How does the math work

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How Does the Math Work?
Version 2.0, revised December 2016
Copyright 2017 © Lender Performance Group, LLC. All rights reserved. Confidential.

Overview
How do we calculate:
o Loan Profitability
o Deposit Profitability
o Other Fee Profitability

Loan Profitability
Includes:
o Interest Income
o Interest Expense & Match Funding
o Non-Interest Expense
o Factoring in Risk
o Loan Loss Reserve: Adjusting Returns for Expected Loss
o Capital: Allocating Economic Capital for Unexpected Loss
o Risk Mitigants: Collateral & Guarantees
o Taxes and Tax Exempt Loans
o Conversion Loans and Rate Locks
o Floating Rate Loan with Floor/Cap

Loan Profitability - Example
o $1MM Commercial Real Estate
o 5 Year Maturity/ Term
o Interest Only
o 5 year term on the funding curve
is 1.64% (funding cost)
o 5.0% Interest Rate (Actual/360)
o No Origination Fee

Loan Profitability – Interest Income
Main Inputs:
o Interest Rate (5.0%)
o Interest Rate Basis (Actual/360)
o Origination Fees ($0)
o Origination Expenses ($12,487)
o Term (60 months)
o Average Balance ($1,000,000)
Interest Income is:
o [Initial Interest Rate] x
o [Adjustment for Interest Rate Basis] x
o [Average Balance] +
o [Origination Fees – Origination Expenses,
Annualized over the Term]
Specifically in this Example:
o 5.0% x (365/360) x $1,000,000 + ($0 - $12,487) x (12/60)
o = $48,197

Loan Profitability – Interest Income Tax Exempt
Main Inputs:
o Interest Rate (3.368%) Bank Qualified Tax Exempt
o Federal Tax Rate 34.9%, 0% State Tax
o Interest Rate Basis (Actual/360)
o Cost of Funds (1.639%)
o Interest Deduction (20%)
o Origination Expenses ($12,487)
Interest Income is (with 0% State Tax Rate):
o ([Initial Tax Exempt Interest Rate] less
o [Cost of Funds x Interest Deduction x Tax Rate])
divided by (1 – Tax Rate) x [Adjustment for Interest
Rate Basis] x
Annualized over the Term]
o {(3.368%-[1.639% x 20% x 34.9%)/(1- 34.9%)} x (365/360) x $1,000,000 +
($0 - $12,487) x (12/60) = $48,197

Loan Profitability – Interest Expense
Main Inputs:
o Yield/Funding Curve
o Term Structure1 (60 months)
o Average Equity (Capital) ($78,798)2
o Average Balance ($1,000,000)
Interest Expense is:
o ([Average Balance]3 x
o [Funding Curve Value at 60 months])
o $1,000,000 x 1.639% = $16,390
1. Because the example is an Interest Only loan, there is a single repayment at
the 60 month term. See the Matched Funding discussion on the following
slide.
2. An alternative method is to include capital as part of the funding, in
that case the equation becomes ([Average Balance – Average Equity]
x [Funding Curve Value at 60 months]). But this method is not
recommended.
3. Average Balance is weighting the monthly balances over the term of
the loan

Loan Profitability Calculations – Match Funding
• Based on a “marginal opportunity cost of funds” funding curve (in our example we use a
composite of the publicly available FHLBs)
• PrecisionLender allows you to use any funding curve that you choose. However, we recommend using a “marginal
market opportunity cost of funds,” such as the Libor/Swap or FHLB. This captures the opportunity cost of other investment
options (e.g. risk-free municipal bonds etc.).
• Sometimes called “match funding,” it’s used to allocate Interest Expense in a way that is “interest
rate risk neutral.”
• Each principal repayment has a re-pricing duration and is match funding separately
• A 60 month fixed rate interest only loan will be funded with 60 month money (only one repayment)
• A 60 month fixed rate amortizing with monthly payments will be funded as a set of 60 separate interest only loans each
maturing with the principal repayment in month 1, 2, 3…60
• Adjustable Rate loans (e.g. a 36/12, 60/12, 36/36 etc.) are treated as if the loan repays and is re-
funded at each adjustment so a 36/12 will be funded with 36 month money and then 12 month
money
• Floating rate loans are considered to re-price monthly and therefore will fund off the shortest
duration on the Funding Curve
• Interest Expense might be adjusted by a Liquidity Premium based upon the term of the floating or adjustable rate
obligation

Loan Profitability Calculations – Match Funding cont’d
o The table to the right shows the calculation of monthly
Interest Expense for a 12 month fully amortizing 5.0%
commercial real estate loan.
o The FHLB Curve for the one to eleven month interest rates are
based on an actual/360 day basis, this is adjusted by
365/360, see column C.
o Column D shows the principal repayment.
o Column E shows the monthly interest associated with each
principal payment.
o Column F is the sum of these payments through the time
period, i.e. the costs in Month 1 is sum of Month 1 to Month
12, while Month 6 is the sum of Month 6 to Month 12.
A B C D E F
Month FHLB Curve
FHLB Curve
Adjusted
Principal
Repayment
Interest for
monthly
repayment Monthly COF
1 0.542% 0.549% 81,414.77$ 37.28$ 633.87$
2 0.582% 0.590% 81,758.71$ 40.20$ 596.59$
3 0.617% 0.626% 82,104.10$ 42.80$ 556.39$
4 0.637% 0.646% 82,450.96$ 44.38$ 513.59$
5 0.691% 0.701% 82,799.27$ 48.34$ 469.21$
6 0.732% 0.742% 83,149.06$ 51.43$ 420.87$
7 0.780% 0.791% 83,500.33$ 55.02$ 369.44$
8 0.811% 0.822% 83,853.08$ 57.46$ 314.42$
9 0.838% 0.850% 84,207.32$ 59.62$ 256.96$
10 0.878% 0.890% 84,563.06$ 62.73$ 197.34$
11 0.917% 0.930% 84,920.30$ 65.80$ 134.61$
12 0.968% 0.968% 85,279.04$ 68.81$ 68.81$
Total 1,000,000.00$ 4,532.14$
(Match Funding is sometimes referred to as “Strip Funding”)

Loan Profitability – Non-Interest Expense
Main Inputs:
o Annual Servicing Expense
o Percent of Average Balance
o Percent of Amount
o Annual Fees
o Participation Fees and Expenses
Non-Interest Expense is:
o [Annual Servicing Expense] + [Percent of
Average Balance x Average Balance] +
[Percent of Amount x Amount] – [Annual Fees]
– [Participation Servicing Fees] + [Participation
Servicing Expense]
In this Example:
o $2,076 + 0.0% X $1,000,000 + 0.0% X $1,000,000 -$0 -$0 +$0 =
$2,076

Loan Profitability Calculations – Factoring in Risk
PrecisionLender allows you a range of options on how to factor in risk. PrecisionLender
uses a more comprehensive (Basel III – style) multi-factor approach. You can also use
different risk assumptions for different products or different products within different
regions.
Multi-Factor Approach
• Loan Loss Reserve and Credit
Capital are based on multiple risk
factors:
• Risk Rating for the borrower (the
borrower Probability of Default or
PD)
• The size of the Exposure at
Default (EAD)
• Collateral and guarantees (these
affect the Loss Given Default or
LGD)
• Loan Loss Reserve and Credit
Capital can also be varied by the
duration of the exposure for each
risk rating

Loan Profitability – Multi-Factor Risk (1 of 4)
Main Inputs:
o Borrower Risk Rating
o Average Balance
o Term Structure1
o Type and Value of Collateral
o Type and Amount of Guarantees
Loan Loss Reserve is:
o [Annual Loss (based on Risk Rating and Term)] x
[Adjusted Exposure at Default2]
Average Equity (Capital) is:
o ([Credit Capital (based on Risk Rating and Term)] x
[Adjusted Exposure at Default2] + [Unmitigatable
Capital3]) x [Average Balance]
1. Because the example is an Interest Only loan, there is a single repayment at the 60
month term. Term affects the duration of the exposure and you can vary Annual
Loss and Credit Capital by duration.
2. Adjusted Exposure at Default is covered in the next slide.
3. Unmitigatable Capital is the total Operational & Market Risk Capital. It does not vary
with Risk Rating or duration.

When using a multi-factor risk approach in PrecisionLender, the lender specifies the type(s) and
amount(s) of collateral. Each type of collateral has a Recovery Factor defined. The Recovery
Factor is the ratio of the present value of the recovered collateral after expenses as a
percentage of the nominal collateral value.
$1MM ($437M)
$563M
Exposure
At Default
Collateral
Mitigation
Adjusted
Exposure
At Default
Collateral Exposure Mitigation:
o 80% LTV ($1.25MM Collateral Value)
o 35% Economic Recovery Rate1
o = (35%) x ($1.25MM) = $437,500
Adjusted Exposure at Default:
o (Exposure at Default) – (Collateral Exposure Mitigation)
o = $1,000,000 – $437,500 = $562,500
Example (before effects of Guarantee and time)2:
o Loan Loss Reserve = $ 562,500 x 0.58% = $3,263
o Average Equity = $ 562,500 x 18.89% + $1,000,000 x 1% =$116,256
1. Each type of collateral type has its own Recovery Rate and a loan can have multiple layers of collateral. For example, the collateral above is
Commercial Real Estate and has a 35% Recovery Rate. A CD held at the bank would have a 95% recovery rate (and therefore is worth more as
a credit risk mitigant).
2. Here we show that the assumed Annual Loss (0.58%) and the Credit Capital (18.89%) are based on the exposure not covered by collateral or
guarantees. As the loan moves closer to maturity, the annual loss and credit capital percentage generally declines, see slide 15.

Loan Profitability – Multi-Factor Risk (3 or 4)
When using a multi-factor risk approach in PrecisionLender, the lender can specify the type(s) and amount(s) of
guarantees. Each guarantee has a Recovery Factor defined that operates like the collateral Recovery Factor.
In addition, each guarantee can have additional origination and servicing expenses associated with it. Finally,
guarantees can either be risky guarantees (e.g. a personal or corporate guarantee) or considered riskless (such
as a government guarantee). Riskless guarantees operate just like collateral except with additional expenses.
Guarantees do not affect the Adjusted Exposure at Default, but instead affect how capital and annual loss are
applied.
$562M
Guarantee
Mitigated
Unmitigated
Adjusted
Exposure
At Default
Credit
Capital
Annual
Loss
$100M
$462M
18.89% x 31.11% 0%2
18.89% 0.58%
Guarantee Mitigation:
o $143,110 Personal Guarantee
o Guarantor is a “3” Risk Rating and that Risk Rating has a 31.11% Guarantee Factor1
o 70% Economic Recovery Rate
o Obligor Is a “3” Risk Rating and has a Credit Capital rate of
o 18.89% (for a 60 month duration)
o = 70% x $143,110 = $100,177 of Guarantee mitigation
Loan Loss Reserves:
o [Unmitigated Exposure] x [Annual Loss]
o $462,323 x .058% = $2,6813
Average Equity (Capital) before time factor:
o [Guarantee Mitigated Exposure] x [Credit Capital Rate] x
[Guarantor Factor] +[Unmitigated Exposure] x [Credit Capital Rate]
o $100,177 x 18,89%X 31.11% + $462,323 x 18.89% + 1% x $1,000,000= $103,2154
1. Each Risk Rating has a Guarantee Factor as an assumption. This approach is taken from the Basel III approach to guarantees.
2. This factor is determined solely by the guarantor’s Risk Rating and is then multiplied by the obligor’s Credit Capital.
3. This is actually the “one-way” double default probability - the obligor annual loss x the guarantor annual loss. It is typically ~0%.
4. This would be for the first month of the loan, there is a calculation for each month where the exposure value would decline with time for an
amortizing loan.

The Credit Capital, Loan Loss and Guarantor factors change over time. This reflects the normal observation that
loans of the same risk rating with a shorter term represent less overall risk than those of a longer duration.
o As part of the credit migration using Basel III analysis, the bank
will determine the credit capital, loan loss and Guarantor
factors based on different durations of a loan.
o The table to the right shows that a loan with ten years to
maturity would have a credit capital rate of 30.00%. At one
year this declines to 10.00%.
o The five year level already discussed of 18.89%, is derived by
the mathematical interpolation between the one and ten
year durations.
o The second table shows the change in credit capital over time
and capital requirement.
Month Credit Capital% Credit Capital Unmitigated Total Capital
1 18.89% $93,215 $10,000 $103,215
2 18.70% $92,304 $10,000 $102,304
3 18.52% $91,394 $10,000 $101,394
4 18.33% $90,483 $10,000 $100,483
5 18.15% $89,573 $10,000 $99,573
6 17.96% $88,662 $10,000 $98,662
24 14.63% $72,258 $10,000 $82,258
25 14.44% $71,346 $10,000 $81,346
26 14.26% $70,434 $10,000 $80,434
27 14.07% $69,522 $10,000 $79,522
40 11.67% $57,658 $10,000 $67,658
41 11.48% $56,745 $10,000 $66,745
42 11.30% $55,832 $10,000 $65,832
43 11.11% $54,919 $10,000 $64,919
60 10.00% $49,438 $10,000 $59,438
average $68,798 $10,000 $78,798

Loan Profitability – Taxes & Other
Net Interest Income:
o [Interest Income] – [Interest Expense]
Other Income:
o Not used for loans (used for Other Fee-Based Products see slide 22)
Pre-Tax Income:
o [Net Interest Income] – [Non Interest Expense] – [Loan Loss Reserves] + [Other
Income]
Taxes:
o [Pre-Tax Income] x ([State Tax Rate] + [Federal Tax Rate] * {1- State Tax Rate})
Net Income:
o [Pre-Tax Income] – [Taxes]
Average Balance:
o The average monthly balance (average assets over the expected life) of the
loan.

Loan Profitability – Forward Rates
We use Implied Forward Rates as part of the match funding process
whenever there is a guaranteed fixed rate on a future commitment.
Examples:
o A Construction loan that converts to Permanent Financing AND the rate on
the Permanent Financing is Fixed and guaranteed at the closing of the
Construction loan.
o Example: a 12 month floating rate Construction loan that converts into a 60 month Commercial Real Estate
loan with a guaranteed fixed rate. To match fund the CRE loan we “buy 72 month money” and “sell 12
month money”
o A fixed rate Construction or Land Development loan with draws scheduled in
the future.
Note: we never use implied forward rates to attempt to predict rates in the future. We use
them as a way to accurately match-fund and allocate Interest Expense.

Loan Profitability – Floating Rate with Floor
Example:
o $1MM Commercial Real Estate Loan
o Interest Only
o Floating Rate at Prime (3.5%) plus 1.5%
(Actual/360)
o Funding Cost is the shortest duration,
typically one month (0.53%) adjusted to
365/360 plus Liquidity premium of 0.45%
o No Origination Fee
o Floor of 5.25%

Loan Profitability – Floating Rate with Floor
Interest Income is:
o [Initial Interest Rate] x
o [Adjustment for Interest Rate Basis] x
Annualized over the Term] +
o Effect of the Floor 1
1. Floor is 5.25% which is above the current rate of Prime at 3.50% plus 1.50%. The Floor is
in effect for 60 months. Black 76 option pricing method is used to determine the value
of that Floor based on relative volatility estimates. Having a Floor will increase interest
income while a Cap will reduce it. See the following for further details:
https://support.precisionlender.com/entries/27828878-PrecisionLender-University-
Understanding-the-Impact-of-Caps-and-Floors

Overview – Deposit Profitability
o Interest Income
o Interest Expense
o Float and Reserves
o Capital

Deposit Profitability – Financial Statement
Interest Income
o (1 - [Float & Reserves]) x [Average Balance] x [Funding Curve Transfer Rate]
o [Funding Curve Transfer Rate] is based on the duration of the deposit. For non-maturity
deposits this is a part of the Product definition. For Timed Deposits, this is set by the Term of the
Timed Deposit.
Interest Expense
o [Average Balance] x [Interest Rate Paid]
Non-Interest Expense
o [Average Annual Operating Expense] - [Average Annual Fee Income]
Average Balance
o The average monthly balance (average liabilities over the expected life) of the deposit. This is
typically the beginning balance.
Average Equity
o [Average Balance] x [Deposit Capital Rate]
o Interest Income: (1- .18%) * $100,000 * 1.1% = $1,098
o Interest Expense: $100,000 * 0.25% = $250
o Non Interest Expense: $692 -$2 = $690
o Average Equity: $100,000 x 2.0% = $2,000

Overview – Other Fee Profitability
o Interest Income
o Interest Expense

Fee Profitability – Product Types
o There are four fee types
o Annual Revenue and Balance – Total average annual revenue is entered plus
the expected average balance, example is wealth management
o Annual Revenue – Only average annual revenue is entered, this amount is
expected to be received over the life of the opportunity, costs of this service
are entered in the Administration Section
o Activity Based – Individual services where the average monthly expected
volume is entered and the related unit revenue and unit cost are applied.
Example is treasury management services
o Expected One Time Revenue – For products where there is a one-time fee
received, example is title insurance

Fee Profitability – Financial Statement
Other Income
o For Activity Based Fee Products, average monthly unit volume
by product type is needed.
o For Other Fee based products, estimated average annual
revenue is needed (see Wealth Management above).
o Note items stated as Eligible Revenue are those that are
checked as “Eligible for Earnings Credits.”
Other Income Example
o [Unit Volume less Waived Units] x (Unit Price less Unit Expense
o Sum for each activity based item (if any)
o For non-activity based product = {[Annual Revenue x (1 –
Expenses as a Percent of Revenue)] – set dollar expense

Fee Profitability – Financial Statement

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