Chap 006

Chapter 6

Interest Rates and Bond Valuation

1 McGraw-Hill/Irwin

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

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Chapter Outline • • • •

Bonds and Bond Valuation More on Bond Features Some Different Types of Bonds Inflation and Interest Rates

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Bond Definitions • • • •

Bond: debt securities, interest-only loan Par value (face value): loan principal, eg: $1000 Coupon rate: periodic interest rate Coupon payment (c): periodic interest payments = coupon rate * par • Time to maturity (t): no. of coupon payment till maturity date • Yield to maturity (r) : market required rate of return on bond. IOW, the discount rate that equals the PV of cash flows to bond price.

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Bond Definitions: Example Consider a 5-year corporate bond with a 10% coupon rate paid annually. The principal amount is $1000 and the market interest rate is 10% . •Coupon=10% * $1000=$100 •year to maturity= 5 •Yield to maturity=10% •Cash Flows: year 1 - 4 = $100 year 5 = 100 + 1000 = $1100

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Bond Valuation Asset value = Present value of all future cash flows Bond value = PV of all payments discounted at YTM = PV of coupon + PV of par = PV of annuity + PV of par

1  1 - (1 + r) t Bond Value = C  r    Where c = coupon payment r = YTM t = numbers of period F = face value (eg:1000)

  F + t (1 + r)   

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Bond valuation-Example Consider a 5-year corporate bond with a 10% coupon rate paid annually. The principal amount is $1000 and the market interest rate is 10%

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PV of Cash Flows as Rates Change 1  1 - (1 + r) t Bond Value = C  r   

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  F +  (1 + r) t  

• Remember, as interest rates increase the PV’s decrease • So, as interest rates increase, bond prices decrease and vice versa 7

Valuing a Discount Bond with Annual Coupons

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• Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 12%. What is the value of the bond?

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Valuing a Premium Bond with Annual Coupons

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• Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 5 years to maturity and the yield to maturity is 8%. What is the price of this bond?

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Bond Prices: Relationship Between Coupon and Yield

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• If YTM = coupon rate, – bond price = par value = $1000 – selling at par, called a par bond

• If YTM > coupon rate, – bond price < $1000 – Selling at a discount, called a discount bond

• If YTM < coupon rate, – bond price > $1000 – Selling at a premium, called a premium bond 10

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Semiannual coupons • Suppose you are looking at a bond that has a 10% coupon paid semiannually and a face value of $1000. There are 5 years to maturity and the yield to maturity is 12%. What is the price of this bond?

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Interest Rate Risk • How sensitive its price to the interest rate changes – Long-term bonds have more interest rate risk than short-term bonds (+ve relationship with time to maturity) – The lower the coupon rate, the greater the interest rate risk (-ve relationship with coupon rate) 12

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Computing YTM • Yield-to-maturity is the rate implied by the current bond price, i.e., the rate that equals the PV of bond’s cash flows with bond price. • Finding the YTM requires trial and error if you do not have a financial calculator.

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YTM with Annual Coupons • Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.

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YTM with Semiannual Coupons • Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.

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Bond Yield – Yield to maturity: market required rate of return on bond. – Current yield = Annual coupon / price • Par bond: CY = YTM • Premium bond: CY > YTM • Discount bond: CY < YTM

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Differences Betw. Debt & Equity • Debt – Not an ownership interest – Creditors do not have voting rights – Interest is considered a cost of doing business and is tax deductible – Creditors have legal recourse if interest or principal payments are missed – Excess debt can lead to financial distress and bankruptcy

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Equity – Ownership interest – Common stockholders vote for the board of directors and other issues – Dividends are not considered a cost of doing business and are not tax deductible – Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid – An all equity firm can not go bankrupt 17

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The Bond Indenture • Contract between the company and the bondholders and includes: – The basic terms of the bonds: par, registered Vs bearer – The total amount of bonds issued – A description of property used as security, if applicable - collateral – Sinking fund provisions – Call provisions: rights to buyback at specific price – Details of protective covenants: +ve Vs -ve 18

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Bond Classifications • Registered vs. Bearer Forms • Security: backed by asset – Collateral – secured by financial securities – Mortgage – secured by real property, normally land or buildings – Debentures – unsecured – Notes – unsecured debt with original maturity less than 10 years

• Seniority – preference in position over other lenders 19

Bond Characteristics and Required Returns

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• The coupon rate depends on the risk characteristics of the bond when issued • Which bonds will have the higher coupon, all else equal? – Secured debt versus a debenture – Subordinated debenture versus senior debt – A bond with a sinking fund versus one without – A callable bond versus a non-callable bond 20

Types of bondsGovernment Bonds

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• Treasury Securities – Federal government debt – T-bills – pure discount bonds with original maturity of one year or less – T-notes – coupon debt with original maturity between one and ten years – T-bonds- coupon debt with original maturity greater than ten years

• Municipal Securities – Debt of state and local governments – Interest received is tax-exempt at the federal level 21

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Taxable Vs Municipal Bonds • A taxable corporate bond has a yield of 8% and a municipal bond has a yield of 6% – If you are in a 40% tax bracket, which bond do you prefer?

– At what tax rate would you be indifferent between the two bonds?

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Zero Coupon Bonds • Make no periodic interest payments (coupon rate = 0%) • Sometimes called zeroes, or deep discount bonds • The entire yield-to-maturity comes from the difference between the purchase price and the par value • Treasury Bills and principal only Treasury strips are good examples of zeroes 23

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Floating Rate Bonds • Coupon rate floats depending on some index value, eg: T-bill interest rate • Examples – adjustable rate mortgages and inflation-linked Treasuries • There is less price risk with floating rate bonds – The coupon floats, so it is less likely to differ substantially from the yield-to-maturity

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Other Bond Types • Income bonds – coupon depends on company’s income

• Convertible bonds – can be converted/swapped to a fixed no. of shares

• Put bond – Holder can sell back to issuer at a stated price

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Inflation and Interest Rates • Nominal rate of interest – quoted rate of interest, includes our desired real rate of return plus an adjustment for expected inflation • Rate on Treasury Bill • Real rate of interest – change in purchasing power

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The Fisher Effect

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• The Fisher Effect defines the relationship between real rates, nominal rates and inflation • (1 + R) = (1 + r)(1 + h), where – R = nominal rate – r = real rate – h = expected inflation rate

• Approximation –R=r+h 27

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Example • If we require a 10% real return and we expect inflation to be 3%, what is the nominal rate?

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Tutorial • Problem 6, 10, 17 and 18 from page 196 • Problem 18: “…sell for 93% of par…” change to “…sell for 91.167% of par…”

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