Bonds And Bond Valuation

Differences Between Debt and 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

• 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

The Bond Indenture • Contract between the company and the bondholders and includes – – – – – –

The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants

Bond Classifications • Registered vs. Bearer Forms • Security – 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

Bond Characteristics and Required Returns • 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

How does adding a “call provision” affect a bond? • Issuer can refund if rates decline. That helps the issuer but hurts the investor. • Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds. • Most bonds have a deferred call and a declining call premium.

When would bonds be called? • In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is likely. • So, expect to earn: – YTC on premium bonds. – YTM on par & discount bonds.

What’s a sinking fund? • Provision to pay off a loan over its life rather than all at maturity. • Similar to amortization on a term loan. • Reduces risk to investor, shortens average maturity. • But not good for investors if rates decline after issuance.

Sinking funds are generally handled in 2 ways 1. Call x% at par per year for sinking fund purposes. 2. Buy bonds on open market. Company would call if kd is below the coupon rate and bond sells at a premium. Use open market purchase if kd is above coupon rate and bond sells at a discount.

Protective Covenants • Agreements to protect bondholders • Negative covenant: Thou shalt not: – pay dividends beyond specified amount – sell more senior debt & amount of new debt is limited – refund existing bond issue with new bonds paying lower interest rate – buy another company’s bonds • Positive covenant: Thou shalt: – use proceeds from sale of assets for other assets – allow redemption in event of merger or spinoff – maintain good condition of assets – provide audited financial information

Bond Ratings – Investment Quality • High Grade – Moody’s Aaa and S&P AAA – capacity to pay is extremely strong – Moody’s Aa and S&P AA – capacity to pay is very strong

• Medium Grade – Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances – Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

Bond Ratings - Speculative • Low Grade – Moody’s Ba, B, Caa and Ca – S&P BB, B, CCC, CC – Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation.

• Very Low Grade – Moody’s C and S&P C – income bonds with no interest being paid – Moody’s D and S&P D – in default with principal and interest in arrears

What factors affect default risk and bond ratings? • Financial performance – Debt ratio – TIE, FCC ratios – Current ratios

• Provisions in the bond contract – – – – –

Secured vs. unsecured debt Senior vs. subordinated debt Guarantee provisions Sinking fund provisions Debt maturity

• Other factors – – – –

Earnings stability Regulatory environment Potential product liability Accounting policies

Importance of bond ratings • Bond interest rate, cost of debt capital • Clientele

Key Features of a Bond • Bond – Contract under which a borrower agrees to make payments of principal and interest on specific dates to the holders of the bond

• Bonds are the most common form of financing

Key Features of a Bond 1.

Par value: Face amount; paid at maturity. Assume $1,000.

2.

Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.

3.

Maturity: Years until bond must be repaid. Declines.

4.

Issue date: Date when bond was issued.

What’s “yield to maturity”? • YTM is the rate of return earned on a bond held to maturity. • We will use the symbol rd or YTM to refer to yield to maturity • YTM is the appropriate discount rate for the bond. It represents the opportunity cost that could be earned on bonds of similar risk.

What’s the value of a 10-year, 10% coupon bond if rd = 10%? 0

1

2

10%

...

V=?

VB =

10

100

$100

(1 + r d )

1

+ . . . +

= $90.91 + = $1,000.

100

$100

(1 + r d )

10

100 + 1,000

$1, 000 + 10 r (1+ d )

. . . + $38.55 + $385.54

The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: PV annuity = $ 614.46 PV maturity value = 385.54 PV annuity = $1,000.00 INPUTS OUTPUT

10 N

10 I/YR

PV -1,000

100 PMT

1000 FV

The Bond-Pricing Equation 1  1  (1 + r ) t d Bond Value = C  rd  

  PAR + t  (1 + rd ) 

What would happen if expected inflation rose by 3%, causing rd = 13%?

INPUTS OUTPUT

10 N

13 I/YR

PV -837.21

100 PMT

1000 FV

When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.

What would happen if inflation fell, and rd declined to 7%? INPUTS OUTPUT

10 N

7 100 I/YR PV PMT -1,210.71

1000 FV

Price rises above par, and bond sells at a premium, if coupon > rd.

The bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the yield to maturity remained at 10%, or at 13%, or at 7%?

Bond Value ($)

rd = 7%.

1,372 1,211

rd = 10%.

1,000

M

837

rd = 13%.

775 30

25

20

15

10

5

0

Years remaining to Maturity

• At maturity, the value of any bond must equal its par value. • The value of a premium bond would decrease to $1,000. • The value of a discount bond would increase to $1,000. • A par bond stays at $1,000 if rd remains constant.

Valuing a Discount Bond with Annual Coupons • 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 11%. What is the value of the bond? – Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5 • B = 369.59 + 593.45 = 963.04

– Using the calculator: • N = 5; I/Y = 11; PMT = 100; FV = 1000 • CPT PV = -963.04

Valuing a Premium Bond with

Annual Coupons • Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? – Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20 • B = 981.81 + 214.55 = 1196.36

– Using the calculator: • N = 20; I/Y = 8; PMT = 100; FV = 1000 • CPT PV = -1196.36

• If coupon rate < rd, discount. • If coupon rate = rd, par bond. • If coupon rate > rd, premium. • If rd rises, price falls. • Price = par at maturity.

What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 0

PV1 . . . PV10 PVM

887

rd=?

1 90

...

9 90

10 90 1,000

Find rd that “works”!

INPUTS OUTPUT

10 N

-887 I/YR PV 10.91

90 PMT

1000 FV

Semiannual Bonds 1.Multiply years by 2 to get periods = 2n. 2.Divide nominal rate by 2 to get periodic rate = rd/2. 3.Divide annual INT by 2 to get PMT = INT/2. INPUTS OUTPUT

2n

rd/2

OK

INT/2

OK

N

I/YR

PV

PMT

FV

Find the value of 10-year, 10% coupon, semiannual bond if rd = 13%.

2(10) INPUTS 20 N OUTPUT

13/2 6.5 I/YR

PV -834.72

100/2 50 PMT

1000 FV

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. – – – –

Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? N = 40; PV = -1197.93; PMT = 50; FV = 1000; CPT I/Y = 4% (Is this the YTM?) – YTM = 4%*2 = 8%

What’s interest rate (or price) risk? Does a 1year or 10-year 10% bond have more risk? Interest rate risk: Rising rd causes bond’s price to fall. kd

1-year

5% $1,048 10%

1,000

15%

956

Change 10-year Change +4.8% -4.4%

$1,386 1,000 749

+38.6% -25.1%

Interest Rate Risk • Price Risk – Change in price due to changes in interest rates – Long-term bonds have more price risk than short-term bonds

• Reinvestment Rate Risk – Uncertainty concerning rates at which cash flows can be reinvested – Short-term bonds have more reinvestment rate risk than long-term bonds

Government Bonds • 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 – Varying degrees of default risk, rated similar to corporate debt – Interest received is tax-exempt at the federal level

Example 7.3 • A taxable 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? • 8%(1 - .4) = 4.8% • The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal

– At what tax rate would you be indifferent between the two bonds? • 8%(1 – T) = 6% • T = 25%

Zero-Coupon Bonds • Make no periodic interest payments (coupon rate = 0%) • The entire yield-to-maturity comes from the difference between the purchase price and the par value • Cannot sell for more than par value • Sometimes called zeroes, or deep discount bonds • Treasury Bills and principal only Treasury strips are good examples of zeroes

Floating Rate Bonds • Coupon rate floats depending on some index value • 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

• Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

Convertible Bonds • Conversion ratio: – Number of shares of stock acquired by conversion

• Conversion price: – Bond par value / Conversion ratio

• Conversion value: – Price per share of stock x Conversion ratio

• In-the-money versus out-the-money

More on Convertibles • Exchangeable bonds – Convertible into a set number of shares of a third company’s common stock.

• Minimum (floor) value of convertible is the greater of: – Straight or “intrinsic” bond value – Conversion value

• Conversion option value – Bondholders pay for the conversion option by accepting a lower coupon rate on convertible bonds versus otherwise- identical nonconvertible bonds.

Inflation and Interest Rates • Real rate of interest – change in purchasing power • Nominal rate of interest – quoted rate of interest, change in purchasing power and inflation • The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation

The Fisher Effect • 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

Example 7.6 • If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? • R = (1.1)(1.08) – 1 = .188 = 18.8% • Approximation: R = 10% + 8% = 18% • Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

Term Structure of Interest Rates • Term structure is the relationship between time to maturity and yields, all else equal • It is important to recognize that we pull out the effect of default risk, different coupons, etc. • Yield curve – graphical representation of the term structure – Normal – upward-sloping, long-term yields are higher than short-term yields – Inverted – downward-sloping, long-term yields are lower than short-term yields