# bonds and bond valuation

TRANSCRIPT

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.

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.

Sinking funds are generally handled in 2 ways

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 bondmust be repaid. Declines.

4. Issue date: Date when bondwas 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%?

V

r rB

d d

$100 $1,

1

000

11 10 10 . . . +

$100

1+ r d

100 100

0 1 2 1010%

100 + 1,000V = ?

...

= $90.91 + . . . + $38.55 + $385.54= $1,000.

++++

10 10 100 1000N I/YR PV PMT FV

-1,000

The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:

$ 614.46 385.54

$1,000.00

PV annuity PV maturity value PV annuity

===

INPUTS

OUTPUT

The Bond-Pricing Equation

tdd

td

)r(1

PAR

r

)r(11

-1

C Value Bond

10 13 100 1000N I/YR PV PMT FV

-837.21

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

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

INPUTS

OUTPUT

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

10 7 100 1000N I/YR PV PMT FV

-1,210.71

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

INPUTS

OUTPUT

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%?

M

Bond Value ($)

Years remaining to Maturity

1,372

1,211

1,000

837

775

30 25 20 15 10 5 0

rd = 7%.

rd = 13%.

rd = 10%.

• 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?

90 90 90

0 1 9 10rd=?

1,000PV1 . . .PV10

PVM

887 Find rd that “works”!

...

10 -887 90 1000N I/YR PV PMT FV

10.91

INPUTS

OUTPUT

Semiannual Bonds1.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.

2n rd/2 OK INT/2 OK

N I/YR PV PMT FV

INPUTS

OUTPUT

2(10) 13/2 100/220 6.5 50 1000N I/YR PV PMT FV

-834.72

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

INPUTS

OUTPUT

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 1-year or 10-year 10% bond have more risk?

kd 1-year Change 10-year Change

5% $1,048 $1,386

10% 1,000+4.8%

-4.4% 1,000

+38.6%

-25.1%15% 956 749

Interest rate risk: Rising rd causes bond’s price to fall.

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