KAL_II Loan Servicing Valuation Model


KAL_II Valuation Variables by Lyle Kalish
1. Loan characteristics
2. Servicing loan states
3. Cashiering - ( Borrower Payment Behavior)
4. Remittance
5. Administrative Cost
6. Service fees
7. Late fees
8. Tax and Insurance Impounds
9. Foreclosure Costs
10. Ancillary Income
11. P&I Balances
Exhibit 1- Loan states Transition Matrix
 1. Loan Characteristics

Three types of loans may be simulated:
 
1. Level payment
 
2. Fixed rate GPM
 
3. Non-negatively amortizing ARM'S
 
 For all three types the Users must input:
 
1. Outstanding Balance
2. Original loan maturity
3. Period of amortization (in case of balloon payments)
 The initial loan balance is defined as being that amount right before the principal adjustment required by the next immediate payment. so, If $50,000 was the outstanding balance of the loan., it is understood that as soon as the current payment comes in (which is due on the first of the month) the balance would be reduced accordingly.
Other inputs depend on the type of loan:
A. Level Payment - Fixed Rate Mortgage (FRM)
1. Annual Interest Rate
 B. Graduated Payment Mortgage -(GPM)
1. Current Payment
2. Number of Payment Changes
3. Month's until next payment change
4. Annual payment increase
5. Current interest
 C. Adaptable - Rate Mortgages (GPM)
1. To what index the interest on the loan is tied. It can be the interest rate forecast in the economic data or one specifically entered.
2. Month of Next change
3. Month's between change
4. Current Interest
5. Maximum annual change
6. Total possible change
7. Margin
 2. Servicing Loan States
 A. General Definition
 Conceptually a "Servicing Loan State" (State) refers to an administrative situation a loan might be in as defined by either:
1. A specific set of cash flows or,
2. A specific set of probabilities defining the likelihood of the loan moving to other states in the future.
 An example of a state would be "Delinquent 1 month" (D1), i.e., the mortgagor's payment is at least 30 days late and has not yet gone 60 days late. It fulfills both criteria. These loans will generate no positive cash flows (no payment, late fee, service fee, etc. ) and may require one payment advance and will definitely cause additional administrative costs specific to the delinquency, perhaps, generation of a letter or a couple of telephone calls. Also, loans can only be delinquent 2 months (D2) if they first are in state D1. There is a zero probability that a loan could go from being good (G) or delinquent 3 months (D3) directly (the next month) to being D2 -- this can only happen from D1.
 B. Model's Definition
 1. Broad
 The model allows for the following possible states:
a. Good (G) - Regular payment is paid during the month it is due, but not necessarily on time. If the loan had been delinquent in preceding months, all delinquent payments plus any fees owed are paid.
b. Delinquent (D1-D24) - Regular payments are missed and additional administrative costs are assumed. A loan 30 days late is assumed - D1, 60 days - D2, and 720 days late ( 2 Years) - D24.
c. Prepays (P) - Borrower Pays off Loan. The User may specify whether during the month of prepayment the borrower pays a full month's interest, no interest, or an amount proportional to the number of days into the month the loan prepays ( according to the prepayment Cashiering Schedule ). No service fee is earned out of this last month's interest. If a borrower is delinquent it is assumed he sends in all delinquent P&I payments, T&I payments as well as late fees owed. Once a loan prepays there is zero probability of it moving to any other state in the future.
d. Terminated (T) - The servicer ceases to administer the loan. This will generally occur when the borrower's property has been foreclosed upon. Servicer may:
(l) Have some "out of pocket cost" and,
(2) May only recover a part of funds advanced to the investor ( P&I and T&I advances or to buy back the Loan).
 2. Condensed States
 The 24 months of possible states of delinquency may not make sense with respect to residential servicing. Therefore for operational ease the model allows for condensed states, i.e., a group of months for which the administration tasks are similar. We have condensed the 24 possible months into 6 states.
States Description Length Months To F/C
1. Good 1 month 0
2. Dl Delinquent 1 1 month 1 Month
3. D2 Delinquent 2 2 month 2 Month
4. D3 Delinquent 3 3 month 3 Months
5. 90+ More than 3 months 2 months 5 months
6. FP Foreclosure process 4 months 9 monthsThe length of time in each condensed state is variable and the total number of months covered need not equal 24 months.
 3. Initial Loan Vector
 The model can begin in a any time during the life of a portfolio (Period 0). The user must define how many loans are in each state (Initial State vector - Exhibit 1). The beginning states refer to the loans on the first day of the first month. A loan that is Good made its last month's payment whereas a loan that is D1 missed its last month's payment. This information can be entered an absolute number or as a percent. If loans are in any condensed (multi-month) state it is assumed they are distributed evenly over the months of that condensed state.
 4. Transitions Matrix
 The transition (Exhibit 1) defines the probabilities of moving from one state to another to another. A different matrix may be defined for each month.
Going down a column, the current states loans can be in are defined and going across the row the state loans can be in next month are specified. Although 24 periods of delinquency are possible the illustration only uses 9. The following aspects of this matrix should be noted:
(1) There are no rows for Terminated (T) or Prepaid (P) because once a loan goes into one of those states they are assumed off the book and therefore can not move to any other state in the future.
(2) As an example of how to read the matrix the first row tells us there is a 95% probability of a loan that was good last month remaining good this month, a 4% probability of it turning D1 and a 1% chance of it prepaying. These probabilities must sum to 1.
(3) The first column indicates the probability of loans in each state being "good" next month. Loans that already were good will remain good with a 95% probability, 50% of these loans that were D1 will turn good, 75% of those that were D2, 75% of those that were D3, and 20% of those that were D9 will turn good.
(4) The matrix assigns a 0 probability of a loan going from D4 to G, or similarly it assigns a probability of 1 to a loan in state D4 going next month to D5. This is because we have defined D4 and D5 to be a combined state 9O+ which once a loan has entered, lt. remains in for both months. Similarly for the foreclosure Process, once a Loan enters it in D6 the loan remains in it through D9. The length and number of these sub-periods is inputted in the model.
(5) Loans can only be foreclosed upon (cease to be serviced) after coming through the complete foreclosure process. Looking at the last row a loan in state D9(the end Or the foreclosure process) has a 20% probability of being reinstated, a 20% chance of prepaying, and a 60% likelihood of completing foreclosure.
 5. Subsequent loan states
 Given the initial sate vector and a transition matrix the model can determine how many loans are in each state during each future months as shown in Exhibit 1. This is done by multiplying the loan state vector for each preceding month by this month's transition matrix. The multiplication is accomplished by multiplying each element of the vector by each corresponding element of each column of the matrix. Period 1's state vector enumerates the number of Loans in each state at the end of period 1 and the beginning of period 2,
 3. Cashiering ( Borrower Payment Behavior )
 The servicer receives funds due to:
1) regular borrower payments;
2) delinquent borrower's becoming current;
3) prepayment of loans;
4) loan foreclosures.
 When these funds come in during the month impacts a variety of aspects of servicing including:
1) Amount of late fees
2) Earnings on P&I and T&I balances
3) Amount of P&I advances
4) Cost of sending current month Late notices
 Therefore, for each of the above categories, the User must specify what percent of the total funds to be received during the month are actually received as of certain days of the month. The User may specify a different percent for each of the 30 assumed days or none in which case the model will assume funds are received evenly over the month (0.033 per day). The model assumes a straight line interpolation between any two days. If the User entered: Day Percent Received
Day Received
10 . 5
20 .8
30 1.0 (Assumed by Model)
the interpretation would be 5% of the funds came in each of the first 10 days of the month, 3% per day for the next 10 days, and 8 per day for the last 10 days. The User must establish a cashiering schedule for each source of funds, good loans, delinquent loans, prepayments, and foreclosures. Each schedule remains constant over the life of the loans.
 4. REMITTANCE
 Remittance refers to the amount of money the Servicer must send to investors and when these remittances are likely to clear from the servicer's account.
The amount depends on what type of advance arrangement id built into the servicing contract. The model allows for three advance possibilities and also lets the User vary the number or months for which required advances must be made.
A. No advances - only payments received are sent to investors.
B. Interest Advanced - payments received plus the interest portion of scheduled payments not received are sent to investors.
C. P&I Advance - P&I payments for all loans on the books are sent to investors whether these payments have been received or not.
The remittance amount also depends on payoffs. If a loan pays off, the loan balance at the beginning of the month is remitted to the investor along with either,
1. A total month's interest if payment advances are required, or
2. The amount of interest paid by the borrower if no advances are required
 In this former case it is possible the servicer might be required to send the investor more funds than they received from the borrower. This is considered a prepayment cost. Principal is not passed through to the investor due to loan foreclosure. Any advances are repaid and the Loan is just dropped from the books.
The User must specify three Inputs to define when the servicer loses the use of the funds (the remittance pattern).
D. "Day of Month Remit to investor" - What day of month must servicer remit checks to investor" For example, in the case of GNMA l's it would be the 15th, and in the case of GNMA 2's it would be the it would be the 18th. An entry of "0" here means the investor draw all payments received out of the P&I account each day. No advances are made with this option.
E. "Number of month's delay" - If the servicer remits to investor in the same month payments are due, the proper input is 0. This would be the same case for GNMA's. If remittance is due the nest month, as is with FHLMC PC's, then 1 is the proper input.
F. "Clearance Pattern of Remittances to Investor" After the servicer remits to the investor the servicer does not lose the use of the fund until the check clears (in those cases when checks are used). The User must specify what proportion of the checks clear each day of the month between the remittance day and the last day of the month ( by which time the model assumes all checks clear). The model assumes a straight line growth between each specified date:
1. Example 1 - Day Fraction
18 1.00
Loss of all remitted funds on the 18th
2. Example 2 - 15 0.5
30 1.0
Loss of 50% of remitted funds on 15th and 3.33% of the remainder of the funds per day so that by the 30th servicer has lost the use of all funds.
 5. Administrative Cost
 The model assumes a basic administrative cost associated with servicing all loans whether good, prepaying or delinquent. This basic cost is inputted as the annual cost of servicing a good loan. Additional administrative costs result from:
A. Good loans for which payments are not received prior to an inputted trigger date. These loans may remain "Good" if their payments are received by month end or become D1 if the payments are not received. This cost should reflect the activity caused, perhaps, a phone call or a letter. in the model these costs are identified as "late notice." These costs can be accounted for inflation.
B. Prepaying loans generate additional paperwork and thus administrative costs. These costs can be adjusted for inflation.
C. Loans in all other states other than "Good" generate additional costs. A loan that is D1 will induce some collection effort as well as additional monitoring effort, perhaps, for the sake of example causing additional expenses of $2. The administrative cost associated with these other states an inputted am monthly value. Projected inflation rates (which can vary over time affect all these costs).
 Example for Month 5
Loans in Monthly Basic + Additional * Inflation = Total
Each State Costperloan State Cost Factor Cost
as of Mon 4
G 74 2 2 1.01 149.48
D1 4 2 2 1.01 16.16
D2 4 2 3 1.01 20.20
D3 4 2 3 1.01 20.20
D4 3 2 4 1.01 18.18
D5 3 2 4 1.01 18.18
D6 2 2 5 1.01 14.14
D7 2 2 5 1.01 14.14
D8 2 2 5 1.01 14.14
D9 2 2 5 1.01 14.14
------
Subtotal 298.96
(Late Notice Good Loans 6 Months) 3 1.10 18.18
P2 1 4 1.01 4 04
--------
Subtotal 22.22
Total 321.18
Average Monthly Cost $3.21
The State Vector for month 4 gives the number of loans in each state at the end of month 4 or the beginning of month 5. It also defines the states for month 5. 4 will remain good until the end of month 5, even if they do not make their payment in month 5.
Late Notices are determined from the cashiering pattern of Good_Loan receipts during the month
P2 - "Prepaying" is not a state at the end of month 4, but refers to an action that occur to the loan during month 5.
 6. Service Fees
 Service fees can be a percent of the outstanding balance of the loan or a dollar amount can be varied over she life of the loan. Service fees are usually paid only when a loan is good, turning good, or prepaying. A loan that was good last month and is to remain good would pay a service fee (assuming a percent) equal to the service fee percent multiplied by the outstanding balance of the loan on the first day of the month
A loan that is becoming D1 this month would pay no service fees, and a loan that was delinquent on the first day of this month but becoming good would pay this month's service fee as well as any past service fees previously not paid due to delinquency.
A prepaying loan pays service fees for all regular payments, but if additional interest is paid during the month of repayment no service fees are paid.
 7. Late Fees
 Late fees are equal to an inputted percent of the P&I payment plus an inputted percent of the current T&I payment.
Late fees result from:
A. Good loans whose payments ( as described by the cashiering schedule ) come in during the current month but after the specified "grace" date (e.g. 15th of the month).
B. Loans which had been delinquent in preceding months which are becoming current pay late fees for each delinquent month. So a loan that was in state D1 would pay at least 1 late fee and a loan that was D9 would pay at least 9 late fees. In addition, that portion of those Loans that pay during the current month after the "grace" date according to their cashiering Table) pay a additional late fee.
C. Loans that are prepaying in the current month will not pay a late fee for that month. However, if they were previously delinquent they must pay late fees for those preceding months.
D. Loans going off the books due to foreclosure pay no Late fees
 8. T&I and Insurance Impounds
 Tax and Insurance Impounds (T&I) are important to servicers because they implicitly or explicitly earn interest on these balances. The value of these impounds depend on:
1) the size of the borrower's T&I payment and the extent of the delinquency of such payments,
2) how often the servicer must send the required payments to the tax authority or the insurance company, and
3) how these funds are utilized.
 Inputted into the model for the typical loan are the number of months of borrower monthly property tax and insurance payments which are remitted at one time and when during the next 12 months these payments will be made. Also inputted is what month (and for how many months) interest should be credited to the borrower's impound account (interest is only credited for positive balances). So, looking at the example, in month 4 and 10, six borrower property tax payments will be sent to the taxing authorities each month 1 insurance premium is sent to the insurance company, and in month 11 borrowers are credited one entire year's interest to their impound account.
Property Tax #Insure Payments # Month Interest
Month Payments Remitted Remitted Credited Imp Acct
1 1
2 1
3 1
4 1
5 6 1
6 1
7 1
8 1
9 1
10 6 1
11 1
12 1 12
A. Month 1 is the first month of the model. Future years are assumed to follow the same pattern.
B. The number of payments issued during any month during the first year must be equal.
C. Growth rates are projected separately for both types of payments. The growth rates may be varied over time and are applicable once every 12 months. The borrower's tax or insurance payment rise by the projected growth rate monthly or starting with the borrower payment occurring during the month the servicer makes the last payment during the year to the taxing authorities or insurance companies. In the example, using the second alternative this would occur in month 10 for taxes and month 6 for insurance.
D. It is assumed the servicer receives the borrower's T&I payment according to the inputted cashiering schedule and remits to tax authorities and insurance companies on the first day of the month.
For the model to know how much is to be paid out of T&I account and when, the User must also input information on what current T&I payments are and how much funds are in the T&I account as if the beginning of the Model.
Inputs 1. Current Impounded property Tax- $300
2. Current Impounded Insurance Premiums - $466
3. Current property Tax Monthly Payment - $100
4. Current Insurance Monthly Payment- $ 67
The following Table shows what would happen to the T&I account if the borrower made all his payments on time:

Property Tax Insurance T&I
Month Out In Out In Balance
1 100 67 933
2 100 67 1100
3 100 67 1267
4 600 100 67 834
S 100 67 1001
6 100 800 74 375
7 100 74 549
8 100 74 723
9 100 74 897
10 600 100 74 481
11 110 74 665
12 110 74 849
13 110 74 1033
E. The borrower's tax payment and insurance payments went up by the expected growth rate during the month in which the Servicer makes the last payment to the tax authorities and the insurance companies respectively. Property tax payments went up by 10% in the 10th month and insurance payments also went up by 10% in the 6th month. We could also let them rise monthly.
F. The initial T&I balances is the sum of balances on hand to begin with plus the first month's T&I. When figuring the initial amount the User should begin with the sum of the Payments which should be on hand if all loans were current and then subtract payments for delinquent loans - one T&I payment for loans "D1", two T&I payments for loans beginning in "D2", etc.
 If the borrower does not make all his payments then the servicer's T&I account will not be as large. In fact, it is possible the servicer would have to make these payments with its own funds if the borrower's T&I payments on hand were not great enough (T&I advanced). For example, if the borrower went delinquent the first month and remained so until the seventh month the T&I balance would appear:

Property Tax Insurance T&I
Month Out In . .Out In Balance
1 0 0 766
2 0 0 766
3 0 0 766
4 600 0 0 166
5 0 0 166
6 0 800 0 (634)
7 700 483 549
1. Once the borrower becomes current the T&I account has the same balance in it as it would have had if it were never delinquent .
2. Delinquency causes the average T&I balance to be lower than it otherwise would have been.
3. The negative T&I balances (advance) shown in the above example occurs mainly because for the sake of simplicity the model asks for inputs in terms of a typical loan. In reality, a servicing portfolio is made up of loans made during all months of the year ( which determines insurance payments) and are located in many states with different tax payment dates. The effect of this diversity is servicers never have to advance their own funds to make tax or insurance payments, they just advance another borrower's impounded funds. This modeling simplification will not misrepresent the value of T&I balances so long as the negative value of having to advanced T&I's is equal to the positive value of having positive balances.
Finally, the value of the Impound balances is given by the following equation,
E t= [ TIt] [Ut1] [it] - [TIt] [impt]
 where:
Et is the monthly earnings generated by T&I balances,
Ut1 is the proportion of T&I balances that the servicer receives credit on - the major factor here is the reserve requirement. If the servicer has these funds in demand deposits the maximum value for Ut1 is 88%, since T&I balances may be held in different type of bank account than P&I payments, a different U is specified for each:
it = monthly earnings rate on impounds:
impt = monthly interest rate that must be paid borrowers on T&I account.
 9. Foreclosure Costs
 Termination through foreclosure can negatively impact the servicer in 5 distinct ways:
1) the possible requirement of having to advance P&I and T&I payments to investors,
2) increased administrative cost,
3) non-recovery of some or all "out-of-pocket cost"
4) non-recovery of none of the advanced P&I, T&I payments and
5) non-recovery of a portion of run as advanced to an investor (Like a GNMA) to buy back the Loan.
 The first two of these are accounted for automatically in the model, the third requires additional inputs, Table 1.
Table- 1 Foreclosure Data

Hard-Out-of-pocket Cost : 3000
Percent Recovered 0.9000
Service Fees Recovered (%) 0.9000
Principal Lost (I) 0.1000
Interest Recovered (%) 0.9000
Interest payments Lost: 2
T&I Advances Recovered (%) 0.9000
A numerical example (Table 2) is presented to help clarify how these foreclosure losses would be calculated.

Table 2 Foreclosure Data
Month Balance Interest Principal S.F.. T&I
0 1000.00
1 995.65 10.00 4.35 1 10
2 991.25 9.95 4.40 1 10
3 986.82 9.92 4.43 1 10
4 982.34 9.87 4.48 1 10
 The mortgagor's last payment on the loan described in Table 2 was in month 0, no payments were made in months 1-4 and thus borrower's outstanding balance is $1000. At the end of month 4 the loan terminates, the investor is given back $1000, and the servicer must calculate foreclosure losses.
A. Hard out of pocket cost - Outside attorney, handyman, etc .
( .1) (3000) - 300
 These costs may be adjusted for inflation.
B. Service Fees Recovered - Since service fees were not earned (on a cash basis) while the loan was delinquent, recovery of service fees allows a reduction of foreclosure cost.
(.9) 4 = (3.60)
 C. Principal Float - How much of the $1,000 of principal given to the investor does servicer get back from insurer, foreclosure sale or investor. These costs may be adjusted for inflation
(.1) (1000) = 100
 D. Interest Recovered C%) - If advances are required which are recoverable, are the interest part of the advances financed at the mortgage rate or some other rate (like a debenture rate)
(.1) (39.74) = 3.97
 E. Interest Payments Lost - Some insurers (like FHA) do not return all interest - if one is not returned, the model assumes "it" is the first - the Largest
F. T&I Advances Recovered
(-1) (40.00) = 4.00
 G. Total Foreclosure Cost = $446.97
Operationally in the model when a Loan forecloses both the P&I and T&I account are fully paid back all advances (whether recovered or not). The model then takes the total foreclosure cost as a one time loss during the period termination. No time delay is allowed between the time the servicer might receive funds from an insurer or foreclosure sale and when they have to remit the funds to the Investor.
 10. Ancillary Income
 Servicers earn income in a variety of ways not previously defined - such as assumptions fees, a variety of insurance premiums, etc. An annual dollar figure per Loan is inputted which is assumed applicable to all loans on the books (whether current or not). Ancillary income can be adjusted for inflation.
 11. P&I Balances
 P&I balances increase when borrowers make their payments, prepay their loans, or when funds are received from foreclosure sales or insurers for loans that have completed foreclosure. P&I balances decrease when regular payments or principal (due to payoffs are remitted to investors). These balances (if positive) generate implicit or explicit interest for the servicer and if negative result in advance cost.
The utilized determinants of P&I balances are:
1. Delinquency patterns
2. Borrower payment patterns
3. Timing of Remittances to investors.
 Additional factors are,
A. If payments have to be advanced if not received. If they do, does the advanced include the whole payment or just the interest, and for how long must the payments be advanced (e.g., until the loan goes into foreclosure or completed foreclosure).
B. Loan remittances in the first month are based on the number of loans on the books and their Initial states at the beginning of the model. This assumes either nothing has changed from the previous month or that any principal that came in during the previous month has already been given to the investor.
C. If the servicer has to advance payments it will cost the servicer an interest rate multiplied by the average outstanding monthly advances. This interest rate can differ from the interest rate used to input an earning from compensating balances.
D. The model will track average monthly compensating balances, average monthly advanced, and the peak amount of advances in each month. The latter figure is important to banks in order to get an idea of how big an advance line that might be required.
E. As explained in this report, the model assumes that all principal repaid prior to model beginning had already been repaid to investors, therefore, there is no reason to begin the model with positive P&I balances. But, since some loans are beginning delinquent (and thus represent receivables for the servicers) the model might begin with a negative balance representing payments not yet received from borrowers but already advanced to investors.

Exhibit 1

Loan States

Transition matrix

Initial State Vector (Period 0)

Loan Count

Probability Matrix

 Loan Count


G D1 D2 D3 D4 D5 D6 D7 D8 D9 P F/C
 
88 G .95 .04









90.6
8 D1 .5
.49








3.52
4 D2 .75

.24







3.92
0 D3 .75


.24






.96
0 D4




1





0
0 D5 .5




.49




0
0 D6






1



0
0 D7







1


0
0 D8








1

0
0 D9 .2








.2 .6 0