The Fundamentals of Public Finance

The Fundamentals of Public Finance Training Manual Presented by: Daniel Kozloff February 25, 209 PFM 735 Market Street pfm.com 43 rd Floor (25) 567-600 PFM Philadelphia, PA 903

I. Finance Basics Time Value of Money Agenda Yield Curve II. Bond Math Terminology Types of Bonds Bond Pricing III. IRS Regulations IV. New Money Transactions Elements of Size Debt Service Structure Bond Structure Yield(s) PFM 2

Finance Basics PFM 3

Simple and Compound Interest Interest Earnings 7.00% Initial Investment,000.00 Compounding interest results in higher ending balances earning interest on previously earned interest Simple Interest Compound Interest Period Beginning Balance 2 3 4 5 6 7 8 9 0 Total Initial investment,000 x.07 = Interest Ending Balance,000 70,070,070,000 x.07 = 70,40,40,000 x.07 = 70,20,20,000 x.07 = 70,280,280,000 x.07 = 70,350,350,000 x.07 = 70,420,420,000 x.07 = 70,490,490,000 x.07 = 70,560,560,000 x.07 = 70,630,630,000 x.07 = 70,700 700 Period 2 3 4 5 6 7 8 9 0 Total Beginning Balance Interest Ending Balance,000 x.07 = 70,070,070 x.07 = 75,45,45 x.07 = 80,225,225 x.07 = 86,3,3 x.07 = 92,403,403 x.07 = 98,50,50 x.07 = 05,606,606 x.07 = 2,78,78 x.07 = 20,838,838 x.07 = 29,967 967 PFM 4

Time Value of Money Future Value $,000 in the future is worth less when stated as a current value. Future Value Time = n Present Value Time = 0 FV n = PV 0 (+r) n PFM 5

Time Value of Money Future Value (cont d) Future Value of $,000 compounded for -0 periods at 7% x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) x (+.07) $070.00 $,44.90,225.04,380.80,402.55,500.73,605.78,78.9,838.46,967.5 $000 0 2 3 4 5 6 7 8 9 0 =000(+.07) +(+.07) +(+.07) +(+.07) +(+.07) +(+.07) +(+.07) +(+.07) +(+.07) +(+.07) =000(+.07) 0 =PV 0 (+r) n PFM 6

Time Value of Money - Future Value Undergraduate tuition is $38,420 today. Assuming a % growth rate, what could a three year old girl expect to pay when she enters college in 5 years? (Assume she will enter college when she is 8.) $38,420 x (+.0) 5 = $44,604 Her parents promised to buy her a VW Jetta when she graduates from college. (She starts college September, 2030 and will graduate June, 2034.) When she begins school, the price tag of a VW will be $5,500. Anticipating an inflation rate of 2% each year, what should her parents expect to pay when she graduates? year year year.75 year 9//30 9//3 9//32 9//33 6//34 $5,500 x (+.02) 3.75 = $6,695 PFM 7

Time Value of Money Present Value $,000 today will be worth more when stated as a value in the future. Future Value Time = n Present Value Time = 0 PV 0 = FV n (+r) n PFM 8

Time Value of Money Present Value (cont d) Present Value of $,000 compounded for -0 periods at 7% 543.93 ( +.07) 582.0 ( +.07) 622.75 ( +.07) 666.34 ( +.07) 72.99 ( +.07) 762.90 ( +.07) 86.30 ( +.07) 873.44 ( +.07) 934.58 ( +.07) 000 ( +.07) $508.35 $543.93 $582.0 $622.75 $666.34 $72.99 $762.90 $86.30 $873.44 $934.58 $000 0 2 3 4 5 6 7 8 9 0 = (.07) = ( (.07) (.07) (.07) (.07) (.07) (.07) (.07) (.07) (.07) FV n + r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) FV n = (+ r) n 000 PFM 9

Time Value of Money Present Value (cont d) Present Value of $,000 compounded for -0 periods at 7% 582.0 ( +.07) ( +.07) 72.99 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) 666.34 ( +.07) ( +.07) ( +.07) ( +.07) 622.75 ( +.07) ( +.07) ( +.07) 000 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) 934.58 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) 873.44 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) 86.30 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) 762.90 ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) ( +.07) $508.35 $543.93 543.93 ( +.07) $582.0 $622.75 $666.34 $72.99 $762.90 $86.30 $873.44 $934.58 $000 0 2 3 4 5 6 7 8 9 0 000 = (.07) (.07) (.07) (.07) (.07) (.07) (.07) (.07) (.07) (.07) FV = (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) (+ r) FV = (+ r) n PFM 0

Future Value and Present Value Assuming the cost of gum is $.5 today and that an inflation rate of.5% has been constant over the past 2 decades, what will the cost of gum be in 5 years? Assuming inflation at.5% what was the cost of gum 5 years ago? 5 years 5 years $.5 (+.05) 5 = $0.92 Today $.5 x (+.05) 5 = $.44 PFM

Perpetuity Perpetuity Equal payments at equal intervals forever $PMT $PMT $PMT $PMT $PMT $PMT 2 3 4 5 Today? PVP = PMT r PFM 2

Perpetuity (cont d) You ve just completed a VERY lucrative real estate transaction and are now a MULTImillionaire (Woo-hoo!!!). In an effort to support your college alma mater, you ve decided to create the R.E.M.M. ( Real Estate Moguls in the Making ) Scholarship Fund. How much would you need to set aside today in order to fund a $0,000/year scholarship forever? (The first scholarships would be distributed one year from now). Assume a 5% investment earnings rate. $200,000 = 0,000.05 PFM 3

Time Value of Money Growing Perpetuity Present value of a growing perpetuity equal payments at equal intervals forever, adjusted for inflation $PMT $PMT $PMT $PMT $PMT $PMT 2 3 4 5 Today? PVP = PMT r - g PFM 4

Time Value of Money Growing Perpetuity How would you adjust the Present Value of a Perpetuity to account for inflation? (Assume inflation rate of 2% annually forever) $333,333 = 0,000.05 -.02 PFM 5

Time Value of Money Annuity An annuity is the difference between two perpetuities. In General, PVA PMT r ( + r) = n a PVP = r a a a PVP = 2 r a a a a a a a So, PV Annuity = PVP PVP2 a a = r r = 0 WRONG! a a a a a a PFM 6

Time Value of Money Annuity To get second perpetuity to time zero, must apply present value to these cash flows. PFM 7

Time Value of Money Annuity A payment stream with equal payments over equal periods of time is called an ANNUITY. 0 2 3 4 5 6 NOT an Annuity 00 00 99.9 00 00 92 0 2 3 4 5 6 NOT an Annuity 00 00 00 00 0 2 3 4 5 6 This is an Annuity 00 00 00 00 00 PFM 8

Time Value of Money Annuity 0 2 3 4 5 6 Annuity in ARREARS (Relative to time 0) Note: n = 5 00 00 00 00 00 0 2 3 4 5 6 Annuity in ADVANCE (Relative to time 0) Note: n = 5 00 00 00 00 00 0 2 3 4 5 6 Either an Annuity in ARREARS (n = 4, starting at 0) or ADVANCE (n = 4, starting at ) 00 00 00 00 PFM 9

Time Value of Money - Annuity In addition to your luck in the real estate market, you ve just won the Powerball! Congratulations!! What would you do:. Accept your $4 million winnings up-front or 2. Receive $ million annually over the next 25 years (beginning one year from now)? Assume 5% investment earnings rate. $ mm $ mm $ mm $ mm $ mm $ mm $4 million or 2 3 4 5 25 Today PFM 20

Time Value of Money Remember the Present Value of Annuity formula: PVA > Lump Sum PVA PMT r ( + r) = n Take the annuity Take the lump sum payment 4,093,945,000,000.05 ( +.05) = 25 PFM 2

Time Value of Money What if the interest rate assumption is 8%? PVA PMT r ( + r) = n Take the annuity Take the lump sum payment 0,674,776,000,000.08 ( +.08) = 25 Lump Sum > PVA PFM 22

Time Value of Money Annuity Let s assume that college will cost $44,604 each year beginning in year 5. How much is that in today s dollars? (Assume 5% rate.) PVA 4 = $58,64 FV 4 = $58,64 PV 0 = $79,883 5 6 7 8 How much would someone s parents need to set aside each year to pay for school? 79,883 PMT.05 ( +.05) = 5 Solve for PMT = $7,696 PFM 23

Time Value of Money Annuity I want to buy a car. The maximum monthly payment that I can make on a four year loan is $300. What is the maximum price that I can afford? (Assume 4% interest rate.) 2 3 4 5 39 40 4 42 43 44 45 46 47 48 PV a = $3,286.65 PVA = PMT r ( + r) 300 PVA =.04 [ 2 ] ( + PVA = $3,286.65.04 2 ) n 48 PFM 24

Term Structure of Spot Rates Until now, we have discounted all the cash flows at a single rate (r). r = 7.00% Period Cash Flow Applicable Rate Discount Factor PV n = /(+r) n Present Value,000 7.00% 0.93458 934.58 2,000 7.00% 0.87344 873.44 3,000 7.00% 0.8630 86.30 4,000 7.00% 0.76290 762.90 5,000 7.00% 0.7299 72.99 6,000 7.00% 0.66634 666.34 7,000 7.00% 0.62275 622.75 8,000 7.00% 0.5820 582.0 9,000 7.00% 0.54393 543.93 0,000 7.00% 0.50835 508.35 Total 7,023.58 PFM 25

Term Structure of Interest Rates In actuality, each cash flow should probably be discounted at the rate applicable to that period. Period Cash Flow Applicable Rate Discount Factor PV n = /(+r) n Present Value,000 3.000% 0.97087 970.87 2,000 4.000% 0.92456 924.56 3,000 5.000% 0.86384 863.84 4,000 6.000% 0.79209 792.09 5,000 7.000% 0.7299 72.99 6,000 8.000% 0.6307 630.7 7,000 9.000% 0.54703 547.03 8,000 0.000% 0.4665 466.5 9,000.000% 0.39092 390.92 0,000 2.000% 0.3297 32.97 Total 6,620.96 PFM 26

Yield Curve Fisher Equation R = r + π Real Rate of Return Inflationary Expectations π Rate r 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 Year PFM 27

Yield Curve (cont d) A normal yield curve forms during market conditions where investors generally believe that there will be no significant changes to the economy (i.e., no inflation) Given these expectations, investors expect long term instruments to offer higher yields than short term instruments Term Structure of Interest Rates Normal Yield Curve This expectation is normal because short-term instruments hold less risk than long-term instruments Yield The farther into the future the bond s maturity, the more time and uncertainty the investor faces before being paid back the principal To invest in a fixed income instrument for a longer time, the investor needs to be compensated for undertaking the additional risk Period 0 2 3 4 5 6 7 8 9 02345678920222232425 Maturity PFM 28

Yield Curve (cont d) A flat rate curve structure reveals that there may be some signs that short-term rates will rise and others that long-term rates will fall Term Structure of Interest Rates Flat Yield Curve When the yield curve is flat, investors can maximize their risk/return tradeoff by choosing securities with the least risk, or highest credit quality. Yield Period 0 2 3 4 5 6 7 8 9 02345678920222232425 Maturity PFM 29

Yield Curve (cont d) Although rare, an inverted yield curve forms during extraordinary market conditions where the expectations of investors are completely inverse to those demonstrated by a normal yield curve Term Structure of Interest Rates Inverted Yield Curve In an inverted yield curve market, investors assume long term rates will decline This curve also implies that investors expect to receive less compensation for assuming more risk Yield Some investors interpret an inverted yield curve as a signal that the economy is going to experience a slow down Before a slow down, it is better for the investor to lock money into longer term investments at present prevailing rates as future rates are assumed to be even lower Period 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 Maturity PFM 30

Inverted Yield Curves and US Recessions % Spread 4.00 3.00 2.00.00 0.00 -.00-2.00-3.00-4.00 962 964 966 968 970 972 974 976 978 980 982 984 986 988 990 992 994 996 998 2000 2002 2004 2006 2008 200 202 204 206 208 UST 0 Yr - Yr Spread UST 0 Yr - Yr Spread PFM SOURCE: Board of Governors of the Federal Reserve System, National Bureau of Economic Research 3

Yield Curve (cont d) The yield curve may be influenced by exceptionally strong or weak investor demand for securities of a given maturity. For example, banks may prefer to purchase securities with terms less than 20 years, eschewing what may be relatively higher interest rates at longer terms. The effect would be to increase demand in the - 20 year range, meaning investors would accept/borrowers would receive lower interest rates on securities maturing during this period. Conversely, a lack of demand after 20 years could elevate interest rates in this segment of the curve. Expectations Risk/Liquidity Premium Market Segmentation Effect Rate 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 Year PFM 32

Yield Curves AAA MMD GO 3.5% 3.0% 2.5% Yield 2.0%.5%.0% 0.5% 0.0% Year Ago Month Ago Current 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 Maturity SOURCE: Thomson-Reuters PFM 33

Yield Curve Ranges 6% 5% MMD Range (over past 0 years) Current MMD Average MMD (over past 0 Years) 4% Yield 3% 2% % 0% 2 3 4 5 7 0 5 20 25 30 Maturity Year SOURCE: Thomson-Reuters PFM 34

Bond Math PFM 35

Why Issue Bonds? States, cities, counties and other public authorities are responsible for funding public projects such as the construction and upkeep of schools, hospitals, highways, sewers, and universities How should issuers fund these capital projects? Option : Use that treasure chest of funds that s been sitting around. What treasure chest of funds??? Option 2: Save up money (maybe from a newly instituted tax) for a long period of time (20 to 30 years) and then build the project once the necessary amount has been saved (i.e., pay as you go funding). Problem: Issuer needs the project now, the project may also be much more expensive in 20 to 30 years. Problem: Unfair - Those that are taxed to fund the project should also be those that benefit from/ use the project (i.e., generational transfer). Option 3: Issue Bonds. Issuers can procure funds today to build the project they need by borrowing money through a bond issuance. The debt service (i.e., principal and interest) on the bonds is paid by the users of the project (i.e., tax-payers, tollpayers, rate-payers). PFM 36

Tax Exemption The IRS deems bonds that are issued for qualified public projects by municipal governments (e.g., state and local governments) and non-profits entities (e.g., school districts, higher education, toll and transit, airports, public power, health care, etc.) taxexempt. The interest income on these bonds are exempt from federal income taxes. Many are also exempt from state income taxes, for owners that reside within those states. Why? Because the capital projects funded by these bonds are for the good of the public. Due to these exemptions, tax-exempt bonds typically carry lower interest rates than comparable, taxable bonds. Taxable Bond Tax-exempt Bond Market Interest Rate 0.00% 6.70% Less Taxes (3.30%) 0.00% Effective Interest Rate 6.70% 6.70% Investors are willing to receive a lower rate since they are not required to pay taxes on interest income. PFM 37

Terminology A Bond is evidence of a loan Buyer of the Bond is the lender or investor Seller of the Bond is the borrower or the issuer or the obligor Principal or Face Amount or Par Amount Amount of loan Maturity date Repayment date of loan may be spread across multiple years Nominal or Coupon rate Interest rate paid periodically on the loan Usually expressed as a percentage of par amount Price Amount a lender will lend in consideration of future receipt of principal and interest payments Yield Single rate that sets the PV of the future principal and interest payments equal to the initial price PFM 38

Terminology (cont d) Bond Components Annuity of Interest / Coupon Payments (Paid Semi-annually by Issuer to Investor) Principal / Par (Paid by Issuer to Investor) Loan Amount (Paid by Investor to Issuer) PV = Price Time Maturity PV = t n = CFn ( + Yield) n Inverse relationship to Price PFM 39

Terminology (cont d) Let s assume a municipality needed to borrow $0 million for a capital project (3/7/) To make it simple, let s just assume that there were 0 investors and each investor lent the municipality $ million over various periods Investors Lending Term Repayment Date Loan Amount Coupon Municipality s Semi-Annual Interest Payment Investor year 0// $,000,000 3.000% $5,000 Investor 2 2 years 0//2 $,000,000 3.25% $5,625 Investor 3 3 years 0//3 $,000,000 3.250% $6,250 Investor 4 4 years 0//4 $,000,000 3.375% $6,875 Investor 5 5 years 0//5 $,000,000 3.500% $7,500 Investor 6 6 years 0//6 $,000,000 3.625% $8,25 Investor 7 7 years 0//7 $,000,000 3.750% $8,750 Investor 8 8 years 0//8 $,000,000 3.875% $9,375 Investor 9 9 years 0//9 $,000,000 4.000% $20,000 Investor 0 0 years 0//20 $,000,000 4.25% $20,625 PFM 40

Terminology (cont d) Semi-Annual Debt Service Schedule for Investor Date Principal Coupon Interest Debt Service PV of Debt Service 3/7/20 4//20 2,000.00 2,000.00,996.03 0//20,000,000 3.000% 5,000.00,05,000.00 998,003.97 Total,000,000 7,000.00,07,000.00,000,000.00 Semi-Annual Debt Service Schedule Date Principal Coupon Interest Debt Service 3/7/20 4//20 23,750 23,750 0//20,000,000 3.000% 78,25,78,25 4//202 63,25 63,25 0//202,000,000 3.25% 63,25,63,25 4//203 47,500 47,500 0//203,000,000 3.250% 47,500,47,500 4//204 3,250 3,250 0//204,000,000 3.375% 3,250,3,250 4//205 4,375 4,375 0//205,000,000 3.500% 4,375,4,375 4//206 96,875 96,875 0//206,000,000 3.625% 96,875,096,875 4//207 78,750 78,750 0//207,000,000 3.750% 78,750,078,750 4//208 60,000 60,000 0//208,000,000 3.875% 60,000,060,000 4//209 40,625 40,625 0//209,000,000 4.000% 40,625,040,625 4//2020 20,625 20,625 0//2020,000,000 4.25% 20,625,020,625 0.00 <==PV of Cashflows minus Principal 3.00% <==yield The yield is determined by finding the rate that sets the PV of Debt Service and the upfront proceeds equal to one another. PFM 4

Terminology (cont d) Option: The right, but not the obligation, to buy or sell a specific amount of a given asset at a specified price (the strike price) during a specified period of time. Call Option: The right, but not the obligation, to buy an asset at a given price Buying a Call Option Profit Out of the Money At the Money In the Money Investor gains $0 $20 $30 Strike Price Market Price In the Money: Strike Price < Market Price At the Money: Strike Price = Market Price Out of the Money: Strike Price > Market Price PFM 42

Terminology (cont d) Option (cont d) Put Option: The right, but not the obligation, to sell a given asset at a specified price during a specific period. The writer of the put is obligated to buy the underlying asset and pay the strike price for it. Buying a Put Option Payoff Option purchaser gains In the money At the money Strike Price Out of the money $0 $20 $30 Market Price In the Money: Strike Price > Market Price At the Money: Strike Price = Market Price Out of the Money: Strike Price < Market Price PFM 43

Form of Bonds Bearer Bonds (not tax-exempt after 6/30/83) Registered Bonds Certificate(d) Register, registrar Immobilized Global Registered Clearing Agency Clearing Corporations - trade confirmation, comparison, clearance, settlement Depository - immobilized securities Book-Entry Form Participant Street Name Beneficial Owner Municipal Bonds: fully registered in the name of depository nominee, book-entry form with global certificate per maturity, deposited with depository (DTC), purchased through Direct Participants, who maintain records for Beneficial Owners PFM 44

Depository Trust Company ( DTC ) $00 million issue secured by specified revenue stream ($) Revenues Revenue Bond Issuer ($) Pledged Revenues Trustee/ Paying Agent GO Bond Issuer ($) Debt Service payments DTC Fully registered in Street Name Cede & Co. $20mm security CUSIP: 23456RP3 = $00 million Immobilized Global Certificates Morgan Stanley ($20 million) J.P. Morgan Private Banking ($0 million) Citigroup ($30 million) ($) $20K Investment Merrill Lynch ($5 million) You/Me Goldman Sachs ($25 million) ($) DS payments Direct Participants (Broker-Dealers) Maintain account balances for beneficial owners Beneficial owner s brokerage statement (No Physical Bonds) PFM 45

Types of Bonds Current Interest Bonds (CIBs) 0 Capital Appreciation Bonds (CABs)/Zero Coupon Bonds 0 Convertible CABs/Deferred Interest Bonds (DIBs) 0 PFM 46

Types of Fixed-Rate Bonds CIBs Dated Date //2007 Delivery //2007 First Interest 4//2007 Final Maturity 4//206 Par 00,000,000.00 Current Interest Bond Date Par Coupon Interest Debt Service //2007 4//2007 750,000 750,000 0//2007,500,000,500,000 4//2008,500,000,500,000 0//2008,500,000,500,000 4//2009,500,000,500,000 0//2009,500,000,500,000 4//200,500,000,500,000 0//200,500,000,500,000 4//20,500,000,500,000 0//20,500,000,500,000 4//202,500,000,500,000 0//202,500,000,500,000 4//203,500,000,500,000 0//203,500,000,500,000 4//204,500,000,500,000 0//204,500,000,500,000 4//205,500,000,500,000 0//205,500,000,500,000 4//206 00,000,000 3.00%,500,000 0,500,000 Total 00,000,000 27,750,000 27,750,000 PFM 47

Types of Fixed-Rate Bonds CABs Dated Date //2007 Delivery //2007 First Interest 4//2007 Final Maturity 4//206 Proceeds 75,923,849.28 Date Capital Appreciation Bond ("CAB") / Zero Coupon Bond Principal Accretion Rate Accretion Debt Service //2007 75,923,849 75,923,849 4//2007 76,49,59 76,49,59 0//2007 77,638,526 77,638,526 4//2008 78,803,04 78,803,04 0//2008 79,985,50 79,985,50 4//2009 8,84,928 8,84,928 0//2009 82,402,702 82,402,702 4//200 83,638,742 83,638,742 0//200 84,893,323 84,893,323 4//20 86,66,723 86,66,723 0//20 87,459,224 87,459,224 4//202 88,77,2 88,77,2 0//202 90,02,679 90,02,679 4//203 9,454,29 9,454,29 0//203 92,826,033 92,826,033 4//204 94,28,423 94,28,423 0//204 95,63,699 95,63,699 4//205 97,066,75 97,066,75 0//205 98,522,67 98,522,67 4//206 00,000,000 3.00% 00,000,000 00,000,000 Total 00,000,000 PFM 48

Types of Fixed-Rate Bonds CCABs and DIBs Dated Date //2007 Delivery //2007 First Interest 4//2007 Final Maturity 4//206 Proceeds 85,527,653.36 Date Convertible Capital Appreciation Bond ("CCAB") / Deferred Interest Bond ("DIB") Principal Accretion Rate Accretion Current Interest Debt Service //2007 85,527,653 4//2007 86,66,723 0//2007 87,459,224 4//2008 88,77,2 0//2008 90,02,679 4//2009 9,454,29 0//2009 92,826,033 4//200 94,28,423 0//200 95,63,699 4//20 97,066,75 0//20 98,522,67 4//202 00,000,000 0//202,500,000,500,000 4//203,500,000,500,000 0//203,500,000,500,000 4//204,500,000,500,000 0//204,500,000,500,000 4//205,500,000,500,000 0//205,500,000,500,000 4//206 00,000,000 3.00%,500,000 0,500,000 Total 00,000,000 2,000,000 2,000,000 PFM 49

Pricing a Bond Price of a Bond = PV Cashflows PV Cashflows = PV Interest Annuity + PV Principal therefore,000 Price of a Bond = PV Interest Annuity + PV Principal Par,000 Par Bond Coupon 5.00% (2.5% paid semi-annually) Yield 5.00% Years 5 Present Value =,000 (Price = 00) 25 25 25 25 25 25 25 25 25 25 COUPON = YIELD PFM 50

Pricing a Bond (cont d) Price of a Bond = PV Cashflows PV Cashflows = PV Interest Annuity + PV Principal therefore,000 Price of a Bond = PV Interest Annuity + PV Principal Par,000 Premium Bond Coupon 5.00% (2.5% paid semi-annually) Yield 4.00% Years 5 Present Value =,044.9 (Price = 04.49) 25 25 25 25 25 25 25 25 25 25 COUPON > YIELD PFM 5

Pricing a Bond (cont d) Price of a Bond = PV Cashflows PV Cashflows = PV Interest Annuity + PV Principal therefore,000 Price of a Bond = PV Interest Annuity + PV Principal Discount Bond Par,000 Coupon 5.00% (2.5% paid semi-annually) Yield 6.00% Years 5 Present Value = 957.34 (Price = 95.734) 25 25 25 25 25 25 25 25 25 25 COUPON < YIELD PFM 52

Mechanics of Variable Rate Debt Variable Rate Bond Usually sold at par (no premiums!) Nominal Maturity (pay down can be flexible) Interest paid on a current basis at rates that are periodically reset Interest Rate Reset Procedure Process by which interest rates are periodically reset on the variable rate debt Interest Rate Mode Term for which interest rates are periodically reset (e.g., daily, weekly) Variable rate debt may be multi-modal, allowing for discreet changes from one interest rate mode to another. Interest Payment Frequency Frequency with which interest is paid to investors ISSUER Variable DS Bondholders Liquidity & Remarketing Principal Variable Interest Expense Maturity PFM 53

Mechanics of Variable Rate Debt Tax-exempt variable rate bonds provide a fluctuating coupon payment stream to investors based on Securities Industry and Financial Markets Association (SIFMA) Index (formerly known as Bond Market Association (BMA)) SIFMA Index: Tax-exempt variable rate demand obligations with outstanding amounts of at least $0 million Highest short-term ratings Interest is paid on a monthly basis Bonds are not subject to the alternative minimum tax Calculated on actual/actual day count basis Usually sold at par Interest Rate Reset Procedure Terms are established for periodic interest rate resets (e.g., daily, weekly) by a remarketing agent. Interest Payment Frequency May be monthly or semi-annual PFM 54 54

Variable Rate Advantages Lower Debt Service Costs Moves borrowing rates to the short end of the yield curve (in upwardly sloping yield curve environment) The mode of variable rate debt may be changed to capitalize on opportunities in the shortterm interest rate market (i.e., weekly to fixed mode) Variable rates have historically been lower than fixed rates 0-yr average SIFMA (0.47%) vs. 0-yr average of 0-yr MMD (2.45%) Debt Flexibility Variable rate debt is typically currently callable with short notice (30 days) at any time Variable rate bonds allow the issuer more flexibility in taking advantage of falling interest rate environment vs. fixed rate bonds with tax code advance refunding limitations Refundable at any time with fixed rate bonds to take advantage of low fixed rates and preserve variable rate debt capacity in future Diversifies Investor Base Variable rate debt appeals to different market segments and investors Asset-Liability Management Hedge interest rate risk inherent in most capital structures Diversify capital structure PFM 55

Variable Rate Demand Obligations Initial Offering Negotiated offering with official statement for full amount of project needs Interest Reset Procedure Interest rates are adjusted by a remarketing agent at the minimum rate required to trade the VRDOs at par Interest Rate Modes Daily Monthly Semiannually Weekly Quarterly Term Interest Payment Frequency Usually monthly or semiannually st business day of month on a modified following business day basis Tender or Put Features VRDO holders may tender the securities on any reset date with notice Liquidity / Credit Enhancement Liquidity required to purchase potentially tendered VRDOs. Issuer may purchase liquidity from a bank or alternatively provide self liquidity In the event of a failed remarketing, VRDOs become bank bonds and interest is paid to the bank at a predetermined rate (up to a maximum rate) until the bonds are successfully remarketed. Bank bond parameters will also typically include an acceleration of principal payments. Redemption Provisions Callable anytime with 30 days notice at par PFM 56

Types of Variable Rate Bonds Auction Rate Securities Modified Dutch Auction No put feature Insurance Commercial Paper Negotiated offering with shorter commercial paper memorandum for only immediate project needs ( - 270 days) Commercial paper is rolled at maturity at interest rates set by the commercial paper dealer Floating Rate Notes Interest rates is determined on a pre-determined frequency by SIFMA resets plus a spread negotiated at pricing May be sold with a maturity (i.e. 3 year maturity) or a put (i.e. 30 year maturity with 3 year put) Put Bonds Often a Term Mode within multi-modal variable document that allows fixed rate for tenor of -7 years May be sold with a maturity (i.e. 3 year maturity) or a put (i.e. 30 year maturity with 3 year put) Private Placements/Direct Purchase Variable Rate direct loan with a bank typically sold as an Index or % of an index plus a spread (i.e., SIFMA plus spread or % LIBOR/SOFR plus a spread) PFM 57

Overview of Different Types of Liquidity Due to the regular remarketing of VR debt, issuers have the opportunity to put bonds back to the issuer, receiving their principal back at any time. Self-liquidity Typically only for AA rated or better institutions Issuer is responsible for funding any failed remarketings with its own resources Issuer must demonstrate ample liquid resources to cover potential put and must have a liquidation procedure policy/memo documented Standby Bond Purchase Agreement (SBPA) Typically only for AA rated or better institutions (sometimes high A credits do selfliquidity but not often) Issuer pays regularly scheduled interest and principal payments SBPA exist only to fund failed remarketings Is not credit enhancement PFM 58

Overview of Different Types of Liquidity (cont d) Direct Pay Letter of Credit (DPLOC) Typically used for borrowers in the BBB to AA range Letter of Credit Bank pays debt service to investors directly and issuer reimburses the Bank, therefore investors look primarily to the credit of the underlying bank. Recently investors care more about underlying credit Hybrid Line of Credit Line of credit dedicated to funding failed remarketings The terms and conditions of the line of credit will essentially mirror that of a SBPA (timing of funding requirements, events in which Bank may get out of the agreement, etc.) Unlike a SBPA where the bond trustee immediately taps the Bank, with a hybrid line of credit the borrower has the responsibility to draw on the line of credit or use its own resources PFM 59

IRS Regulations PFM 60

IRS Regulations of Municipal Bonds Benefit of tax-exempt bonds: Cost of financing is generally lower for issuers public benefit for public projects Interest paid to bondholders is not includable in their gross income for federal income tax purposes. This tax-exempt status remains throughout the life of the bonds provided that all applicable federal tax laws are satisfied both at the time the bonds are issued and throughout the term of the bonds. Federal Laws Tax Code 954 and 986-03, 4-50 Constitution Regulations Rulings, Revenue Procedures, Private Letter Rulings Primary objectives of federal laws No private activity No arbitrage PFM 6

Private Activity Bonds (PABs) No part of tax-exempt issue can be considered private activity (Section 4): Two tests:. Private Business Use Test: >0% of the proceeds of an issue will be used for private trade or business use. AND 2a. Private Payment or Security Test: >0% of debt service on the bond issue is secured (directly or indirectly) by a private business use. OR 2b. Private Loan Financing Test: proceeds of issue used to make or finance loans to nongovernmental entities is greater than the lesser of 5% or $5M. PFM 62

Yield Restriction Direct or indirect investment of the gross proceeds of an issue in investments earning a yield materially higher than the yield of the bond issue (Arbitrage Yield) Gross Proceeds : Sale Investment Transferred Replacement Materially higher : Investments Yield Limit Above Arbitrage Yield Refunding Escrows 0.00% Replacement Proceeds 0.00% Program Investments:.500% Student Loans 2.000% Mortgage Bonds:.25% Tax-exempt Investments: N/A PFM 63

Exceptions to Yield Restriction Temporary Periods Capital Projects: 3 years Working Capital Expenditures: 3 months Reasonably Required Reserve and Replacement Funds (4-R) <0% funded with bond proceeds Reasonably Required, is lesser of: 0% Par Amount Maximum Annual Debt Service 25% Average Annual Debt Service Minor Portion, lesser of: 5% of sale proceeds $00,000 PFM 64

Arbitrage Rebate If proceeds are unrestricted, still subject to rebate For non-purpose investments, rebate liability equals difference between FV of receipts at arbitrage yield vs. FV of receipts at investment yield versus payments Payable every 5 years after date of issuance (90% within 60 days) If not paid, bonds become arbitrage bonds Taxable Penalties Exceptions to Arbitrage Rebate: Small Issuer: $5mm or less in calendar year or $0mm for public school expenditures Spending Exception: 6 month (any issue) 8 month (capital projects) 24 month (construction projects) PFM 65

New Money Transactions PFM 66

Tao of Municipal Modeling Refunding Escrow(s) Other Elements of Size Construction Fund Capitalized Interest Size Costs of Issuance Bond Insurance Debt Service Reserve Fund Underwriter s Discount Bond Structure Structure Yield Debt Structure PFM 67

Sizing A government needs to build a new bridge. At the time, the estimated completion was three years and total project costs totaled $500 million. Construction for the project began March 5, 20, although it took 3 years until all projects became fully operational. (Revenues securing the debt service (i.e., bridge tolls) became available to pay debt service on the bonds on March 5, 204.) PFM 68

Construction Fund Draw Schedule 35,000,000 Construction Draws 30,000,000 25,000,000 ($ Dollars) 20,000,000 5,000,000 0,000,000 5,000,000 0 3//20 4//20 5//20 6//20 7//20 8//20 9//20 0//20 //20 2//20 //202 2//202 3//202 4//202 5//202 6//202 7//202 8//202 9//202 0//202 //202 2//202 //203 2//203 3//203 4//203 5//203 6//203 7//203 8//203 9//203 0//203 //203 2//203 //204 2//204 PFM 69

Construction Fund Schedule Gross Funded Gross funded Construction Fund Interest earnings not needed to fund scheduled draws PFM 70

Construction Fund Schedule Net Funded Net funded Construction Fund Interest earnings + draws on principal fund scheduled draws PFM 7

Construction Fund (cont d) Sources and Uses Required, as bonds are sold in denominations of $5,000 (a.k.a. Rounding ) PFM 72

Costs of Issuance Verification Agent (Refunding) Feasibility Consultant / Traffic Engineer Bond Counsel Tax Counsel Printer ISSUER Special Counsel Financial Advisor Registrar Paying Agent Escrow Agent Trustee Rating Agencies Trustee Counsel PFM 73

Costs of Issuance (cont d) Cost of Issuance PFM 74

Costs of Issuance (cont d) Sources and Uses up from $478,740,000 PFM 75

Underwriter s Discount Issuer bonds $995.50 Syndicate Account $4.50 / $,000 of par Underwriters bonds $000 Buyer Component Management Fee Takedown Risk Expenses Old Days $5.00 20.00.00 4.00 $30.00 Today $0.00 3.00 0.00.50 $4.50 PFM 76

Underwriter s Discount (cont d) Underwriter s Discount PFM 77

Underwriter s Discount (cont d) Sources and Uses up from $479,025,000 PFM 78

Debt Service Reserve Fund Security for investors in case the issuer is unable to meet debt service obligations Provides short-term liquidity Interest generated from DSRF can be used to subsidize other funds (i.e., reduce initial deposit size in project fund) or pay debt service costs Sized to meet investor needs, subject to IRS constraints Reasonably Required Reserve and Replacement Fund (4-R) Lesser of: 0% of Par.25X Average Annual Debt Service Maximum Annual Debt Service ( MADS ) PFM 79

Debt Service Reserve Fund - Formula Verification Annual Debt Service Reserve Requirement = MADS Formula Verification PFM 80

Debt Service Reserve Fund Earnings DSRF interest earnings used to offset debt service payments Gross-funded Debt Service Reserve Fund Why not Net Fund? PFM 8

Debt Service Reserve Fund Net Debt Service DSRF interest earnings Net Debt Service PFM 82

Debt Service Reserve Fund (cont d) Sources and Uses up from $480,575,000 increased par = increased UD PFM 83

Bond Insurance Monoline insurance companies guarantee timely payment of debt service in consideration of an up front insurance premium Premium charged equals a percentage of insured debt service Issuer may borrow at rating of insurer 2007 (pre-recession) Insurance Companies Moody's S&P Fitch Ambac Aaa AAA AAA FSA Aaa AAA AAA FGIC Aaa AAA AAA CIFG Aaa AAA AAA XL Capital Aaa AAA AAA MBIA Aaa AAA AAA Source: Moody s, Fitch, and S&P As of December 2, 207 2007 and today TODAY Insurance Companies Moody's S&P Fitch FSA/Assured Guaranty Municipal Corp A2 AA WD Ambac WD WD WD FGIC WD WD WD MBIA Insurance Corp Caa CCC WD National Public Finance Guarantee Corp/MBIA Illinois A3 A WD Syncora Guarantee Inc/XL Capital Assurance WD WD WD CIFG WD WD WD Assured Guaranty Corp A2 AA WD ACA NR WD WD Radian Asset Assurance WD WD WD Berkshire Hathaway Assurance Corp. Aa AA+ NR Build America Mutual Assurance Company NR AA NR PFM 84

Bond Insurance Premium Verification Annual Debt Service Multiply aggregate debt service by 60 bps Formula Verification PFM 85

Bond Insurance (cont d) Sources and Uses up from $54,25,000 increased MADS = increased DSRF increased par = increased UD PFM 86

Capitalized Interest Portion of bond proceeds set aside to pay interest on the bonds for a specified period of time Commonly utilized over the construction period of a revenue-producing project to ensure that debt service expense is not required to be paid from project revenues until the project is operational and producing revenues Most commonly net-funded Capitalized period usually lasts less than three years PFM 87

Capitalized Interest (cont d) Principal not amortized during capitalized interest period Capitalized Interest Capitalized Interest through 3/5/204 PFM 88

Capitalized Interest (cont d) Net Debt Service Gross Capitalized Interest Requirements Capitalized Interest Fund Net funded PFM 89

Capitalized Interest (cont d) Sources and Uses up from $520,325,000 increased MADS = increased DSRF increased par = increased UD increased DS = increased insurance premium PFM 90

Tao of Municipal Modeling Debt Structure Refunding Escrow(s) Other Elements of Size Construction Fund Capitalized Interest Size Costs of Issuance Bond Insurance Debt Service Reserve Fund Underwriter s Discount Bond Structure Structure Yield Debt Structure PFM 9

Level Debt Service Level Debt Service PFM 92

Level Debt Service (cont d) 30,000,000.00 Level Debt Service 25,000,000.00 20,000,000.00 ($Dollars) 5,000,000.00 0,000,000.00 5,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest PFM 93

Level Principal Amortization Level Principal PFM 94

Level Principal Amortization (cont d) 40,000,000.00 Level Principal 35,000,000.00 30,000,000.00 25,000,000.00 ($Dollars) 20,000,000.00 5,000,000.00 0,000,000.00 5,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest PFM 95

Deferred Principal Amortization Deferred Principal PFM 96

Deferred Principal Amortization (cont d) 60,000,000.00 Deferred Principal 50,000,000.00 40,000,000.00 ($ Dollars) 30,000,000.00 20,000,000.00 0,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest PFM 97

Accelerated Principal Amortization Accelerated Principal PFM 98

Accelerated Principal Amortization (cont d) 60,000,000.00 Accelerated Principal 50,000,000.00 40,000,000.00 ($Dollars) 30,000,000.00 20,000,000.00 0,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest PFM 99

Uniform Debt Service Uniform Debt Service PFM 00

Uniform Debt Service (cont d) 60,000,000.00 Uniform Debt Service 50,000,000.00 ($Dollars) 40,000,000.00 30,000,000.00 $ $ Unused $ $ Revenues 20,000,000.00 0,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest Revenue Constraint PFM 0

Proportional Debt Service Proportional Debt Service PFM 02

Proportional Debt Service (cont d) 60,000,000.00 Proportional Debt Service 50,000,000.00 40,000,000.00 % % Debt Service % % Coverage ($Dollars) 30,000,000.00 20,000,000.00 0,000,000.00 0.00 //202 //203 //204 //205 //206 //207 //208 //209 //2020 //202 //2022 //2023 //2024 //2025 //2026 //2027 //2028 //2029 //2030 //203 //2032 //2033 //2034 //2035 //2036 //2037 //2038 //2039 //2040 //204 Principal Interest Revenue Constraint PFM 03

Uniform vs. Proportional Debt Service UNIFORM DEBT SERVICE PROPORTIONAL DEBT SERVICE Revenue Constraint Revenue Constraint Debt Service Debt Service PFM 04

Let s Size Some Bonds! Assumptions Underwriter s Discount Dated/Delivery: 5/7/205 First Interest: 7//205 First Possible Maturity: //6 Last Maturity: //2045 Gross Project Fund Costs: $500,000,000 Level Monthly Project Draws: 6//5 Project Fund Life: 3 years Project Fund Earnings Rate: 3% Interest compounded monthly Net Funded Cost of Issuance: Bond Counsel: $50,000 Trustee $5,000 Trustee Counsel: $2,000 Rating Agencies: $5,000 Financial Advisor: $50,000 Contingency: $5,000 Management Fee: $/bond Takedown: $2.50/bond Risk: $0 Underwriter's Counsel: $25,000 MSRB, Dalcomp, SIFMA: $0.03per bond Out-of-pocket: $5,000 Miscellaneous: $5,000 Capitalized Interest: 2 years Capitalized Interest Earnings Rate: 3% Net Funded DSRF: Lesser of 0% of par.25*average annual debt service MADS Insurance: 60 bps on total debt service Par structure (5% coupons/ 5% yields) PFM 05

Tao of Municipal Modeling Bond Structure Refunding Escrow(s) Other Elements of Size Construction Fund Capitalized Interest Size Costs of Issuance Bond Insurance Debt Service Reserve Fund Underwriter s Discount Bond Structure Structure Yield Debt Structure PFM 06

Coupon/Yield Relationships For a given coupon, the price an investor is willing to pay for a bond is inversely related to the yield. Original Issue Discount (OID) Par Bond Original Issue Premium (OIP) General Rule Coupon<Yield Coupon=Yield Coupon>Yield Price<00 Price=00 Price>00 Example (20-year bond)* Coupon=4.00% Yield=5.00% Price=87.448 Coupon=5.00% Yield=5.00% Price=00.000 Coupon=6.00% Yield=5.00% Price=2.55 *Assumes settlement date of //06 and final maturity of //26 PFM 07

Issuer/Investor Preferences Given the same proceeds and present value of debt service, you would think an issuer would be essentially indifferent between issuing OID, Par, or OIP Bonds OID Par OIP Par Amount 55,860,000 50,000,000 42,565,000 Coupon 3.000% 3.75% 5.000% Yield 3.750% 3.75% 3.750% Price 89.53% 00.000% 7.478% Proceeds 50,00,962 50,000,000 50,004,5 Assumes 20 year bond Retail investors are typically less sensitive to coupon Typically buy and hold Less sensitive to market discount rules Retail-only order periods allow par bonds to be pre-sold Demand is strongest in years - 0 and 20 Institutional investors are NOT indifferent to coupon Interest rate views (price protection, coupon reinvestment, duration and convexity management) Possible tax implications (market discount rule) Cash flow needs (replace refunded higher coupon bonds) PFM 08

Price Volatility Premium bonds provide price protection against rising interest rates. Discount bonds provide opportunity for investors to enhance their return in falling rate environment. Most price appreciation Price Volatility OID Par OIP Purchase Date //06 //06 //06 Maturity //26 //26 //26 Coupon 3.000% 3.750% 5.000% Yield 3.750% 3.750% 3.750% Price 89.53% 00.000% 7.478% Purchase Date 4//06 4//06 4//06 Maturity //26 //26 //26 Coupon 3.000% 3.750% 5.000% Yield 3.000% 3.000% 3.000% Price 00.000%.% 29.636% % Price Change.76%.% 0.349% Falling Interest Rate Environment Rising Interest Rate Environment` Purchase Date 4//06 4//06 4//06 Maturity //26 //26 //26 Coupon 3.000% 3.750% 5.000% Yield 4.500% 4.500% 4.500% Price 80.503% 90.248% 06.490% Least price depreciation % Price Change (0.066%) (9.752%) (9.353%) PFM 09

Investor Preferences: Yield Curve Maturity Range Premium or Discount Targeted Investors 5 years Par Par Moderate Premium Moderate Premium 6 0 years Par or slight discount Custom Premiums Custom Premiums Custom Premiums 7 years Custom Premiums Custom Premiums Custom Premiums Custom Premiums 8 2 years Custom Premiums Custom Premiums Custom Premiums Par/Slight Discount 22 30 years Custom Premiums Custom Premiums Custom Premiums Retail Banks/Trusts Corporations Money Managers Retail Banks/Trusts Money Managers Bond Funds Money Managers Intermediate Funds Property/Casualty Derivative Product Creators Property/Casualty Bond Funds Arbitrage Retail Property/Casualty Arbitrage Bond Funds PFM 0

Pricing Callable Bonds Depending on the type of bond an investor holds, the call option an issuer holds may affect the yield that the investor expects Par Discount Premium Settlement Date 0//2007 0//2007 0//2007 Maturity 0//2027 0//2027 0//2027 Call 0//207 0//207 0//207 Price* 00 87.448 2.55 Coupon 5.000% 4.000% 6.000% Yield (to Maturity) 5.000% 5.000% 5.000% Yield (to Call) 5.000% 5.660% 4.432%** *to maturity **Yield to worst If a callable premium bond is called, the investor receives a lower yield than originally represented ( yield to worst ) PFM

Pricing of Callable Premium Bonds MSRB rules require issuers to sell OIPs at the price and yield that constitutes the worst case for the investor (i.e., lower yield, higher price). A higher coupon premium bond has a better chance of being called, but a bigger kick to maturity if it is not called. Delivery Date 0//07 Maturity Date 0//27 Coupon 6.000% Price to Maturity (PTM) 2.55 YTM 5.000% Call Date 0//7 Call Price 00.000 Yield to Worst (at call date) 4.432% Price to Call (PTC) 2.556 Yield to Maturity (YTM) 5.000% Issuer s best case (bonds called) / Investor s worst case Issuer s worst case (bonds not called) / Investor s best case ( =.57% = Kick to Maturity ) The MSRB and IRS rules for callable premium bonds can have an adverse impact on the economics of an issuer s deal particularly refundings. Because callable premium bonds are priced on a yield to worst basis, it results in diminished production compared to callable par bonds, callable discount bonds or any type of non-callable bond. PFM 2

Pricing of Callable Premium Bonds (cont d) Callable premium bonds are usually denoted with an asterisk or footnote when priced to a date other than the final maturity date. PFM 3

Bond Pricing Reports for Callable Premium Bonds PFM 4

Mandatory Redemption Provisions What are the implications if you are selling 30-year bonds and investors are only interested in years - 24 and year 30? 24 30 Debt service structure will not be level Yields may have to increase in order to interest buyers in years 25-29 (increased cost to issuer) To mitigate this, underwriters may spread out the 30 year par amongst the 25-30 year maturities as mandatory sinking funds. All maturities will be priced to the 30 year period. 24 30 PFM 5

Mandatory Redemption Provisions (cont d) Term Bond PFM 6

Mandatory Redemption Provisions (cont d) PFM 7

Optional Redemption Provisions PFM 8

Tao of Municipal Modeling Arbitrage Yield Refunding Escrow(s) Other Elements of Size Construction Fund Capitalized Interest Size Costs of Issuance Bond Insurance Debt Service Reserve Fund Underwriter s Discount Bond Structure Structure Yield Debt Structure PFM 9

Bond Statistic Yields Single rate that sets PV of debt service and other payment obligations equal to the Purchase Price or Target Value TIC All-in-TIC Arbitrage Yield Par Value 200,000,000 200,000,000 200,000,000 + Accrued Interest 0 0 0 + Premium (Discount) 0 0 0 - Underwriter's Discount (2,000,000) (2,000,000) - Cost of Issuance Expense (300,000) - Other Amounts (,533,066) (,533,066) Target Value 98,000,000 96,66,934 98,466,934 Target Date (Delivery Date) 5/7/205 5/7/205 5/7/205 Yield 5.28445% 5.42023% 5.67482% PFM 20

Annual Debt Service ANNUAL DEBT SERVICE Dates Par Coupon Interest Debt Service 5/7/205 //206 5,900,000 5.00% 6,500,000 22,400,000 //207 6,695,000 5.00% 9,205,000 25,900,000 //208 7,530,000 5.00% 8,370,250 25,900,250 //209 8,405,000 5.00% 7,493,750 25,898,750 //2020 9,325,000 5.00% 6,573,500 25,898,500 //202 20,295,000 5.00% 5,607,250 25,902,250 //2022 2,30,000 5.00% 4,592,500 25,902,500 //2023 22,375,000 5.00% 3,527,000 25,902,000 //2024 23,495,000 5.00% 2,408,250 25,903,250 //2025 24,670,000 5.00%,233,500 25,903,500 Total 200,000,000 55,5,000 255,5,000 PFM 2

All Start with Semi-Annual Debt Service Each is present valued at different rate SEMI-ANNUAL DEBT SERVICE Dates Par Coupon Interest Debt Service 5/7/205 7//205,500,000,500,000 //206 5,900,000 5.00% 5,000,000 20,900,000 7//206 4,602,500 4,602,500 //207 6,695,000 5.00% 4,602,500 2,297,500 7//207 4,85,25 4,85,25 //208 7,530,000 5.00% 4,85,25 2,75,25 7//208 3,746,875 3,746,875 //209 8,405,000 5.00% 3,746,875 22,5,875 7//209 3,286,750 3,286,750 //2020 9,325,000 5.00% 3,286,750 22,6,750 7//2020 2,803,625 2,803,625 //202 20,295,000 5.00% 2,803,625 23,098,625 7//202 2,296,250 2,296,250 //2022 2,30,000 5.00% 2,296,250 23,606,250 7//2022,763,500,763,500 //2023 22,375,000 5.00%,763,500 24,38,500 7//2023,204,25,204,25 //2024 23,495,000 5.00%,204,25 24,699,25 7//2024 66,750 66,750 //2025 24,670,000 5.00% 66,750 25,286,750 BOND STATISTICS TIC All-In-TIC Arb Yield,500,000,500,000,500,000 20,900,000 20,900,000 20,900,000 4,602,500 4,602,500 4,602,500 2,297,500 2,297,500 2,297,500 4,85,25 4,85,25 4,85,25 2,75,25 2,75,25 2,75,25 3,746,875 3,746,875 3,746,875 22,5,875 22,5,875 22,5,875 3,286,750 3,286,750 3,286,750 22,6,750 22,6,750 22,6,750 2,803,625 2,803,625 2,803,625 23,098,625 23,098,625 23,098,625 2,296,250 2,296,250 2,296,250 23,606,250 23,606,250 23,606,250,763,500,763,500,763,500 24,38,500 24,38,500 24,38,500,204,25,204,25,204,25 24,699,25 24,699,25 24,699,25 66,750 66,750 66,750 25,286,750 25,286,750 25,286,750 Total PFM 200,000,000 55,5,000 255,5,000 255,5,000 255,5,000 255,5,000 22

Offsets in Calculations Differ TIC All-in-TIC Arbitrage Yield Par Value 200,000,000 200,000,000 200,000,000 + Accrued Interest 0 0 0 + Premium (Discount) 0 0 0 - Underwriter's Discount (2,000,000) (2,000,000) - Cost of Issuance Expense (300,000) - Other Amounts (,533,066) (,533,066) Target Value 98,000,000 96,66,934 98,466,934 Bond Insurance PFM 23

All Start with Semi-Annual Debt Service TIC All-in-TIC Arbitrage Yield Target Value 98,000,000 96,66,934 98,466,934 Target Date (Delivery Date) 5/7/205 5/7/205 5/7/205 Yield 5.28445% 5.42023% 5.67482% SEMI-ANNUAL DEBT SERVICE BOND STATISTICS Dates Par Coupon Interest Debt Service TIC All-In-TIC Arb Yield 5/7/205 7//205,500,000,500,000,488,454,488,05,488,565 //206 5,900,000 5.00% 5,000,000 20,900,000 20,2,752 20,85,946 20,28,279 7//206 4,602,500 4,602,500 4,337,756 4,327,962 4,340,234 //207 6,695,000 5.00% 4,602,500 2,297,500 9,562,02 9,498,67 9,578,052 7//207 4,85,25 4,85,25 3,746,338 3,730,539 3,750,34 //208 7,530,000 5.00% 4,85,25 2,75,25 8,944,20 8,845,700 8,969,073 7//208 3,746,875 3,746,875 3,85,627 3,65,964 3,90,65 //209 8,405,000 5.00% 3,746,875 22,5,875 8,354,806 8,223,593 8,388,5 7//209 3,286,750 3,286,750 2,654,4 2,632,552 2,659,59 //2020 9,325,000 5.00% 3,286,750 22,6,750 7,795,0 7,633,205 7,836,26 7//2020 2,803,625 2,803,625 2,50,305 2,28,648 2,55,83 //202 20,295,000 5.00% 2,803,625 23,098,625 7,265,527 7,074,845 7,34,052 7//202 2,296,250 2,296,250,672,732,652,634,677,850 //2022 2,30,000 5.00% 2,296,250 23,606,250 6,758,993 6,54,359 6,84,444 7//2022,763,500,763,500,220,4,203,3,224,482 //2023 22,375,000 5.00%,763,500 24,38,500 6,276,402 6,033,489 6,338,370 7//2023,204,25,204,25 79,286 778,7 794,496 //2024 23,495,000 5.00%,204,25 24,699,25 5,88,94 5,55,522 5,886,307 7//2024 66,750 66,750 384,944 378,083 386,698 //2025 24,670,000 5.00% 66,750 25,286,750 5,38,389 5,092,386 5,455,296 Total PFM 200,000,000 55,5,000 255,5,000 98,000,000 96,66,934 98,466,934 24