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Interest Rates and Bond Valuation

Chapter 6

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Prepare for Capital Budgeting Part 2: Understand financial statement and cash flow

C2-Identify cash flow from financial statementC3-Financial statement and comparison

Part 3: Valuation of future cash flowC4-Basic conceptsC5-More exercise

Part 4: Evaluate stocks and bonds C6-BondC7-Stock

Part 5: Capital budgeting

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Different Types of Loans

Amortized

Interest only

Pure discount

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1.Bond Definitions Bond: Public debt securities issued by corporation or

government. Usually interest is paid by the borrower every period, and the principal is repaid at the end of the loan.

Par value (face value): The principal amount of a bond that is repaid at the end of the loan term.

Coupon rate: The annual coupon of a bond divided by its face value is called the bond's coupon rate.

Coupon payment: Stated interest payment made on a bond.

Maturity date: Date on which the principal amount of a bond is paid.

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2. Bond Value If a bond has five years to maturity, an $80 annual

coupon, and a $1000 face value, it will be paid back to bondholder like this:

What is the coupon rate? How much is this bond worth?

Time 0 1 2 3 4 5Coupon 80 80 80 80 80Face Value 1000Market Price ?

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Bond Value Yield or Yield to maturity (r): The rate required in the

market on a bond. If the YTM of the bond is 10%, then how much is the bond

worth? ($924.18) Why?

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Bond Value Finding the market price of a bond requires discounting the

coupons and par value at the market rate (yield or yield to maturity, r ).

Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum

t

t

r)(1

F

rr)(1

1-1

C Value Bond

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Bond Prices: Relationship Between Coupon and Yield If coupon rate = YTM, then bond price = par value

Called a par bond If coupon rate < YTM, then bond price < par value

Why? Selling at a discount, called a discount bond

If coupon rate > YTM, then bond price > par value Why? Selling at a premium, called a premium bond

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

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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

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Valuing a Discount Bond with Annual Coupons

Using the calculator: PV of annuity: N = 5; I/Y = 11; PMT = 100;

CPT PV = -369.59 PV of par: N=5; I/Y=11; FV=1000;

CPT PV= -593.45 B=369.59+593.45=963.04

Or N=5; I/Y=11; PMT=100; FV=1000; CPT PV=-

963.04

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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

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Valuing a Premium Bond with Annual Coupons Using the calculator:

PV of annuity: N = 20; I/Y = 8; PMT = 100;

CPT PV = -981.81 PV of par: N = 20; I/Y = 8; FV = 1000;

CPT PV = -214.55 B=981.81+214.55=1196.36

or N = 20; I/Y = 8; PMT = 100; FV = 1000 CPT PV = -1196.36

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The Bond-Pricing Equation

t

t

r)(1

F

rr)(1

1-1

C Value Bond

Last Step in Time Value Calculation:Double check how frequently the interest is earned, and make sure the number of period matches with the period rate.

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Valuing Semiannual Coupon Bond Coupon rate = 14%, semiannual coupons YTM = 16%; Maturity = 7 years; Par value = $1000 Find present values based on the payment period

How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 = 917.56

Calculator PMT = 70; N = 14; I/Y = 8; FV = 1000; CPT PV = -917.56

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

bond price Finding the YTM requires trial and error if you do not

have a financial calculator and is similar to the process for finding r 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)

t

t

r)(1

F

rr)(1

1-1

C Value Bond

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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. Will the yield be more or less than 10%? N = 15; PV = -928.09; FV = 1000; PMT = 100 CPT I/Y = 11%

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Table 6.1

50%

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3. Bond Markets Primarily over-the-counter transactions with

dealers connected electronically Extremely large number of bond issues, but

generally low daily volume in single issues Makes getting up-to-date prices difficult,

particularly on small company or municipal issues

Treasury securities are an exception

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Bond Quotations

What company are we looking at? What is the coupon rate? If the bond has a $1000 face

value, what is the coupon payment each year? When does the bond mature? What is the current yield? How is it computed? What was the trading volume on that day? What is the quoted price? How does the bond’s yield compare to a comparable

Treasury note/bond?

Company Coupon Maturity Last Price Last Yield EST Spread UST EST Vol (000s)

GM 8.375 July 15, 2033 100.641 8.316 362 30 763,528

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Treasury Quotations

What is the coupon rate on the bond? When does the bond mature? What is the bid price? What does this mean? What is the ask price? What does this mean? How much did the price change from the previous

day? What is the yield based on the ask price?

Rate Maturity(M/Y) Bid Asked CHG Ask YLD9.000 18-Nov 145:25 145:26 22 4.51

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4. Factors Affecting Required Return Anything that affects the risk of the cash flows

to the bondholders, will affect the required returns (yield to maturity) Default risk and some bond features Interest rate risk and time to maturity

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4.1 Compare 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

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The Bond Indenture Contract between the company and the bondholders

and includes The basic terms of the bonds: maturity, face value,

coupon, etc. The total amount of bonds issued A description of property used as security, if

applicable Sinking fund provisions Call provisions Details of protective covenants

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Bond Classifications 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

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Bond Characteristics and Required Returns For which bonds Investors will ask for a higher

required return, 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

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4.2 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

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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

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4.3 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

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5.1 Interest Rate Risk

The risk that arises from fluctuating interest rates. It depends on how sensitive the bond price is to interest rate changes. The greater portion of the bond’s value comes from cash flow in the future, the more sensitive it is to interest rate changes.

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

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

75%

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Figure 6.2: Maturity vs. Interest Risk

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5.2 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 nominal rate of interest includes real rate of return plus an adjustment for expected inflation

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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

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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.

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5.3 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

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Figure 6.6 – Upward-Sloping Yield Curve

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Figure 6.6 – Downward-Sloping Yield Curve

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Figure 6.7 – Treasury Yield Curve

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6. Factors Affecting Required Return Default risk premium – bond ratings Interest rate risk premium – term structure Taxability premium – municipal versus taxable

bonds Liquidity premium – bonds that have more

frequent trading will generally have lower required returns

Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns

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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

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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”

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Other Bond Types Income bonds Convertible bonds Put bond There are many other types of provisions that

can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns

100%

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Review Questions1. What is face value/par value/coupon rate/coupon

payment/maturity date/yield to maturity of a bond?

2. How do you find the value of a bond and why do bond prices change?

How to find the present value of the bond's coupon payments and face value respectively?

What is a par/discount/premium bond?

How will interest rate affect the bond prices for bonds with different maturities? How will interest rate affect the bond prices for bonds with different coupon rates? Assume other things are the same.

3. What is the primary type of bond markets?

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Review Questions (cont ..)4. What are the differences between debt and common stock?

What is a bond indenture and what are some of the important features?

What are bond ratings and why are they important?

What are Treasury bonds and Municipal bonds? How will tax rate affect the municipal bonds’ and taxable bonds’ coupon rates?

5. What is interest rate risk? How does inflation affect interest rates? What is the term structure of interest rates? What are the components of term structure of interest rates?

6. What factors determine the required return on bonds?

What is zero coupon bond and floating rate bond?