October 2, 2008
Peter Taylor, Managing Director, Public Finance Department
Matthew Koch, Vice President, Public Finance Department
Introduction to Bond Math
Presentation to CDIAC
Agenda
Agenda
I. What is a Bond?
II. Key Concepts of Municipal Bonds
III. Yield Curve
IV. Fixed vs. Variable Rate Debt
V. Amortization Structures
VI. Key Calculations from a Bond Sale
VII. Question and Answer
What is a Bond?
What is a Bond?
What is a Bond?
A bond is a debt instrument that allows issuers to finance capital needs. It obligates the issuer to pay
to the bondholder the principal plus interest.
–
A buyer of the bond is the lender or investor.
– A seller of the bond is the borrower or issuer.
When an investor purchases a bond, he is lending money to a government, municipality, corporation,
federal agency or other entity.
In return for buying the bond, the issuer promises to pay the investor a specified rate of interest during
the life of the bond and to repay the face value of the bond (the principal) when it “matures,” or comes
due.
In addition to operating covenants, the loan documents require issuer to spend the bond proceeds for
the specific projects.
Among the types of bonds an investor can choose from are: U.S. government securities, municipal
bonds, corporate bonds, mortgage and asset-backed securities, federal agency securities and foreign
government bonds, among others.
A bond can also be thought of as a contract between the issuer and investor. This contract specifies,
for example, the terms of the bonds, the funds from which debt service will be paid and any operating
covenants.
1
Source of Repayment for Debt Service
What is a Bond?
General Obligation (“GO”) Bonds are secured by a pledge of the issuer’s full faith, credit and taxing
power. The “full faith and credit” backing of a General Obligation bond implies that all sources of
revenue, unless specifically excluded, will be available to pay debt service on the bonds.
Appropriation Bonds are secured by a “promise to pay” with legislatively approved appropriations.
These are generally supported by the General Fund of issuer, unlike General Obligation bonds where
funds are often not paid from the General Fund.
–
Examples include Certificate of Participation (COPs) and Leased Revenue Bonds (LRBs).
Revenue Bonds are payable from a specific stream of revenues, such as a user fee or dedicated tax,
and are not backed by the full faith and credit of the issuer. They are issued to finance specific
enterprises or projects and are usually secured solely by revenues from those projects. Revenue bonds
can generally be grouped into the following categories:
–
Utilities
–
Higher Education, Healthcare and Other Not-For-Profit
–
Housing
–
Transportation
–
Industrial Development, Pollution Control, and Other Exempt Facility Bonds
–
Securitized Revenue Bonds
2
2
Bond Covenants and Other Security Features of Revenue Bonds
What is a Bond?
Rate Covenants - Under a rate covenant, the issuer pledges that rates will be set at a level sufficient to
meet operation and maintenance expenses, renewal and replacement expenses, and debt service. An
alternative form of rate covenant requires that rates be set so as to provide a safety margin above debt
service, after operation and maintenance expenses are met.
–
Example: “The Board will fix, charge and collect fees so that the Revenues will at all times be
sufficient in each Fiscal Year to pay Operating and Maintenance Expenses and to provide funds at
least equal to 115% of (1.15 times) the Principal and Interest Requirements….”
Additional Bonds Test (ABT) - Protects existing bondholders from the risk that their security will be
diluted by the issuance of additional debt. The Additional Bonds Test must be met by the issuer in
order to borrow additional debt secured by the same revenue source as the outstanding bonds.
–
Example: “The Net Revenues in each of the two Fiscal Years immediately preceding the date of
issuance of such proposed Additional Bonds must be equal to at least 130% of the estimated Annual
Debt Service for the year following the proposed issuance.”
3
Bond Covenants and Other Security Features of Revenue
Bonds (cont.)
What is a Bond?
Debt Service Reserve Fund - Provides a cushion to make timely debt service payments in the event of
temporary adversity. Federal law limits the amount of tax-exempt bond proceeds that can be used to
fund the debt service reserve fund to the lesser of:
•
10% of the principal amount of the issue;
•
Maximum annual debt service; and
•
125% of average annual debt service on an issue.
–
May also be required for appropriation debt.
–
Many times a DSRF is not required for highly rated credits (e.g. UC Regents and CSU).
Other Covenants - Additional covenants might include a provision for insuring the project, a review
by an independent auditor, or a prohibition against the sale of the project’s facilities prior to repayment
of outstanding debt, among others.
4
Uses of Bond Proceeds
What is a Bond?
New Money
Bonds issued to provide new or additional
funding for a project.
Refunding
Bonds issued to refinance certain existing bonds
(proceeds used to repay old bonds). Refundings
can be used to produce savings, restructure debt
service or release the issuer from restrictive
operating covenants.
5
Key Concepts of Municipal Bonds
Key Concepts – Basic Terminology
Key Concepts of Municipal Bonds
Principal
Debt Service
Maturity
Original Issue Discount
Serial Bonds
Original Issue Premium
Term Bonds and Sinking Funds
Bond Proceeds
Coupon
Capital Appreciation Bonds
Yield
Callable Bonds
Price
Insurance
Interest
Bond Conventions
6
Principal and Maturity
Key Concepts of Municipal Bonds
Maturity - Date on which principal payments are due
– Typically, maturity dates are generally no longer than 30 years
– Most bond issues have principal maturing each year until the final maturity date of the series
Principal - Also known par amount, or face value, of a bond to be paid back on the maturity date
– Typically, bonds are sold in $5,000 principal denominations, often $100,000 for variable rate bonds
Maturity Date Principal
1/1/2011 $8,705,000
1/1/2012 $9,005,000
1/1/2013 $9,325,000
1/1/2014 $9,685,000
1/1/2015 $10,170,000
1/1/2016 $10,705,000
Total $57,595,000
7
*
Serial and Term Bonds
Key Concepts of Municipal Bonds
Bonds can either mature annually (serial bonds) or as term bonds.
A term bond is a series of sequential amortizations. Payments of principal prior to the term bond’s
final maturity are referred to as sinking fund payments.
Maturity Date Principal Coupon
1/1/2011 $8,705,000 3.50%
1/1/2012 $9,005,000 3.50%
Serial Maturities
1/1/2013 $9,325,000 3.90%
1/1/2014 $9,685,000 5.00%
1/1/2015 $10,170,000* 5.25%
Term Bond
1/1/2016
$10,705,000* 5.25%
Total
$57,595,000
*Sinking fund payment
8
Coupon, Interest and Debt Service
Key Concepts of Municipal Bonds
Coupon - Percentage rate (based on principal/par amount) of annual interest paid on outstanding bonds
– Can be fixed or variable
Interest - Cost of borrowing money for the issuer
–
Usually paid periodically
- Semi-annually for fixed-rate bond
- More frequently for variable-rate bonds
– Interest is calculated by multiplying principal by coupon (adjusted for length of period between
interest payments)
Debt Service - Sum of all principal and interest on a bond
Year
Principal Coupon Interest Debt Service
2010 $2,563,713 $2,563,713
2011 $8,705,000 3.50% $2,563,713 $11,268,713
2012 $9,005,000 3.50% $2,259,038 $11,264,038
2013 $9,325,000 3.90% $1,943,863 $11,268,863
2014 $9,685,000 5.00% $1,580,188 $11,265,188
2015 $10,170,000 5.25% $1,095,938 $11,265,938
2016 $10,705,000 5.25% $562,013 $11,267,013
Total $57,595,000
$12,568,466 $70,163,466
9
Bond Pricing
Key Concepts of Municipal Bonds
Price – Discounted present value of debt service on an individual maturity. Debt service is
calculated using the coupon and discounted at the yield.
Debt Present Value to
Date Principal Coupon Interest Service 1/1/2009 at 3.82%
1/1/2009
7/1/2009 $1.75 $1.75 $1.72
1/1/2010 $1.75 $1.75 $1.69
7/1/2010 $1.75 $1.75 $1.65
1/1/2011 $100.00 3.50% $1.75 $101.75 $94.33
Total $100.00 $7.00 $107.00 $99.39
Price $99.39
Par Amount $8,705,000.00
Purchase Price $8,651,812.45
10
Bond Pricing (cont.)
Key Concepts of Municipal Bonds
As a result, price and yield move in opposite directions.
Yield Price
Coupon
11
Par, Discount and Premium Bonds
Key Concepts of Municipal Bonds
Par Bonds
Yield Price
– Coupon equals yield
– Purchase price equals principal amount
Coupon
Discount Bonds
Yield
– Coupon less than yield
Yield
Price
Coupon
Coupon
Price
– Purchase price less than principal amount
Premium Bonds
– Coupon greater than yield
– Purchase price greater than principal amount
12
Par, Discount and Premium Bonds (cont.)
Key Concepts of Municipal Bonds
Maturity Date Principal Coupon Yield Price
1/1/2011 $8,705,000 3.50% 3.82% 99.389
Discount Bonds
1/1/2012 $9,005,000 3.50% 3.85% 99.017
1/1/2013 $9,325,000 3.90% 3.90% 100.000
Par Bond
1/1/2014 $9,685,000 5.00% 3.94% 104.768
Premium Bonds
1/1/2016 $20,875,000 5.25% 4.02% 107.440
Total $57,595,000
13
Original Issue Discount and Original Issue Premium
Key Concepts of Municipal Bonds
Original Issue Original Issue
Maturity Date Principal Price Premium Discount Proceeds
1/1/2011 $8,705,000 99.389 ($53,188) $8,651,812
1/1/2012 $9,005,000 99.017 ($88,519) $8,916,481
1/1/2013 $9,325,000 100.000 $9,325,000
1/1/2014 $9,685,000 104.768 $461,781 $10,146,781
1/1/2016 $20,875,000 107.440 $1,553,100 $22,428,100
Total $57,595,000 $2,014,881 ($141,707) $59,468,174
14
Capital Appreciation Bonds (CABs)
Key Concepts of Municipal Bonds
CABs pay no periodic interest until maturity. The bonds accrete in value as interest accrues.
– Usually sold as serial bonds, but can be structured as term bonds.
At maturity an amount equal to the initial principal invested plus the interest earned, compounded
semiannually at the stated yield, is paid.
They are sold in denominations of less than $5000 representing their present value and pay $5000 at
maturity.
Though CABs are often more expensive (sold at a higher yield) than current interest bonds, they are
used to achieve particular debt service patterns.
–
Example: A CAB maturing in 2011 may have a par amount of $90,595 but will have a value of
$100,000 when it matures. The difference between $100,000 and $90,595 represents the interest on
the bond.
Accreted Value of CAB from Delivery to Maturity
$102,000
$90,000
1/1/2009 7/1/2009 1/1/2010 7/1/2010 1/1/2011
CAB Accreted Value
$92,000
$94,000
$96,000
$98,000
$100,000
15
Callable Bonds
Key Concepts of Municipal Bonds
Callable bonds can be redeemed by an issuer before their actual maturity on and after a specified call
date (an optional redemption provision).
Many times, fixed-rate bonds will be callable 10 years after issuance at a price of par. Historically,
many municipal bonds were sold with 10-year call features where the bond was callable at 102 and
declined to par by the 12th year.
Municipal bonds are sold with embedded call features to provide restructuring flexibility and/or
refinancing savings in the future.
Investors charge the issuers for this flexibility – through a higher yield and lower price – thereby
increasing the cost of the financing at the time of issuance.
–
Issuers need to weigh this increased flexibility and the possibility of savings down the road against
this increased cost.
16
Bond Insurance
Key Concepts of Municipal Bonds
Issuers purchase bond insurance in order that debt service will be paid even if there are insufficient
revenues.
–
In exchange for this, investors will pay a higher price (lower yield) for an insured bond.
Premium paid upfront, based on original debt service schedule; no credits for refundings or early
repayment of bonds.
Payments by insurer are a “loan” or an “advance” that have to be paid back
–
Not like property or health insurance
–
A form of “credit enhancement”
The cost of an insurance policy needs to be compared to the observed market spread between
insured and uninsured bonds. It makes sense to only insure those maturities for which the cost of
the policy is less than 'cost' of issuing uninsured bonds.
The market for bond insurance has changed significantly over the last year. For example, several
insurers have been downgraded. Also, it is unclear what the effects of Moody’s move to a Global
Scale will be on bond insurance.
17
Bond Conventions
Key Concepts of Municipal Bonds
Basis Point
–
Yields on bonds are usually quoted in terms of basis points, with one basis point equal to one one-
hundredth of 1 percent.
•
.50% = 50 basis points
Day Count
–
30/360
•
Usually for tax-exempt fixed rate bonds
–
Actual/Actual
•
Usually for tax-exempt variable rate bonds
Pricing
–
Truncate to 3 decimals
18
Yield Curve
Current Yield Curve Compared to Yield Curves from One
and Two Years Ago
Yield Curve
U.S. Treasury Yield Curve: 9/1/2006, 9/1/2007 and 9/1/2008
Yi el d
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
1 2 3 4 5 6 7 8 9 10 111213 14151617 1819 202122 2324252627 282930
Maturity (Years)
9/1/2006 9/1/2007 9/1/2008
21
Fixed vs. Variable Rate Debt
Fixed and Variable Rate Debt Issuance
Fixed vs. Variable Rate Debt
Total Municipal Debt Issuance, 1990-Present
Billions
$500
453
$450
431
407
390
388
$400
365
342
$350
314
$300
290
85%
289
259
89%
255
88%
234
$250
226
216
209
195
$200
162
358
$150
$100
$50
$0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
(YTD)
Fixed Rate
82%
68%
84%
76%
76%
73%
79%
79%
90%
77%
86%
85%
86%
84%
85%
90%
Variable Rate
22
Fixed vs. Floating-Rate Bonds
Fixed vs. Variable Rate Debt
Advantages
No Interest Rate Risk - Budget Certainty
No Ongoing Credit Support Needed
Traditional Investors Include: Bond Funds,
Insurance Companies, Arbitrage Accounts,
Trust Departments and Retail Investors
Fixed Rate Bonds
Disadvantages
Higher Initial and Expected Interest Expense
Less Flexible Call Feature than Floating Rate
Bonds
Potentially Higher Issuance Costs
Fixed rate financings remain the most common approach in the current market.
Variable Rate Bonds
Easy to Restructure
Lower Expected Cost of Capital
Used to Diversify Debt Portfolio
Traditional Investors Include: Money Market
Funds, Corporations and Retail Investors
Interest Rate Risk
Budgeting Uncertainty
Unpredictable Pricing of Support Costs
Additional Administrative Involvement
Advantages
Disadvantages
Given the Fed’s recent rate increases, variable rates have increased from their historical lows two years ago, with
SIFMA recently resetting at 1.84%. This compares to a 20-year average of 3.15%.
23
Credit Enhancement for VRDBs
Fixed vs. Variable Rate Debt
Credit enhancement is a means of substituting the credit of the issuer with that of a higher rated third
party guarantor.
–
Similar to insurance in the case of fixed-rate bond, credit enhancement improves the
marketing for bonds.
–
Credit enhancement typically takes the form of bond insurance or letters of credit (LOC).
Bond Insurance
Typically provided by commercial banks.
Premium is based on amount of debt
outstanding and paid over time.
Most LOCs carry an initial term shorter than the
term of the bonds and must be renewed or
replaced at each expiration date.
Several well-established bond insurers.
Premium is based on projected total debt
service and paid up-front as a one time fee.
In effect for life of bond issue.
Letters of Credit (LOC)
24
Amortization Structures
Alternate Amortization Structures
Amortization Structures
Issuers can use amortization structures to shape their overall debt structure pattern.
Level Principal Level Debt Service
Total Debt
Total Debt
Maturity Date Principal Interest
Service
Maturity Date Principal Interest
Service
1/1/2010 $2,538,905 $2,538,905
1/1/2010 $2,563,713 $2,563,713
1/1/2011 $9,620,000 $2,538,905 $12,158,905
1/1/2011 $8,705,000 $2,563,713 $11,268,713
1/1/2012 $9,620,000 $2,202,205 $11,822,205
1/1/2012 $9,005,000 $2,259,038 $11,264,038
1/1/2013 $9,620,000 $1,865,505 $11,485,505
1/1/2013 $9,325,000 $1,943,863 $11,268,863
1/1/2014 $9,615,000 $1,490,325 $11,105,325
1/1/2014 $9,685,000 $1,580,188 $11,265,188
1/1/2015 $9,615,000 $1,009,575 $10,624,575
1/1/2015 $10,170,000 $1,095,938 $11,265,938
1/1/2016 $9,615,000 $504,788 $10,119,788
1/1/2016 $10,705,000 $562,013 $11,267,013
Total $57,705,000 $12,150,208 $69,855,208
Total $57,595,000 $12,568,463 $70,163,463
25
1990 1993 1996 1999 2002 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035
Year
Debt Service
Series 1990 Debt Service
1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 2025 2028 2031 2034
Year
Debt Service
Series 1990 Debt Service Series 1995 Debt Service
Impact of Issuing Multiple Stand-Alone Level Debt Service
Issues Over Time
Amortization Structures
Multiple Stand-Alone Level Debt Service Structures
Debt Service
1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 2025 2028
Year
Series 1995 Debt Service Series 2000 Debt Service Series 2005 Debt Service
26
2005 2010 2015 2020 2025 2030 2035 2040
2005 2010 2015 2020 2025 2030 2035 2040
2005 2010 2015 2020 2025 2030 2035 2040
2005 2010 2015 2020 2025 2030 2035 204
0
Principal Amortization Options
Amortization Structures
Wrapped Debt Service Structure
Accelerated/Front-Loaded Debt Service Structure
Debt Service
Debt Service
2008 2013 2018 2023 2028 2033 2038 2043
2008 2013 2018 2023 2028 2033 2038 2043
Year
Year
Existing Debt Service New Money Debt Service
Existing Debt Service New Money Debt Service
Deferred/Back-Loaded Debt Service Structure
Increasing Debt Service Structure
Year
Debt Service
Existing Debt Service New Money Debt Service
Year
Debt Service
New Money Debt Service
2008 2013 2018 2023 2028 2033
2038
2043
2008 2013 2018 2023 2028 2033 2038 2043
27
Key Calculations from a Bond Sale
Key Calculations From a Bond Sale
Key Calculations from a Bond Sale
Sources and Uses of Funds
Issuance Expenses
Net Debt Service Schedule
Yield Calculations
28
Sources and Uses of Funds
Key Calculations from a Bond Sale
Sources:
Bond Proceeds
Par Amount $57,595,000
Net Premium 1,873,174
Total Sources
$59,468,174
Uses:
Project Fund Deposit $50,000,000
Other Fund Deposits
Debt Service Reserve Fund 5,946,817
Capitalized Interest Account
2,489,242
Delivery Date Expenses
Costs of Issuance 500,000
Underwriter's Discount 387,975
Bond Insurance 140,327
Other Uses of Funds
Additional Proceeds 3,813
Total Uses
$59,468,174
29
Issuance Expenses
Key Calculations from a Bond Sale
Borrower’s Costs of Issuance
Rating Agency Fees
Issuer/ Authority Fee
Bond Counsel Fee
Borrower’s Counsel Fee
Trustee Fees
Auditor's Fee
Printing and Mailing Costs
Miscellaneous and Contingency
Components of Underwriters’ Discount
Takedown
Management Fee
Underwriters’ Counsel
DTC
CUSIP
BMA Assessment
Dalcomp
Electronic Order Entry
Dalcomp Wire Charge
Cal PSA
CDIAC
Day Loan
Out-of-Pocket and Closing Costs
Verification Agent (if refunding)
30
Net Debt Service Schedule
Key Calculations from a Bond Sale
Gross Debt
Capitalized
Net Debt
Maturity Date Principal Coupon Interest Service Interest Service
1/1/2010 $2,563,713 $2,563,713 $2,563,713
1/1/2011 $8,705,000 3.50% $2,563,713 $11,268,713 $11,268,713
1/1/2012 $9,005,000 3.50% $2,259,038 $11,264,038 $11,264,038
1/1/2013 $9,325,000 3.90% $1,943,863 $11,268,863 $11,268,863
1/1/2014 $9,685,000 5.00% $1,580,188 $11,265,188 $11,265,188
1/1/2015 $10,170,000 5.25% $1,095,938 $11,265,938 $11,265,938
1/1/2016 $10,705,000 5.25% $562,013 $11,267,013 $11,267,013
Total $57,595,000 $12,568,463 $70,163,463 $2,563,713 $67,599,750
31
Yield Calculations
Key Calculations from a Bond Sale
Yield is the discount rate at which the present value of future debt service payments are equal to the
proceeds of the issue.
The most common measures of the borrowing cost of a bond issue are the arbitrage yield, true interest
cost (TIC) and all-in TIC.
For short or non-callable issues, each is differentiated by which costs it takes account of. For
example…
Arbitrage
Yield TIC All-In TIC
Par Value
+ Premium (Discount)
- Credit Enhancement/Insurance
- Underwriter's Discount
- Cost of Issuance Expense
$57,595,000
1,873,174
-140,327
$57,595,000
1,873,174
-140,327
-387,975
$57,595,000
1,873,174
-140,327
-387,975
-500,000
Net Proceeds $59,327,847 $58,939,872 $58,439,872
32
Yield Calculations for a Bond Issue
Key Calculations from a Bond Sale
In this example, the debt service used to calculate the Arbitrage Yield, TIC and All-In TIC are the
same. The difference between them is the 'target' value.
Arbitrage
Yield TIC All-In TIC
Discount Rate* 3.98% 4.14% 4.34%
1/1/2008 -$59,327,847 -$58,939,872 -$58,439,872
7/1/2008 1,281,856 1,281,856 1,281,856
1/1/2009 1,281,856 1,281,856 1,281,856
7/1/2009 1,281,856 1,281,856 1,281,856
1/1/2010 9,986,856 9,986,856 9,986,856
7/1/2010 1,129,519 1,129,519 1,129,519
1/1/2011 10,134,519 10,134,519 10,134,519
7/1/2011 971,931 971,931 971,931
1/1/2012 10,296,931 10,296,931 10,296,931
7/1/2012 790,094 790,094 790,094
1/1/2013 10,475,094 10,475,094 10,475,094
7/1/2013 547,969 547,969 547,969
1/1/2014 10,717,969 10,717,969 10,717,969
7/1/2014 281,006 281,006 281,006
1/1/2015 10,986,006 10,986,006 10,986,006
* Also known as the Internal Rate of Return, or IRR.
33
Question and Answer
Questions and Answers
Question and Answer
Peter Taylor, Managing Director Matthew Koch, Vice President
Barclays Capital Barclays Capital
10250 Constellation Boulevard, 25
th
Floor 555 California Street, 41
st
Floor
Los Angeles, CA 90067 San Francisco, CA 94104
Phone: (310) 481-4908 Phone: (415) 274-5372
Fax: (212) 548-9039 Fax: (415) 274-5380
34
