Bond Pricing: Understanding Par, Premium, and Discount Bonds, Study notes of Public finance

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Group Exercise & Discussion: Bond Math

February 2019

KNN Public Finance

Joanna Bowes Managing Director, Partner  Manager of KNN Education Group  23 plus years of experience in public finance  Financial Advisor  Underwriter  Investment Banker  Expertise with complex financing issues  MBA, University of Connecticut; BA, Northwestern University Erwin Tam Vice President  Quantitative lead for KNN Education Group  14 plus years of experience in public finance  Financial Advisor  Investment Banker  Public-Private Partnerships  Prior experience with RBC Capital Markets, Bear, Stearns & Co. Inc., and PFM  BA, University of California, Berkeley  KNN Public Finance is an employee-owned independent municipal advisory firm  Headquartered in Oakland, with additional offices in Los Angeles and Newport Beach  All advisors are registered with the MSRB, with Series 50 licenses

General Bond Terminology

 Principal or Par Total amount borrowed  Coupon Interest due to the investor, typically paid semiannual  Yield Rate of return to the investor  Price The price an investor will pay to receive the yield  Maturity Date at which principal is due to the bondholder  Dated Date Date from which an investor is entitled to receive interest  Delivery Date Settlement date of the bond (closing date for primary bond issuance)  Debt Service Total principal and interest payments on bond  Call Date Redemption date of a bond prior to maturity at the option of the issuer  Call Premium Dollar amount over 100% which is paid to the investor when bonds are called

Bond Pricing Terminology

 Par Bond  Coupon and Yield are equal  Price equal to 100.  Every $1,000 of bonds issued will produce $1,000 in proceeds  Premium Bond  Coupon is greater than Yield  Price greater than 100.  Every $1,000 of bonds issued will produce over $1,000 in proceeds  Similar to receiving points in a mortgage  Discount Bond  Coupon is less than Yield  Price less than 100.  Every $1,000 of bonds issued will produce less than $1,000 in proceeds  Capital Appreciation Bonds are Discount Bonds  Similar to paying points in a mortgage

Bond Pricing

Par Bonds  If coupon and yield are the same, the price of the bond is 100. Premium Callable Bonds  Bond price needs to be calculated assuming bonds are redeemed on the call date and at maturity  Whatever results in the lower bond price, is the price of the bond  A callable (at par) premium bond will always have its lowest price at the call date  For a theoretical 20 year bond, 5% coupon and 4% yield with a 10 year par call: Bond Price Rounding  Prices are shown as truncated to the 3rd^ decimal

Bond Price

to Call Date

= 108.175^ Bond Price

to Maturity

X

Bond Pricing Formula in Excel

 Excel’s Price Function has 6 components  Settlement [Delivery Date]  Maturity [Maturity]  Rate [Coupon]  Yld [Yield]  Redemption [Call Premium]  Frequency [Semi-annual, 2]

 100.000 (par bond)  105.000 (premium bond)  95.000 (discount bond)

Bond Price and Bond Proceeds

Par bonds result in the same amount of bonds and proceeds Premium bonds require less bonds to be issued to receive the same proceeds Discount bonds require more bonds to be issued to receive the same proceeds An issuer wants $1,000,000 new proceeds for a project. How much does it need to issue to receive that amount, assuming the following bond prices:

Changes in Yield and Bond Price

 When yield changes, bond price changes:

Coupon Yield Price

Coupon Yield Price

 Yield and Price are inversely related  As yields increase, price of a fixed-rate bond decreases  As yields decrease, price of a fixed rate bond increase Yield Free Increase in Yield

Debt Service Example

 Calculating total debt service for a bond with:  $1,000,000 principal, 5.0% coupon and a 5 year term  Total Debt Service = Principal + (Principal x # of semi-annual periods x ½ of coupon) $1,000,000 + ($1,000,000 x 10 x ½ of 5.0%) $1,000,000 + ($1,000,000 x 10 x 2.5%) $1,000,000 + ($1,000,000 x .25) $1,000,000 + $250, $1,250, Date Principal Coupon Interest Total Debt Service 7/1/ 1/1/2020 25,000 25, 7/1/2020 25,000 25, 1/1/2021 25,000 25, 7/1/2021 25,000 25, 1/1/2022 25,000 25, 7/1/2022 25,000 25, 1/1/2023 25,000 25, 7/1/2023 25,000 25, 1/1/2024 25,000 25, 7/1/2024 1,000,000 5.00% 25,000 1,025, Total 1,000,000 250,000 1,250,

Group Activity: Introduction

 The City of King’s Landing is issuing $300 million in Certificates of Participation (COPs) to fund capital improvement projects  The City needs your help in explaining bond pricing

Question 2: Review

For the each of the bonds, assume a 20-year maturity and identify the bond price and the terminology describing the type of bond

Coupon Yield Price Terminology

3.0% 3.0% 100.000 Par

4.0% 3.0% 114.957 Premium

2.0% 3.0% 85.042 Discount

Question 3: Review

Coupon Yield Price Terminology

2.0% 2.0% 100.000 Par

3.0% 2.0% 116.417 Premium

4.0% 2.0% 132.834 Premium

2.0% 4.0% 72.644 Discount

3.0% 4.0% 86.322 Discount

4.0% 4.0% 100.000 Par

For the each of the bonds, assume a 20-year maturity and identify the bond price and the terminology describing the type of bond

Question 5: Review

The 20-year bond in question 2 was non-callable.  Which bond will have a difference in price with a 10-year par call? C  Based on your previous answer, will the bond price be higher or lower with a 10-year par call as compared to a non-callable bond? Lower

Bond Coupon Yield Non-Call

Price

Callable

Bond

Price

A 2.0% 3.0% 85.042 85.

B 3.0% 3.0% 100.000 100.

C 4.0% 3.0% 114.957 108.

Question 6: Review

Based on the following bonds, what would be the principal amount of bonds needed to generate $ million in proceeds for each bond? (Round up to $5,000)

Coupon Yield Price Principal

New Proceeds

(Price/100)

Principal

Amount Required