,800,000.$49,900,000 of the total receivables are current, $5,750,000 of the receivables are over 30 days past due,$1,270,000 of the receivables are over 60 days past due, and $880,000 are over 90 days past due. In addition,$1,100,000 of receivables were written off. Total monthly principal and interest payments per month are $1,560,000. Calculate the delinquency ratio, default ratio, and monthly payment rate for this ABS. Answer: The delinquency ratio 1.522%, computed by dividing the value of credit card receivables over 90 days past due by the total credit card receivables pool ($880,000 / $57,800,000). The default ratio is 1.903%, calculated by dividing the amount of written off credit card receivables by the total credit card receivables pool ($1,100,000 / $57,800,000). The monthly payment rate (MPR) is 2.699%, calculated as the percentage of monthly principal and interest payments divided by the total credit card receivables pool ($1,560,000 /$57,800,000). M B S Performance Tools The debt service coverage ratio (DSCR), weighted average coupon (WAC), weighted average maturity (WAM), and weighted average life (WAL) are performance tools used to analyze MBS. The debt service coverage ratio (DSCR) is calculated by dividing net operating income (NOI) by the total amount of debt payments. Net operating income is the income or cash flows that are left over after all of the operating expenses have been paid. The DSCR is a performance tool that measures the ability of a borrower to repay the outstanding debt associated with commercial mortgages. A DSCR less than one indicates that the underlying asset pool of commercial mortgages do not generate sufficient cash flows to cover the total debt payment. Total debt service refers to all costs related to servicing a companys debt. This often includes interest payments, principal payments, and other obligations. As investors confidence levels in the securitization increase, the required DSCR decreases, and vice versa. For residential mortgages, this ratio is typically between 2.5 and 3.0. However, higher DSCR are needed with more risky receivables where the value of the receivables is highly discounted in the event of a default. Page 290 2018 Kaplan, Inc. Topic 35 Cross Reference to GARP Assigned Reading – Choudhry, Chapter 12 Example: Debt service coverage ratio Suppose an MBS has net operating income from commercial mortgaged properties equal to$89,572,500. The total debt payments for notes issued against these mortgages is equal to $87,958,000. Calculate the debt service coverage ratio (DSCR). Answer: The DSCR is equal to 1.02, calculated as$89,572,500 / $87,958,000. A DSCR greater than one implies that there is sufficient cash flows generated from the underlying mortgage pool to meet debt payments. However, this is a very low DSCR for mortgages. The weighted average coupon (WAC) is calculated by multiplying the mortgage rate for each pool of loans by its loan balance and then dividing by the total outstanding loan balance for all pools. Thus, it measures the weighted coupon of the entire mortgage pool. The WAC is compared to the net coupon payable to investors as an indication of the mortgage pools ability to pay over the outstanding life of the MBS. Example: Weighted average coupon Suppose an MBS is composed of three different pools of mortgages:$6 million of mortgages that yield 7.8%, $10 million of mortgages that yield 6.0%, and$4 million of mortgages that yield 5%. Calculate the weighted average coupon (WAC).
The WAC is calculated as follows:
WAC = [0.078(6 million) + 0.06(10 million) + 0.05(4 million)] / (6 million +10 million
+ 4 million)
= (0.468 million + 0.6 million + 0.2 million) / 20 million = 1.268 million / 20 million = 0.0634 or 6.34%
If notes issued by the SPV are for 5.5%, for example, then an excess spread will be generated if there are no defaults on the original mortgages.
The weighted average maturity (WAM) is the weighted average months remaining to maturity for the pool of mortgages in the MBS. To calculate the WAM, the weight of each MBS pool is multiplied by the time until maturity of each MBS pool, and then all the values are added together. (Note that the weight is determined by taking the total value of the pool for one maturity and dividing that by the total value of all loans.)
2018 Kaplan, Inc.
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Topic 35 Cross Reference to GARP Assigned Reading – Choudhry, Chapter 12
The volatility of an MBS is directly related to the length of maturity of the underlying securities. The WAM is calculated based on stated maturity dates or reset dates. A WAM calculated based on stated maturity dates includes the liquidity risk of all mortgage securities in the portfolio by using the actual maturity date. A WAM calculated based on reset dates captures the effect of prepayments on the maturity of the loans.
Example: Weighted average maturity
Suppose an MBS is composed of three different pools of mortgages: $6 million of mortgages that have a maturity of 180 days,$10 million of mortgages that have a maturity of 360 days, and $4 million of mortgages that have a maturity of 90 days. Calculate the weighted average maturity (WAM). Answer: The WAM is calculated as follows: WAC = [180(6 million) + 360(10 million) + 90(4 million)] / (6 million + 10 million + 4 million) = (1,080 million + 3,600 million + 360 million) / 20 million = 5,040 million / 20 million = 252 days The weighted average life (WAL) of the mortgage notes issued is calculated by summing the time to maturity multiplied by a pool factor using the following formula: WAL = (a / 365) x PF(t) Figure 4 illustrates how WAL is calculated for an MBS with an initial outstanding balance for the entire pool of$89,530,000. The pool factor, PF(t), is the outstanding notional value adjusted by the repayment weighting. The actual days, a, until the next payment are stated in column B. This amount in column B is then divided by 365 in column F to calculate the time to maturity. The amount in column F is multiplied by column C to compute each individual notes weighted life and this is recorded in column G. WAL is then determined as the summation of column G.
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2018 Kaplan, Inc.
Topic 35 Cross Reference to GARP Assigned Reading – Choudhry, Chapter 12
Figure 4: Calculation ofWAL
A
Payment
Date
11/21/2008 1/26/2009 4/26/2009 7/26/2009 10/25/2009 1/24/2010 4/25/2010 7/25/2010 10/24/2010 1/24/2011 4/24/2011 7/24/2011 10/24/2011 1/24/2012 4/24/2012 7/24/2012 10/24/2012 1/24/2013 4/24/2013 7/24/2013
B
Actual Davs (a)
66 90 91 91 91 91 91 91 92 90 91 92 92 91 91 92 92 90 91
Prepayment Forecasting
C
PFft) 1.00 0.94 0.89 0.83 0.75 0.73 0.68 0.63 0.58 0.54 0.49 0.45 0.41 0.37 0.33 0.29 0.25 0.22 0.18 0
D Paid
Principal
5,059 4,941 4,824 4,706 4,588 4,471 4,353 4,235 4,118 4,000 3,882 3,765 3,647 3,529 3,412 3,294 3,176 3,058 16,472
E
F
Outstanding Balance (000s)
89,530 84,471 79,530 74,706 70,000 65,412 60,941 56,588 52,353 48,235 44,235 40,353 36,588 32,941 29,412 26,000 22,706 19,530 16,472
0
a / 365 0.1808 0.2466 0.2493 0.2493 0.2493 0.2493 0.2493 0.2493 0.2521 0.2466 0.2493 0.2521 0.2521 0.2493 0.2493 0.2521 0.2521 0.2466 0.2493
0
WAL =
G
(al365) x
p m 0.1808 0.2318 0.2219 0.2069 0.1870 0.1820 0.1695 0.1571 0.1462 0.1332 0.1222 0.1134 0.1033 0.0922 0.0823 0.0731 0.0630 0.0542 0.0449
0
2.565