The Math Behind
Loan Modification
A Webinar for Housing Counselors
and Loan Modification Specialists
Presented by Bill Allen
Deputy Director, HomeCorps
Overview
• Types of loan modifications
• Estimating eligibility at intake
– estimating Debt To Income ratio (DTI)
– estimating Loan To Value ratio (LTV)
– estimating the “best-case” loan modification
• Understanding the Net Present Value Test (NPV)
• Understanding an offer
– confirming full amortization
– post-modification DTI, a HAMP tier 2 example
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Types of Loan Modifications
Fully-Underwritten Permanent First Lien Loan Modifications:
• HAMP
• HAMP Tier 2
• Fannie Mae/Freddie Mac Standard Modification
• FHA loan modifications (including FHA-HAMP and mods with a “partial claim”)
• “In-house” modifications with HAMP-like underwriting requirements
Distinguish from other “modifications” and related foreclosure prevention options:
• “Straight-capitalization” – no change to the contractual terms of the loan
• Fannie Mae/Freddie Mac Streamline modifications – no underwriting
• Temporary modification – interest rate returns to the contractual rate after time
• Forbearance – portion of payment is deferred for a time period but is still owed
• Repayment – arrearages are paid over time
in addition to the contractual payment
• Refinancing (including HARP and FHA Short Refi) – creates an entirely new loan
• 2MP – for second liens only
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Review – simplified HAMP
modification waterfall
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• Determine a target payment—31% DTI
• Capitalize arrearages (increasing the principal balance
due)
• Change the terms of the loan in the following order to
try and reach the target payment…
– Reduce the interest rate to a step rate with an initial floor
of 2% for the first five years
– Extend the maturity date to a max of 40 years
– Forbear up to 1/3 of the principal, but not more than
enough to bring the interest bearing principal to 100% LTV
• If the target payment was reached, test the NPV
• If NPV positive, offer the borrower a trial plan
The Intake Interview
(1) Breakdown of the Monthly Mortgage Payment
– You’ll want to know principal & interest (P&I), taxes, insurance, and HOA fees (if any)
– A breakdown of P&I is not necessary, but you should ask if the current payment is an interest-
only payment
(2) Estimate of Monthly Gross Income by Source
– “Gross-up” non-taxable income by 25% (multiply by 1.25)
– “Gross-up” any net income amounts by 25% (multiply by 1.25)
– “Gross-down” rental income by 25% (multiply by 0.75)
– P&L statements: income = profit + salary +/- certain adjustments
– Unemployment benefits are not counted
(3) Estimate of the Property Value
– A recent appraisal is best, but online tools such as Zillow can provide a rough estimate
(4) Unpaid Mortgage Balance after Capitalization
– If no statement is available, you can roughly estimate the unpaid balance as:
unpaid principal + (number of months delinquent) x (monthly P&I payment)
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Example #1 – The Simple Family
(1) Breakdown of the Monthly Mortgage Payment
– $2115 principal and interest
– $300 property taxes
– $75 homeowner’s insurance
–
$2490 total monthly mortgage payment
(2) Gross income by source
– Ms. Simple’s paystub shows: $2300/mo. gross income.
– Mr. Simple’s SSDI: $1200.
– Because SSDI is non-taxable, gross Mr. Simple’s income up to $1500/mo.
– Gross monthly income =
$3800
(3) Estimate Property Value
– Zillow shows:
$225,000
(4) Unpaid Mortgage Balance After Capitalization
– Original 30 year mortgage in May 2007 was $275,000 at 8.5% interest
– The Simples paid on time until November 2013, but are now six payments behind. The
unpaid principal is $257,731 + $10,962 in unpaid interest.
– Total balance after capitalization would be
$268,693.
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Estimating DTI and LTV
Calculate current DTI and post-HAMP P&I payment
• Debt / Income = $2490 / $3800 = 0.655 or 65.5% DTI
• Post-HAMP Total Payment: $3800 x 0.31 = $1178 / mo.
• Post-HAMP P&I: Subtract taxes and insurance
$1178 - $300 - $75 = $803 / mo.
Calculate LTV after Capitalization
• LTV = Unpaid Balance / Property Value
• $268,693/$225,000 = 1.19 = 119% LTV
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Estimate the Monthly Payment of the
“Best-Case” Loan Modification
• Where the borrower meets the HAMP eligibility criteria, use HAMP’s program
limits to test your “Best-Case” loan modification, by finding the lowest allowable
monthly payment using a mortgage calculator or MS Excel formula.
• If you know in advance the borrower doesn’t qualify for HAMP, for example if their
DTI is already below 31%, use the program limits for the next best loan
modification for which they could qualify, typically HAMP tier 2 or a
Fannie/Freddie standard mod.
– HAMP tier 2: Principal reduced to 115% LTV, 30 yr PMMS rate + 0.05% (4.25%), 40 years
– Fannie Mae Standard Mod: Principal reduced to 115% LTV, 4.625% interest, 40 years
• The program limits for HAMP are 2% minimum interest rate, 40 year maximum
amortization period, and lowering the interest bearing principal balance to the
value of the property.
• For the Simples, we’ll assume they are otherwise eligible for HAMP: 2% rate, 40
year amortization, $225,000 interest bearing principal
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Calculating a Monthly Payment
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Microsoft Excel
Function for calculating a loan payment
=PMT( rate/12, years*12, -principal, -balance at maturity)
=PMT(.02/12,40*12,-225000,0)
$681.36
Using a Calculator
P: principal, J: monthly interest rate, N: number of months
M = P * ( J / (1 - (1 + J)^ -N)).
225000 * ( (.02/12) / (1 - (1 + (.02/12))^(-(40*12))
681.36
. . . or use one of the hundreds of mortgage
calculators available for free online.
Compare Results
• Compare the post-HAMP P&I to the payment under the best-case loan
modification.
• If the best-case loan mod results in a payment which is
less than your estimated
post-HAMP payment, the borrower is within the range where they may qualify for
HAMP. Again, assuming they meet all the other eligibility criteria.
• If the best-case loan mod is more than the post-HAMP P&I, then you can be
reasonably confident the loan servicer will not be able to reach an affordable
payment by modifying the loan and the borrower should consider other loss
mitigation options such as a short sale.
• In the case of the Simples, the best-case loan modification could reduce their P&I
payment to $681.36, HAMP only requires that the payment be reduced to $803.
So, the Simples may be eligible for a HAMP modification if they meet the other
eligibility criteria and the modification is Net Present Value (NPV) positive.
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The Net Present Value Test
• Compare the present value of the proposed modified loan for the
investor against the present value of the probability weighted
returns to the investor if the loan was not modified.
• Neither the HAMP guidelines nor the GSEs require servicers to
disclose all of the inputs used in their NPV tests.
• For homeowner’s with “certain mortgages” who are entitled to
receive a Right to Request a Modified Mortgage Loan under M.G.L.
Ch. 244 s. 35B, state law and regulations require the creditor to
conduct a compliant NPV analysis, provide the borrower with the
servicer’s anticipated recovery at foreclosure, and provide a
summary of the NPV analysis along with any denial.
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No Modification Scenario
Modification Scenario
NPV Factors
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-
Probability
Weighted Value
of Loan
Modification
Probability
Weighted Value of
Non-Modification
Outcomes
= NPV
No re-default -> Present value
of the new modified loan
Re-default -> loss from
escrow advances and loss
from foreclosure
Loss from
Foreclosure
Reinstatement
Positive Impact on NPV
Higher Credit Score
Decrease in Property Value
Negative Impact on NPV
Lower Credit Score
Increase in Property Value
Borrower Equity
Positive Impact on NPV
Affordability of modification
Negative Impact on NPV
Likelihood of reinstating the loan
No Modification Scenario
Modification Scenario
NPV Example, FDIC model
Simple Family
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-
= NPV
Loss from
Foreclosure
Reinstatement
60%
40%
85%
15%
Re-default rate and reinstatement rate
are creditor assumptions specific to
the property location and borrower
specific data such as credit score
No re-default -> Present value
of the new modified loan
Re-default -> loss from
escrow advances and loss
from foreclosure
(271,436) + 206,324 =
(65,112)
(255,449) + 137,511 =
(117,938)
Present value of future
cash flow of
modification payments
discounted by Freddie
Mac Rate: 5.4%
Unpaid
Principal
Balance
Present value of anticipated
Loss from foreclosure after re-
default
Present value of REO property less
foreclosure costs and future
escrow advances
$0
Modification
-$65,112
Default on Mod.
-$117,938
(260,062) + 144,041 =
(116,021)
Present value of
loss from
foreclosure
Present value of
REO property
Foreclosure
-$116,021
0.60 x (65,112)
+ 0.40 x (117,938)
________________________
(86,242)
0.85 x (116,021)
+
0.15 x 0
________________________
(98,618)
= $12,376
Positive
NPV
Note that even though the bank is losing
money by modifying the loan, the model
shows they are likely to lose more money if
they do not modify the loan.
Understanding an Offer—
Amortization
• Amortization
– It’s important to understand whether the modified loan
payments will completely pay-off the loan by the maturity
date. This is called a “fully-amortized” loan.
– One way to confirm this, is to calculate the fully amortized
payment by using the interest bearing principal as the loan
balance, along with new interest rate and new maturity
date.
– If these inputs result in a payment that is higher than the
proposed modified payment, then the loan does not fully
amortize and there will be a balloon payment due at the
maturity of the loan. This balloon payment will be in
addition to any payment due as a result of principal
forbearance.
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Understanding an Offer—
Amortization Example
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Using a Calculator
P: principal, J: monthly interest rate, N: number of months
M = P * ( J / (1 - (1 + J)^ -N))
Example Modification Offer:
$225,000 interest bearing principal, remaining $43,693 forbearance
3.0% fixed interest
30 years
The proposed P&I payment is a fixed payment of $897/mo.
Given these terms the fully amortizing payment should be:
M = P * ( J / (1 - (1 + J)^ -N))
M = 225000 * ( (0.03/12) / ( 1 – ( 1 + (0.03/12))^(-1*(30*12)))
M = $948.61
So, if the Simple’s accepted this modification. In 30 years, at maturity there
would still be a portion of the interest bearing principal unpaid, in addition to, the
$43,693 of principal forbearance.
Example #2 - Intake
(1) Breakdown of the Monthly Mortgage Payment
– $2015 principal and interest
– $280 property taxes
– $85 homeowner’s insurance
–
$2380 total monthly mortgage payment
(2) Gross income by source
– Borrower #1 paystub: $4200/mo. gross income.
– Borrower #2 P&L statement: $200/mo. loss, but draws a $3200/mo. salary
– Rent one bedroom for $900/mo. Rental income grossed down: $675
– Gross monthly income = $8075/mo.
(3) Estimate Property Value
– Zillow shows:
$375,000
(4) Unpaid Mortgage Balance After Capitalization
– Original 30 year mortgage in June 2006 was $425,000 with an ARM that adjusted to 11%
– Family previously fell behind and had the loan modified to a new balance of $400,000 at 5%
interest but have recently fallen behind again.
– Recent statement shows the new balance after capitalization of delinquent interest and third-
party fees would approximately $413,000.
– The loan is not owned by Fannie Mae or Freddie Mac
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Example #2 - Analysis
Calculate current DTI and post-modification P&I payment
• Debt / Income = 2380 / 8075 = 0.295 or 29.5% DTI
– At this point you know that it’s unlikely this family will qualify for HAMP tier I because
their DTI is already below the target payment
– However, given the uncertainty with how the underwriter might treat the borrower’s
profit and loss income, or the rental income, it may be helpful to evaluate the family
under both tiers 1 and tier 2 of HAMP.
Calculate LTV after Capitalization
– Unpaid Balance/Prop. Value = $413,000/$375,00 = 1.10 = 110% LTV
Estimate the “best-case” loan modification
– Using HAMP tier 2 program limits: 4.25%, 40 years, reduce principal to 115% LTV
=PMT( rate/12, years*12, -principal, -balance at maturity)
=PMT(.0425/12,40*12,-413000,0)
=1790.85 / mo. is the estimated payment under HAMP tier 2
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Example #2 - Results
• For HAMP tier 2, instead of comparing to the 31% target payment,
you want to confirm there was at least a 10% payment reduction
and that the post-modification DTI is between 10% and 55%. Post
modification DTI includes taxes, insurance, and HOA fees.
• Payment reduction:
(Prior Payment – Modified Payment) / Prior Payment
(2380 – 1790) / 2380 = 0.25 = 25% payment reduction
• DTI range:
10% DTI = 0.10 x $8075 = $807.50
55% DTI = 0.55 x $8075 = $4441.25
$1790 P&I + $280 taxes + $80 insurance = $2150
$2150 is well within the acceptable post-modification DTI range.
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Questions
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