Interest Rates and Bond Valuation

Chapter 6

Key Concepts and Skills Know the important bond features and

bond types Understand bond values and why they

fluctuate Understand bond ratings and what they

mean Understand the impact of inflation on

interest rates Understand the term structure of interest

rates and the determinants of bond yields

Chapter Outline Bonds and Bond Valuation More on Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields

Issuer (Seller) of Bonds (Borrower) = “Bond Issuer”

Bonds = Debt = Liability = Long-term debt 1 Bond usually means the corporation borrows

$1000 (face value) Corporations usually issue many Bonds

Bond Issue: The total number of bonds that a corporation issues

at the same time, in denominations of $1,000 or $5,000 each

Like any contractual debt: Bond issuer pays periodic interest to the

bondholder Bond issuer pays the face value back at the end

of the bond term

Issuer (Seller) of Bonds (Borrower) = “Bond Issuer”

When you issue a bond, you borrow the money, then use the money to buy assets that earn more cash than the cash you have to pay out to the bondholder

Leverage Example:

Borrow money at 8% interest and buy a machine that earns the corporation 13%

The difference between 13% and 8%, or 5%, is left for the stockholders

Buyer of Bonds (Lender) = “Bondholder”

Bonds = Asset 1 Bond usually means the borrow lends

money to the corporation or government Like any contractual debt:

Bondholders are paid periodic interest for loaning money to the corporation and are paid back the face value at the end of the bond term

When you buy a bond you are paying for a future steam of cash flow

Bond Vocabulary: Face value = par value = loan repayment at maturity =

FV Annual interest payments = “annual coupon”

Coupon is from the days when you presented coupon to get paid interest

Annual interest rate (not discount rate) = coupon rate = annual interest rate for calculating interest payments = annual coupon/face value

Number of interest payments per year = n Periodic rate (not discount rate) = periodic coupon rate =

(annual coupon rate)/n The book is inconsistent with the use of “coupon” (sometimes

annual, sometimes semi-annual) Periodic interest payment = periodic rate*face = PMT Years until maturity = term of bond = years until paying

back face value and last periodic interest payment = x Maturity = specified date on which principal is repaid

Bond Vocabulary: Yield To Maturity (YTM) = discount rate

used to value bond = i = YTM YTM = Bond Yield = Required Return =

Market Rate = Rate required in the market on a bond

YTMs are quoted like APRs YTM = (Period Discount Rate) * n

Example: YTM = 10% and bond pays semiannual interest payments, then period discount rate = YTM/n = .10/2 =.05 Effective Annual Yield on the Bond = (1+.10/2)2

= .1025

Bonds Bonds are interest only loans

Corporations/Governments borrow money, pay interest each period, then pay back face amount at end of bond term

Corporations/Governments plan to issue bonds and then set the coupon rate, but by the time they actually issue the bond the financial markets have already calculated a discount rate for the future values that is often different than the coupon rate

Corporations/Governments issue bonds and get the “cash in” (Bonds sold in primary market)

Many Bonds from Corporations/Governments can be traded in the financial markets (Bonds sold in the secondary market)

Bonds Each bond has a price expressed as a

percentage of the face value: For example, 103 means 1.03 times the

face value of the bond When the corporation issues the $1,000

face-value bond, it receives $1,030 At maturity, the corporation pays back

only the face value of $1,000 103 and 103% and 1.03 all convey the

same meaning The bond is selling for 3% above the face value

Example 1 On January 1, Cox Construction Corp. issues 750

10-year bonds with a face of $1000 with a coupon rate of 9% at 103, with interest payable semiannually, on June 30 and December 31

Face Value = 750 * $1,000 = $750,000.00Bond Annual Interest Rate 9%Years Until Maturity 10Percentage Of Face Value 1.03Semiannually (2 Times A Year) 2Interest Payment Date June 30Interest Payment Date December 31

Cox Construction Corporation

This Bond with its 9% coupon, is priced to yield 8.74% at $1,030

Face Value = 750 * $1,000 =

xPercentage Of

Face Value= Bond Price

$750,000.00 x 1.03 = $772,500.00

Face Value = 750 * $1,000 =

xBond Annual Interest Rate

=Yearly Interest

Payment$750,000.00 x 9% = $67,500.00

Yearly Interest Payment

÷Semiannually (2 Times A Year)

=

Periodic Cash Interest Payment (Due June 30 &

Dec. 31)$67,500.00 ÷ 2 = $33,750.00

Years Until Maturity

xSemiannually (2 Times A Year)

=Total Number Of

Payments10 x 2 = 20

Periodic Cash Interest Payment (Due June 30 & Dec. 31)

Total Number Of Payments To Be Made

Amount Of Cash Bondholder Pays Bond Issuer

Yearly Interest Payment

But If The Loan Has A Face Value Of $750,000, Why Did The Bondholder Pay $772,500?

If a corporation offers a rate of interest that is higher than the market rate for similar securities, investors may be willing to pay a premium for the bond

If a corporation offers a rate of interest that is lower than the market rate for similar securities, investors will demand a discount on the bond

6% 8% 10.0%

8% 8% 8.0%

Record Bond At Premium

Record Bond

Without Pre. Or Dis.

Record Bond At Discount

YTM (Market) Rate For Similar Securities

Interest Rate On Bond

What Are Similar Securities? Similar securities are bonds or other

investment vehicles issue by other corporations (different than the one being considered) that have similar business and financial risks

The similarities could be: Similar credit ratings Similar business activities Similar capital structure

Below 1.00(Example: 93 or 0.93)

100(Example: 1.00)

Above 1.00(Example: 107 or 1.07)

Record Bond At Discount

Record Bond With No Premium Or Discount

Record Bond At Premium

Selling Price For Bond

Bond Prices

YTM > Coupon Rate YTM < Coupon Rate

Definitions Premium

The excess of the price received over the face value of a bond

YTM < Coupon Rate “Bond sold at a premium”

Discount The amount by which the issue price is

less than the face value of a bond YTM > Coupon Rate “Bond sold at a discount”

The Issuance of Bonds at a Discount: Example 2

On January 1, Muller, Inc., issues 700 6%, 20-year bonds with a face value of $1,000, at 96, with interest to be paid semiannually, on June 30 and December 31

Face Value = 700 * $1,000 = $700,000.00Bond Annual Interest Rate 6%Years Until Maturity 20Percentage Of Face Value 0.96Semiannually (2 Times A Year) 2Interest Payment Date June 30Interest Payment Date December 31

Muller, Inc.

This Bond with its 6% coupon, is priced to yield 6.25% at $960

Face Value = 700 * $1,000 =

xPercentage Of Face

Value= Bond Price

$700,000.00 x 0.96 = $672,000.00

Face Value = 700 * $1,000 =

- Bond Price = Discount

$700,000.00 - $672,000.00 = $28,000.00

Face Value = 700 * $1,000 =

xBond Annual Interest

Rate=

Yearly Interest Payment

$700,000.00 x 6% = $42,000.00

Yearly Interest Payment

÷Semiannually (2 Times A Year)

=Periodic Cash Interest Payment (Due June

30 & Dec. 31)$42,000.00 ÷ 2 = $21,000.00

Years Until Maturity xSemiannually (2 Times A Year)

=Total Number Of

Payments20 x 2 = 40

Total Number Of Payments To Be Made

Discount

Amount Of Cash Bondholder Pays Bond Issuer

Periodic Cash Interest Payment (Due June 30 & Dec. 31)

Yearly Interest Payment

Bond Valuation

1) Present Value of Principal Paid at Maturity Date (Bond’s Face Value):

PV of Lump Sum Deposited (Present Value of Loan Principal or Bond’s Face Value) (Chapter 6)

LSLS n*x

FVPV =

i1+

n

2) Present Value of All Future Periodic Interest Payments:

PV of regular payments at regular intervals (Valuation for contractual Bond Payments) (Chapter 6)

-(n*x)

An

i1 - 1+

nPV = PMT*

in

3) Present Value of Principal Paid at Maturity Date & Present Value

of All Future Periodic Interest Payments (Chapter 6):

LSLS

n*x

FVPV =

i(1+ )

n

+ -(n*x)

An

i1-(1+ )

nPV = PMT*in

=

LSLS n*x

FVPV =

i1+

n

+

-(n*x)

An

i1 - 1+

nPV = PMT*

in

Bond

Pri

ce (

Valu

ati

on

) fr

om

C

ash

Flo

w P

ers

pect

ive

Excel Bond Valuation from Bondholder’s

Point of View: =PV(rate,nper,pmt,fv,type) =PV(YTM/n,n*x,PMT,FV,0)

Bond Valuation from Bond Issuer’s Point of View: =PV(rate,nper,pmt,fv,type) =PV(YTM/n,n*x,-PMT,-FV,0)

Finding YTM rate from Bondholder’s Point of View: =RATE(nper,pmt,pv,fv,type,guess) =RATE(n*x,PMT,-PV,FV,0)

Example 3

# of Bonds 800

Face Value $ 1,000.00

Date Issue 1/1/2004

Interest Payment Dates 6/30/2004

12/31/2004

Bond Coupon/Interest Rate 8.0000%

Number Of Periods Per Year (semi annual) 2

Years Until Bond Matures 20

Annual Market Rate = YTM 7.0000%

Assumptions

$885,420.29 … … PV Years

0 1 2 3 4 39 40(32,000.00) (32,000.00) (32,000.00) (32,000.00) (32,000.00) (32,000.00)

(800,000.00)

Bond Valuation: how much cash in will the coporation get when it issues the bond and the price is 110.68% and the (YTM) Market Rate Per Period (Discount Rate) is 3.50%?

Example 3

LSLS

n*x

FVPV =

i(1+ )

n

+ -(n*x)

An

i1-(1+ )

nPV = PMT*in

=

LSLS n*x

FVPV =

i1+

n

+

-(n*x)

An

i1 - 1+

nPV = PMT*

in

Example 3

Bond Face Value $800,000.00 Total Periods For Bond (# of PMT) 40Bond Coupon Rate Per Period 4.00%Bond Interest Payments Per Period $32,000.00 (YTM) Market Rate Per Period (Discount Rate) 3.50%Price Of Bond $885,420.29 Premium $85,420.29

News Paper Price Quote = $885,420.29/$800,000.00 110.68%

Calculated Amounts

CF Is From Point Of View Of Issuer

40 0.035 885,420.29 -32,000.00 -800,000.00

PV PMT FVn YTM/n

Bond Values And Why They Fluctuate Bond Valuation:

As time passes, interest rates change in the market place

As new information about the company, the industry, the economy comes out, interest rates change

As time passes the amount of cash paid out to the bondholder does not change

Because of this the value of the bond will fluctuate

Rates , Bond Value Rates , Bond Value

26

Graphical Relationship Between Price and YTM

600

700

800

900

1000

1100

1200

1300

1400

1500

0% 2% 4% 6% 8% 10% 12% 14%

27

Valuing a Discount Bond with Annual Coupons Payments (Example 4)

Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years left until maturity. The yield to maturity is 11%. What is the value of the bond What is the price to you, buying in the secondary market?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 Answer: “You would be willing to pay $963.04

cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 11% at $963.04.”

28

Valuing a Premium Bond with Annual Coupons Payments (Example 5) Suppose you are looking at a bond that has a 10% annual

coupon rate and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the value of the bond what is the price to you?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 = 1196.36Answer: “You would be willing to pay

$1196.36 cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 8% at $1196.36.”

Interest Rate Risk The risk that arises for bond owners from

fluctuating interest rates How much interest rate risk a bond has

depends on: How sensitive its price is to interest rate

change The sensitivity depends on two things:

All things being equal, the longer the time to maturity, the greater the interest rate risk

All things being equal, the lower the coupon rate, the greater the interest rate risk

Interest Rate Risk And Time To Maturity

Interest Rate Risk To Loss Of Principal (current price)

Longer time to maturity1. Small changes in market rate have

substantial affect on bond value2. Face value is discounted over many periods

and thus compounding magnifies small interest rate changes

Lower Coupon rate1. Bond with lower coupon rate is

proportionally more dependent on the face value

(Bond with larger coupon rate has a larger cash flow early in life, so value less sensitive to discount rate)

Interest Rate Risk Increases At A Decreasing Rate

0%

2%

4%

6%

8%

10%

12%

0 5 10 15 20 25 30 35

Years To Maturity

Inte

rest

Rat

e R

isk

33

Computing YTM Yield-to-maturity is the rate implied by the

current bond price Finding the YTM requires trial and error

(iteration) if you do not have a financial calculator and is similar to the process for finding i with an annuity

If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

34

YTM with Annual Coupons (Example 6)

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

Will the yield be more or less than 10%?

35

YTM with Semiannual Coupons (Example 7)

•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?

Use One Bond YTM To Find Price Of Another Bond: Example 8

Similar Bonds have similar YTM ratesBond 1 Bond 2

Settlement date (day sold) 10/22/2005 10/23/2005Maturity Date 10/22/2017 10/23/2017Years to Maturity 12 12Coupon Rate 10% 12%Face Value $1,000 $1,000Semi Annual 2 2Interest Payment $50 $60Dollar Bond Price 935.08 $1,066.68Bond Price 0.93508 Discount Period Rate 5.49%YTM = Discount Period Rate*2 = 5.49%*2 = 10.99% 10.99%

BelowMarketrate =

discount

Above =

pre

miu

m

Bonds and Stocks: Like stock, bonds bring capital (money)

into the corporation so that it can invest in profitable projects Bondholders are creditors

They have a fixed claim to cash flow Stockholders are owners

They have a residual claim to cash flow

Bonds and Stocks Debt is not an ownership interest in the firm

Creditors do not have voting rights Interest is tax deductible

Dividends are not tax deductible Unpaid debt is a liability

Legal claim against assets If debt is not paid creditors have the legal claim to

assets before shareholders One of the costs of issuing debt is the possibility that

you will not be able to make interest payments creditors force firm into bankruptcy firm is terminated

This does not arise when equity is issued Corporations try to create hybrid financial instruments

that are Debt/Equity in order to have: Tax benefits of debt Bankruptcy benefits of equity

39

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

Bond Terms and Types Bonds = Long-term debt

Privately placed Directly placed with the lender

Public-issue bonds Offered to the public

Finance jargon” Long-term debt = funded debt Short-term debt = unfunded debt Example: “A firm planning to fund its debt

requirements may be replacing short-term debt with long-tern debt”

Bond Terms and Types Trustee (Investment Bank, other…)

Appointed by the corporation to represent bondholders

Must make sure terms are obeyed Must manage sinking fund Must represent bondholders in default

Indenture “The written agreement between the

corporation and the lender detailing the terms of the debt issue”

Bond Types Registered Form

The form of bond issue in which the registrar of the company records ownership of each bond

Payment is made directly to the owner of the bond

Bearer Form The form of bond issue in which the bond is

issued without record of the owner’s name Payment is made to whoever holds the bond Uncommon in the USA

Bond Types Security:

Generic term that means Stocks or Bonds or other investment vehicles that are backed by an asset

A document indicating ownership or creditorship; a stock certificate or bond

Dictionary definition of Security: Something deposited or given as

assurance of the fulfillment of an obligation; a pledge; collateral

Bond Types Debt securities are classified according to the

collateral and mortgages used to protect the bondholder Securities Backed By Collateral

Collateral = any asset pledged on the debt (often means assets such as stocks or bonds – financial assets)

If the borrower does not pay the interest and principal to the bondholder, the bondholder can take the collateral

Mortgage Securities Debt secured by a mortgage on real assets

(property, but not cash or inventory) of the borrower Called:

Mortgage Trust Indenture, or Trust Deed Most utility and railroad bonds are secured by a

pledge of assets

Bond Types Unsecured Debt

These creditors have a claim on property not otherwise pledged

Debenture Unsecured debt (maturity >= 10 years) Most financial and industrial companies’ public

bonds are debentures Note

Unsecured debt (maturity < 10 years)

Subordinate Debt Must give preference to superior debt Debt is not subordinate to equity

Bond Types Sinking Fund

An account managed by the trustee for the purposed of repaying the bonds, or early bond redemption

Bond Issuer must put away some money each period to save up in order to pay off the bond

Protective Covenant A part of the indenture limiting certain actions

that might be taken in order to protect the lender

Negative (thou shalt not): Example: Limit the amount of dividends paid

Positive (thou shalt): Example: CA/CL must be greater than 1.5

Bond Types Call Provision

An agreement giving the corporation the option to repurchase the bond at a specific price prior to maturity

Call Premium (Pay for the Option) The amount by which the call price > par value Example: Bond face = $1,000, Call Price = $1,100 Call Price goes down over time

Deferred Call Provision Can call only after a certain date

Call Protected Bond Can’t be redeemed by issuer

Make-Whole Call When bond called, bondholder gets PV of future cash

flows at a reasonable rate Derivative security jargon:

Call = Buy Put = Sell

Financial Markets Primary Markets

Original sale of equity or debt Corporation issues security

Secondary Markets After original sale of equity or debt You sell/buy security Dealer Markets (Over-the-counter markets

(OTC)) Dealers buy and sell for themselves Most debt is sold this way Example: NASDAQ

Auction Markets (Exchanges) Brokers and agents match buyers and sellers Most of the large firms’ equity is sold this way Example: NYSE

49

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

Bond Ratings And What They Mean Bond Rating firms:

Moody’s Standard and Poor’s (S&P)

They rate:1. The likelihood of default2. The probability that creditors are protected

They ask they question: What is the risk associated with the firm issuing the debt?

They do not rate the probability of bond value change due to interest rate risk

The Debt Crisis of 2007 shows that Ratings can be less than accurate:

How do they take risky loans and repackage them to get a AAA “Super Senior” rating? (That’s what they did!)

51

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

52

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

Some Different Types of Bonds Government Bonds

Treasury BillYears < 1

Treasury Note1< years < 7

Treasury BondsOther

No default riskTreasury issues are exempt from

state income tax (must pay Fed IT)

U.S. NATIONAL DEBT CLOCK The Outstanding Public Debt as of 13 Nov 2007 at 11:28:01 PM GMT is:

The estimated population of the United States is 303,525,093so each citizen's share of this debt is $30,039.21. The National Debt has continued to increase an average of$1.49 billion per day since September 29, 2006!

TotalDebt incurred per

dayDebt incurred per

second$9,117,654,602,533.09 $1,400,000,000.00 $16,203.70

Some Different Types of Bonds Municipal Bonds “Munis”

State and local government debt Example: Bond to build Highway These do have varying degrees of default risk Almost always callable Coupons exempt from federal income taxes

(must pay State IT) Attractive to high-income/high-tax bracket

investors Because of this the yields are lower

Which do you (with 25% Fed tax Bracket) prefer: corporate bond that yields 5%, or a muni (with comparable risk and maturity) that yields 3.90%?

.039 > .05(1-.25) = .0375

Some Different Types of Bonds Zero Coupon Bonds

A bond that makes no coupon payments, and thus is initially priced at a deep discount

Issuer must deduct interest every year Tax Benefit A deductions for taxes (fewer

taxes paid like cash coming in) even though no cash going out (interest expense)

Bondholder must accrue interest revenue every year

Taxes paid on revenue Cash going out (taxes paid) even though cash is not coming in (interest revenue)

Regular amortization table is constructed to track interest accrual

Pure Discount Loans (Zero Coupon) Borrow an amount today, then pay back

principal and all interest at the end of the loan period

Example: US Government Treasury Bills, or T-bills (government loans < 1year)

*

FVPV =

i1+

n

n x Loan amount

received todayPaybackAmount

Example 9:Pure Discount Loans (Zero Coupon)

Example 10:Interest Only Bond v. Zero Coupon Bond

Interest Only Bond Zero Coupon BondFirm Needs: $10,000,000.00 Firm Needs: $10,000,000.00Years to Maturity 20 Years to Maturity 20Coupon Rate 11% Coupon Rate 11%YTM 11% YTM 11%Tax Rate 35% Tax Rate 35%Compounding/year 1 Compounding/year 1 Face Value = $1,000 Face Value = $1,000

1) How many Bonds do we need to issue?Interest Only Bond Zero Coupon Bond

Cash in for 1 bond = PVan +

PVls= 1,000.00

Cash in for 1 bond = PVan +

PVls= 124.03

Number of Bonds = $10,000,000.00/1000 = 10,000.00

Number of Bonds = $10,000,000.00/124.03 = 80,623.12

Fewer Bonds issued today More Bonds issued today

2) What is FV and PV of cash flows to bondholder?Interest Only Bond Zero Coupon Bond

FV = FVan + FVls= $80,623,115.36 FV = FVls= $80,623,115.36

PV = $10,000,000.00 PV = $10,000,000.00

Interest Only Bond v. Zero Coupon Bond

3) Cash Flows

Interest Only Bond ==> Cash Flow to Issuers:PV =$10,000,000 … …

0 1 2 3 19 20($1,100,000.00) ($1,100,000.00) ($1,100,000.00) ($1,100,000.00) ($1,100,000.00)

($10,000,000.00)

Zero Coupon Bond ==> Cash Flow to Issuers:PV =$10,000,000 … …

0 1 2 3 19 20

Interest Only Bond v. Zero Coupon Bond

4) Actual Cash Going Out For Issuer:Interest Only Bond Zero Coupon Bond

Yearly Interest PMT $1,100,000.00Years 20Total Interest Paid $22,000,000.00Amount Paid at Maturity $10,000,000.00Total Paid Out = $32,000,000.00 Total Paid Out = $80,623,115.36

Important PointsInterest Only Bond Zero Coupon Bond

PV and FV of cash flows are the same, however, the timing of cash flows is different

This option implies that the company has the cash to pay early

This option implies that the company has a lack of cash to pay back until the very end

This option requires that the company pays back sooner and will thus pay less interest

This option allows company to use cash to earn a return on the cash it borrowed early, but it must pay

back more cash later and much more interest

Interest Only Bond v. Zero Coupon Bond

Interest Expense and Tax RatesTax Rate 35%

Total Interest Expense = After Tax Deduction + Tax Shield$13.6437 (1 - 0.35)*(13.6437) + 0.35*13.6437$13.6437 $8.87 + $4.78

Interest Only Bond Zero Coupon BondCoupon Rate 11.00% Coupon Rate 11.00%

Tax Expense $1,100,000.00 Principal on books $124.03 Tax Shield $385,000.00 Interest Expense $13.64 Cash Outflow $715,000.00 Tax Sheild $4.78

Implied Cash Outflow $8.87 Actual rate given tax benefit of deduction (compare actual cash out to principal to show After Tax Interest Rate ) = 715000/10000000 = 0.0715 8.87/124.03 = 0.0715

or orInterest Rate times one minus the tax rate = actual rate given tax benefit of deduction = After Tax Interest Rate = 0.11*(1 - 0.35) = 0.0715 0.11*(1 - 0.35) = 0.0715

Floating-Rate Bonds

1. Coupon Payments are adjustable Rated can be tied to an interest rate index

such as the Treasury bill interest rate or 30-year Treasury bond rate

Rate and payments are adjusted periodically

2. Holder may have the right to redeem the note at par on the coupon payment date after some specified amount of time

1. This is called a “Put” Provision

3. The coupon rate has a floor and ceiling1. “Capped” or “Collared” means they have an

upper and lower barrier

Other Bonds: Income Bonds:

Coupon payments are dependent on the company income

Convertible Bonds Debt that can be converted to a fixed amount of equity

anytime before maturity at the holder’s option Half Debt half equity? How do you list it on the Balance Sheet?

Put Bond Allows holder to force the issuer to buy the bond back

at a stated price (reverse of a call) CoCo and NoNo Bonds

These have many features that require complex valuing techniques. Because the features can be valuable to the bondholder, the YTM could be negative!

Bond Markets Because the bond market is almost entirely OTC,

it has little or no transparency (can’t see a great deal of Buy/Sells to gage market value of bonds)

US Treasury market is the largest security market in the world

Terminology: Bid Price

The price a dealer is willing to pay for a security Ask Price

The price a dealer is willing to take for a security Bid-ask spread

Bid – Ask = Dealers Profit

The Impact Of Inflation On Interest Rates Inflation

Increase in price over time Example:

Price of milk now = $3.39/gal. Price of milk in 1 year = $3.56/gal.

Inflation and Interest Rates Real Rates

Base interest rate that does not take inflation into consideration

The percentage change in buying power Interest rates or rates of return that have

been adjusted downward from the nominal rate for inflation

Nominal Rates Interest rates or rates of return that have not

been adjusted downward for inflation % change in the number of dollars you have The nominal rate of interest includes our

desired real rate of return plus an adjustment for expected inflation

The Fisher Effect (Irving Fisher) The Fisher Effect defines the relationship

between real rates, nominal rates and inflation

R =r + h + r*h r = (R-h)/(1+h) = (1+R)/(1+h) - 1 (1 + R) = (1 + r)(1 + h)

R = nominal rate r = real rate h = expected inflation rate

Approximation R = r + h

Mike Price now 3.39How many milk do you buy? 100Total price $339.00

Amount now in bank $339.00APR (n=1) = R = Nominal 10%Bank amount in 1 year $372.90

Mike price in 1 year 3.56Milk Inflation = 3.39/3.56 = 5.0147%

Can you buy 10.00% more? 110.00

How many can you buy today = $372.90/3.56 = 104.75

Real Rate = r = (0.1 - 0.050147)/(1 + 0.050147) = 4.7472%

Real Rate of return is = how much more can we buy with our money!!! 4.7472%

Exam

ple

11

:

70

Example 6.6 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.

The Fisher Effect

R = r + h + r*h

Nominal real

compensation for the decrease in the value of

money originally invested

because of inflation, h

compensation for dollars

earned that decrease in

value because of inflation

3 Components to Nominal

Real rate is hard to observe directly, so we observe it indirectly: r = (R-h)/(1+h) = (1+R)/(1+h) - 1

Real Rate is fairly constant Take into consideration taxes:

r (R*(1-taxrate)-h)/(1+h)

The Term Structure Of Interest Rates And Determinants Of Bond Yields The risks associated with loaning

money are added into a “base” interest rate known as the real rate

Bond Yields represent 6 effects: Some Components of Interest

Rates:1. Real Rate2. Inflation Premium3. Interest Rate Risk Premium4. Default Risk Premium5. Taxability Premium6. Liquidity Premium

Real Rate1. Compensation investors demand

for foregoing the use of their money

2. Basic component underlying every interest rate

3. When real rate high, all rates tend to be high

4. Doesn’t really determine shape of term structure (overall effect)

Inflation Premium1. The portion of a nominal interest

rate that represents compensation for expected future inflation

2. Very strongly influences the shape of term structure

3. Inflation expected increase structure upward

4. Inflation expected decrease structure downward

Interest Rate Risk Premium1.Compensation demanded for

bearing interest rate risk2. longer-term bonds have a much

greater risk of loss resulting from changes in interest rate than so short-term bonds

3.This premium increases at a decreasing rate

Term Structure Of Interest Rates (Based On Pure Discount Bonds)1. This shows the relationship between short and

long-term interest rates2. Tells us what the nominal interest rates are on

default-free (Treasury), pure discount securities of all maturities

3. This shows the relationship between nominal interest rates on default-free, pure discount securities and time to maturity

4. These rates are “pure” because they involve no risk of default

5. The term structure tells us the pure time value of money for different lengths of time

Upward sloping = long-term rates > short-term rates Downward sloping = long-term rates < short-term rates

Upward-Sloping Yield Curve

Downward-Sloping Yield Curve

Term Structure Of Interest Rates Assumes:

Real Rates remain constant Inflation linear

Rates could be “Humped” Rates increase at first, but then decline

as we look at longer-termed notes

Treasury Yield Curve A plot of the yields on Treasury

Notes and Bonds relative to Maturity Treasury Yield Curve and the Term

Structure Of Interest Rates re almost the same thing The difference is:

Treasury Yield Curve Based On Coupon Bond Yields

Term Structure Of Interest Rates Based On Pure Discount Bonds

Treasury Yield Curve (Coupon Bond Yields)

Default Risk Premium1.Bonds other than Treasury: Credit

risk/default risk2.The portion of a nominal interest

rate or bond yield that represents compensation for the possibility of default

3.Lower rated bonds have higher yields

Taxability Premium1. The portion of a nominal interest

rate or bond yield that represents compensation for unfavorable tax status

Remember municipal versus taxable Bonds that are taxed at both the state

and Federal level are less favorable than a bond that is only taxed at the Fed. level

Liquidity Premium The portion of a nominal interest rate or

bond yield that represents compensation for a lack of liquidity Liquidity:

How quickly an asset can be converted to cash Example:

Maybe the bond is hard to sell quickly and therefore would require a premium for that lack of liquidity

Less liquid bonds have higher yields than more liquid bonds

Three Principles in Bond Finance1. Rates are inversely related to price

1. Market rate , Bond Price 2. Par, Discount, Premium

Market rate = Coupon Rate Bond sells at Par or Face Value

Market rate > Coupon Rate Bond sells at a Discount

Market rate < Coupon Rate Bond sells at a Premium

3. The more years there are to maturity, the higher the interest rate risk becomes

1. “Interest rate risk to loss of principal”

Bond Vocabulary: Current Yield =

Annual Interest Payment/Closing Price Not equal to YTM (unless bond sells for par); it

does not include the capital gain from discounted face value (principal)

Premium Bond CY >YTM

Discount Bond CY <YTM

In all cases (Current Yield) + (Expected one-period capital gain/loss yield of the bond) must be equal to the YTM

Securitization Securitization = “The process of Securitization

involves the collection or pooling of loans and the sale of securities backed by those loans (Cash flows in loan) Whereas, Banks once made loans and kept them on

their books, now they can initiate loans and then sell the loans to someone else.

Securitization = packaging a set of cash flows and then selling claims (bonds or other) against them Claims = asset backed securities

This means that the cash is the asset that backs it