This document discusses various quantitative tools for analyzing loans and portfolios. It introduces the key variables in time value of money calculations, including number of periods, interest rate, present value, payment per period, and future value. It demonstrates how changing these variables, such as increasing the number of periods or interest rate, impacts the total cost of credit. The document also discusses compounding interest and its effect on the effective interest rate. Risk and the costs associated with lending are also covered.

1. An Introduction

2.  Create Awareness of some Quantification Tools
 Effect of Compounding
 Risk
 Impact of Term Extension
 Why Fixed Rates Create Break Costs

3. QUALITATIVE QUANTITATIVE
 CAMPARI  The 5 Variables
 5 Cs  Compounding
 Drivers of Interest
 Risk
 Term Extension

4.  Management of the Loan book
 Portfolio
 Correlations
 Portfolio Risk
 Economic Capital
 Facility specific
 Default & Migration (deterioration)
 Exposure at Default & Loss Given Default

6.  Character  Amount
 Know your customer  Size of loan
 Ability  Repayment
 To repay  income, savings, asset
 Margin disposal
 Pricing: cost of funds,  Insurance
risk, profit  Credit enhancement
 Purpose  Security
 Guarantee
 Use of loan proceeds

7.  Character
 Know your customer
 Capacity
 Ability and sources of repayment

8. Current Arrangement
Can Legal
Pay
New Arrangement
Ability
Forbearance
Can’t Legal
Sympathetic
Pay (Subject to Cost
Work-out
Benefit Analysis)
Don’t Want to Pay Want to Pay
Attitude

9.  Character
 Know your customer
 Capacity
 Ability and sources of repayment
 Capital
 How much is the borrower investing in the project?
 Conditions
 What are the loan covenants?
 Collateral
 Security & Credit Enhancement

10. What are the key factors?

11.  The Variables:
 Number of Periods (N)
 Interest rate (i)
 Present Value (PV)
 Payment per Period (PMT)
 Future Value (FV)

13.  The Variables:
 Number of Periods (N) 1
 Interest rate (i) 10%
 Present Value (PV) €100
 Payment per Period (PMT) €110
 Future Value (FV) €0

14. €100
C
a €50
s
h
€0
F
0 1
l
o €110 in the year
(€50)
w
(€100)
Years

15. 1 Year
Repayment €110.00
No. of Years x1
Total €110.00
Loan Value €100.00
Cost of Credit €10.00

16.  The Variables:
 Number of Periods (N) 2
 Interest rate (i) 10%
 Present Value (PV) €100
 Payment per Period (PMT) €57.62
 Future Value (FV) €0

17. €60
€40
C
a €20
s €0
h
0 1 2
(€20)
F
(€40)
l €57.62 per year
o (€60)
w
(€80)
(€100)
Years

18. 1 Year 2 Years
Repayment €110.00 €57.52
No. of Years x1 x2
Total €110.00 €115.04
Loan Value €100.00 €100.00
Cost of Credit €10.00 €15.04

19.  The Variables:
 Number of Periods (N) 3
 Interest rate (i) 10%
 Present Value (PV) €100
 Payment per Period (PMT) €40.21
 Future Value (FV) €0

20. €40
C €20
a
€0
s
0 1 2 3
h (€20)
F (€40)
l €40.21 per year
o (€60)
w
(€80)
(€100)
Years

21. 1 Year 2 Years 3 Years
Repayment €110.00 €57.52 €40.21
No. of Years x1 x2 x3
Total €110.00 €115.04 €120.63
Loan Value €100.00 €100.00 €100.00
Cost of Credit €10.00 €15.04 €20.63

22.  The Variables:
 Number of Periods (N) 5
 Interest rate (i) 10%
 Present Value (PV) €100
 Payment per Period (PMT) €26.38
 Future Value (FV) €0

23. €20
C
€0
a
0 1 2 3 4 5
s
(€20)
h
(€40)
F
€26.38 per year
l (€60)
o
w (€80)
(€100)
Years

24. 1 Year 2 Years 3 Years 5 years
Repayment €110.00 €57.52 €40.21 €26.38
No. of Years x1 x2 x3 x5
Total €110.00 €115.04 €120.63 €131.90
Loan Value €100.00 €100.00 €100.00 €100.00
Cost of Credit €10.00 €15.04 €20.63 €31.90

25.  The Variables:
 Number of Periods (N) 10
 Interest rate (i) 10%
 Present Value (PV) €100
 Payment per Period (PMT) €16.27
 Future Value (FV) €0

26. €20
€0
C
a 0 1 2 3 4 5 6 7 8 9 10
s (€20)
h €16.27 per year
(€40)
F
l (€60)
o
w (€80)
(€100)
Years

27. 1 Year 2 Years 3 Years 5 years 10 years
Repayment €110.00 €57.52 €40.21 €26.38 €16.27
No. of Years x1 x2 x3 x5 x 10
Total €110.00 €115.04 €120.63 €131.90 €162.70
Loan Value €100.00 €100.00 €100.00 €100.00 €100.00
Cost of Credit €10.00 €15.04 €20.63 €31.90 €62.70

28.  Repayments reduced
 More time to repay
 Total Cost of Credit increases
 More borrowed for longer
 Bank’s Exposure increases
 More later

29. 1 Year 2 Years 3 Years 5 years 10 years
Repayment €110.00 €57.52 €40.21 €26.38 €16.27
No. of Years x1 x2 x3 x5 x 10
Total €110.00 €115.04 €120.63 €131.90 €162.70
Loan Value €100.00 €100.00 €100.00 €100.00 €100.00
Cost of Credit €10.00 €15.04 €20.63 €31.90 €62.70

30.  The Variables:
 Number of Periods (N)
 Interest rate (i)
 Present Value (PV)
 Payment per Period (PMT)
 Future Value (FV)
 Interest Calculations
 How many payments per year? Compounding
 How often is interest charged?

31.  Daily Interest Rate:
 Late Payment of CAT
 A mere 0.0219% per day!
 What is the APR?
 The rate if interest was compounded once a year

33.  More Frequent  Effect of
Charging Compounding
 Higher Effective Rate  Once a Year
 Example  Twice a year?
 Rate of 10%  Once a Quarter?
 PV = 100  Once a Month?
 No payments in the
year
 Calculate the Future
Value (FV)

34. €100
C
a €50
s
h
€0
F
0 1
l
o €110 in the year
(€50)
w
(€100)
Years

38.  Costs of Funds
 Cost of Borrowing
 Risk
 Credit Risk
 Interest Rate Risk
 Capital Required (driven by Risk)
 Equity: Dearer than Debt
 Expenses
 Administration
 Profit Margin

39.  Liquidity Preference Theory (JM Keynes)
 Transactions Motive
 Cash for Pints!
 Parking
 Precautionary Motive
 Rainy Day
 Speculative Motive
 Speculation
 Supply & Demand
 Inter-Bank Liquidity

40.  Bank of Ireland
 Homeloan Variable Rates for existing customers
 Variable VRP15 – all amounts, all LTVs
 3.85% (APR: 3.9%)
Lending criteria and terms and conditions apply. Security and insurance required. The
maximum mortgage is normally 90% of the property value. As a general rule, mortgage amounts
up to 4-5 times an individual's gross annual income are considered and will vary according to
individual circumstances. A typical variable rate mortgage of €100,000 over 20 years costs
€596.94 per month (Annual Percentage Rate (APR) 3.9%). The cost of your monthly repayments
may increase. A 1% interest rate rise will increase this repayment to €650.08 (APR4.9%). This is
an increase of €53.14 per month. Information correct as at the 19th December 2011. Bank of
Ireland Mortgage Bank is a member of Bank of Ireland Group. Bank of Ireland and Bank of
Ireland Mortgage Bank, trading as Bank of Ireland Mortgages are regulated by the Central Bank
of Ireland.
http://personalbanking.bankofireland.com/mortgages/first-time-buyers-package#rates-accordion

41. Lending criteria and terms and conditions apply. Security and insurance required. The
maximum mortgage is normally 90% of the property value. As a general rule, mortgage amounts
up to 4-5 times an individual's gross annual income are considered and will vary according to
individual circumstances. A typical variable rate mortgage of €100,000 over 20 years costs
€596.94 per month (Annual Percentage Rate (APR) 3.9%). The cost of your monthly repayments
may increase. A 1% interest rate rise will increase this repayment to €650.08 (APR4.9%). This is
an increase of €53.14 per month. Information correct as at the 19th December 2011. Bank of
Ireland Mortgage Bank is a member of Bank of Ireland Group. Bank of Ireland and Bank of
Ireland Mortgage Bank, trading as Bank of Ireland Mortgages are regulated by the Central Bank
of Ireland.
http://personalbanking.bankofireland.com/mortgages/first-time-buyers-package#rates-accordion

42. NPV & IRR

43.  Money Today
 Is worth more than money tomorrow!
 How much?
 What is your “exchange rate”?
TVM Game

44. €500 €400
€300 €300
€250 €200
C €100
a
s €0
h 0 1 2 3 4 5
(€250)
F
l (€500)
o
w (€750)
(€1,000)
(€1,000) Years

45. €100
IRR
The rate which yields an NPV of €0!
€50 In this case, the IRR is 8.01%
€0
-€50
-€100
-€150

47.  Costs of Funds
 Cost of Borrowing
 Risk
 Credit Risk
 Interest Rate Risk
 Capital Required (driven by Risk)
 Equity: Dearer than Debt
 Expenses
 Administration
 Profit Margin

48. €100
C
a €50
s
h
€0
F
0 1
l
o €110 in the year
(€50)
w
(€100)
Years

49. OK Total
Nominal €110.00
Probability 1.0
Expected Return €110.00 €110.00
Interest Rate 10%
Value of Debt €100.00

50. You would pay €80 for a loan note paying 10%
with a 20% probability of default
OK Default Total
Nominal €110.00 €0.00
Probability 0.8 0.2
Expected Return €88.00 €0.00 €88.00
Interest Rate 10%
Value of Debt €80.00

51. OK Default Total
Nominal €110.00 €0.00
Probability 0.8 0.2
Expected Return €88.00 €0.00 €88.00
Interest Rate 10%
Value of Debt €80.00
€110
€80
?

53.  Bonds Denominated
in €uro
 No currency risk
 Issued by Different
Countries
 Credit Risk
 Germany – Best
 Greece – Worst
 March 3rd
 Germany 1.81% 1.92%
 Greece 38.8% 37.1%
February 25th 2012

54.  Costs of Funds
 Cost of Borrowing
 Risk
 Credit Risk
 Interest Rate Risk
 Capital Required (driven by Risk)
 Equity: Dearer than Debt
 Expenses
 Administration
 Profit Margin

55.  Banks are in Business to Make Profit!
 Cover Expenses
 Yield a Profit
 How priced
 Included in the Margin

56. The main restructure options!

57.  The Variables:
 Number of Periods (N)
 Interest rate (i)
 Present Value (PV)
 Payment per Period (PMT)
 Future Value (FV)
This is a term extension

58.  Monthly Repayments
 Fall
 Increase Affordability
 Term Increases!
 Balance Outstanding Increases
 Example
 €100,000 @ 5% over 20 years
 Becomes… Should the Rate be the same?
 €100,000 @ 5% over 25 years

60. €100,000
€80,000
€60,000
€40,000
€20,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

61. €100,000
€80,000
€60,000
€40,000
€20,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

62. €100,000
€80,000
€60,000
€40,000
€20,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

63. €35,000
€30,000
€25,000
€20,000
€15,000
€10,000
€5,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

64.  The Variables:
 Number of Periods (N)
 Interest rate (i)
 Present Value (PV)
 Payment per Period (PMT)
 Future Value (FV)
This is a Bullet Repayment
( “split” mortgage)

65.  Monthly Repayments
 Fall
 Increase Affordability
 Term?
 May Increase
 Alternative Source of Repayment?
 Balance Outstanding Increases
 Example
 €100,000 @ 5% over 20 years
 Becomes… Should the Rate be the same?
 €100,000 @ 5% over 20 years owing €30k in year 20!

66. €35,000
€30,719
€30,000
Source of Repayment:
€25,000 Asset Sale?
Pension Lump Sum?
€20,000 Inheritance?
Term Extension?
€15,000
€10,000
€5,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

67.  The risk you will have a default
 Risk of a failure
 What drives risk?
 Many Factors…
 Length of a loan!

68. 1.00
0.75
Default
Any Default
0.50
0.25
0.00
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

69. 1.00
0.75
Default
Any Default
0.50
0.25
0.00
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

70. 1.000
0.995
0.990
Default
0.985 Any Default
0.980
0.975
0.970
0.965
0.960
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

71. 1.0000
0.9995
0.9990
Default
0.9985 Any Default
0.9980
0.9975
0.9970
0.9965
0.9960
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

72.  Security?
 Default does not mean total loss
 Exposure at Default
 Security
 Other Costs

73.  “Kicking the Can”
 Not always the right answer
 Risk
 Length of a loan
 Riskiness of a repayment
 The more repayments…
 The greater the overall risk
 Asset Value
 Cover: “positive” equity
 Asset value vs loan value

74. What Happens?

75.  Fixed Rates Provide Certainty
 Customer Knows Repayment Amount
 Risk?
 Interest Rates Change!
 Rates Go Up…
 Bank Loses money
 Rates Go Down…
 Bank Makes Money
 Manage Interest Rate Risk
 Interest Rate Swap

76. Variable Variable
Counterparty A BANK Counterparty B
Fixed Fixed
Investors Receive Investors Receive
Fixed Variable

77. Variable Variable
Counterparty A BANK Counterparty B
5% 5%
Investors Receive Investors Receive
Fixed Variable

78. Variable Bank Depositor
Variable Variable
Counterparty A BANK Counterparty B
Fixed Fixed
Fixed
Interest Rate
Risk is “Locked Out”
Investors Receive
Fixed
Fixed Rate
Mortgage
Holder

79. Variable Variable
Counterparty A BANK Counterparty B
5% Fixed
3%
Interest Rate
Risk is “Locked Out”
Investors Receive
Fixed
The Replacement Swap is at 3%... not 5%.

80.  The Mortgage was 5%
 The new counterparty is 3%
 Gap 2%
 What is the Break Cost?
 Let’s use the Earlier Example
 20 year Mortgage
 5%
 €100,000

81. 20 years
€100,000
€80,000
€60,000
€40,000
€20,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

82. €5,000
€4,000
€3,000
Loss
€2,000 New Amt
€1,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

83. €2,000
€1,500
€1,000
Loss
€500
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

84. Period New Amt Loss 5% PV Value
0 €3,000 €2,000 1 €2,000
1 €2,909 €1,940 0.952381 €1,848
2 €2,814 €1,876 0.907029 €1,702
3 €2,714 €1,809 0.863838 €1,563
4 €2,609 €1,739 0.822702 €1,431
5 €2,499 €1,666 0.783526 €1,305
6 €2,383 €1,589 0.746215 €1,186
7 €2,261 €1,508 0.710681 €1,072
8 €2,134 €1,422 0.676839 €962
9 €2,000 €1,333 0.644609 €859
10 €1,859 €1,239 0.613913 €761
11 €1,711 €1,141 0.584679 €667
12 €1,556 €1,037 0.556837 €577
13 €1,393 €929 0.530321 €493
14 €1,222 €815 0.505068 €412
15 €1,042 €695 0.481017 €334
16 €854 €569 0.458112 €261
17 €656 €437 0.436297 €191
18 €448 €298 0.415521 €124
19 €229 €153 0.395734 €61
20 €0 €0 0.376889 €0
Total €24,195 €17,807

85.  Interest Lost
 Calculate
 Take the Present Value
 Amortising Swaps
 Difficult to Value
 Our Example is simplified!
 For Example, the 5% is a bit more complicated!!
 “Break” Costs
 CPC Rules

87.  I can afford €1,000 per month… how much can
I borrow?
 APR 3.9%
 20 Years €167,521
 25 Years €192,912
 30 Years €213,887

90. The Impact of a Term Extension

91.  Trackers are Loss Making
 ECB rate + margin
 ECB rate is LESS than our cost of funds
 CCMA
 Cannot move someone from a tracker due to arrears
 Impact of term extension
 Funding a greater exposure at loss making rates!

92. €100,000
€80,000
€60,000
€40,000
€20,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

93. €35,000
€30,000
€25,000
€20,000
€15,000
€10,000
€5,000
€0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

94.  Cash Recovery
 Earnings
 Inheritance
 Asset Disposal
 How much Cash?
 Principal
 Cost of Funds
 Profit
 Risk Premium

95.  Many Variables  Regulatory Compliance
 Term Extension  CCMA
 Sources of Repayment  CPC
 Income
 Asset Disposal  Need to “fit” customer’s
 House? circumstances
 Risk  Sustainability
 P[D] – Probability of
Default ↑
 LGD – Loss Given
Default?

96.  Costs
 Taking Possession is Expensive
 Liability for NPPR
 Currently €200 p.a.
 Insurance
 Maintenance
 Sustainability
 Need to prove in hindsight (keep your workings)

97. Current Arrangement
Can Legal
Pay • Restructure –
New Arrangement is a people
business.
Ability
Forbearance
• The quants
are just a
support
Can’t Legal
Sympathetic
Pay (Subject to Cost
Work-out
Benefit Analysis)
Don’t Want to Pay Want to Pay
Attitude

98.  Qualitative Factors
 5 Cs
 Campari
 Quantitative Factors
 Interest Rate
 Risk