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Interest Rates and Bond Valuation

Chapter 7

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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Chapter Outline• Bond Definition• Bond Features• Valuation of a Bond• Bond Relationships• Inflation and Interest Rates• Determinants of Bond Yields• Bond Ratings• Bond Markets

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A bond is a contract between two parties: one is the investor (you) and the other is a company or a government agency (like a municipal bond)

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You are the investor

The company (or government) is borrowing the money

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A bond contains three key items:

1. The par value (usually $1,000)

2. The length of time (often 10 or 20 years)

3. A coupon interest rate

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You lend money to the borrower and you will get back your original investment plus interest.

The interest is determined by the coupon interest rate.

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For example: A 6% coupon interest rate yields: (the coupon interest rate) x ( the par value)

(6%) x ($1,000) = $60 per year for each year of the bond.

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Let’s look at this visually using the time line:

1 2 3 4 5

$60 $60 $60 $60 $60

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Let’s look at this visually using the time line:

Now let’s add the maturity value…

1 2 3 4 5

$60 $60 $60 $60 $60$1,000

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So the investor receives the principle ($1,000) and earned interest ($60 per year) as payment for loaning the company money.

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Types of Bonds1. Government Bonds2. Zero Coupon Bonds3. Floating-Rate

Bonds4. Catastrophe (Cat)

Bonds5. Income Bonds6. Convertible Bond7. Put Bond8. Sukuk9. James Bond

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From the previous chapters on the time value of money you know how to bring back a single payment (lump sum) and an annuity.To value a bond, just put both pieces together!

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Let’s look at this visually using the time line:

1.The annuity2.The single

payment (lump sum)$60 $60 $60 $60 $60

$1,000

1 2 3 4 50

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Now bring each back into present value terms:First the annuity…Secondly, the lump sum…

$60 $60 $60 $60 $60

$1,000

1 2 3 4 50

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The Bond Pricing Equation

t

t

r)(1FV

rr)(1

1-1C Value Bond

Notice that r = the discount rate used to bring back the future dollars.This discount rate has a name in bonds:

The Yield to Maturity (YTM).

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Your finance calculator can compute both parts (the annuity and the lump sum) simultaneously

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A bond valuation example:

• 5 year bond • 14% as the discount rate (YTM)

• 6% coupon interest rate

• $1,000 maturity value

5 years = N

14% = Discount rate (YTM)

$60 = Payment (PMT)

$1,000 = FV

PV = ?

-725.35

1st2nd

TI BA II Plus

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Student alert!Keep it simple:

Once you have computed the annuity amount, you can throw away the “coupon interest rate”. You need the dollar amount of the annuity, not the coupon interest rate itself.

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Bond RelationshipsKey concept:

If the YTM is greater (>)than the coupon interest rate, then the value of the bond will be less than < $1,000.

Conversely, if the YTM is < the coupon interest rate, then the value of the bond will be > $1,000.

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Bond Relationships(using the previous numerical example)

Discount Rate(YTM)

Coupon Interest

Rate

Present Value of

the Bond

6% 6% $1,0004% 6% >$1,000

9% 6% <$1,000

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Graphical Relationship Between Price and

Yield-to-maturity (YTM)Bo

nd P

rice

Yield-to-maturity (YTM)

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Bond Valuation

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The Fisher EffectThe Fisher Effect defines the

relationship between real rates, nominal rates, and inflation

(1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rateh = expected inflation rate

ApproximationR = r + h

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Fisher Effect ExampleIf 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%An 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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Term Structure of Interest Rates

Yield curve – graphical representation of the term structureNormal – 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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Upward-Sloping Yield Curve

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Downward-Sloping Yield Curve

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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 strongMedium 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 and B– S&P BB and B– Considered possible

that the capacity to pay will degenerate.

• Very Low Grade– Moody’s C (and below)

and S&P C (and below)• income bonds with no

interest being paid, or• in default with principal

and interest in arrears

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1. A bond’s value is the present value of all expected future earnings.

2. As the risk of a bond goes up, the price or value goes down.

3. The closer the bond is to maturity, the more likely the value will approach the par value.

What are the most important topics of this chapter?

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Questions?

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Terminology

• Bond• Par value (face value)• Coupon rate• Coupon payment• Maturity date• Yield or Yield to Maturity

(YTM)

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Formulas

t

t

r)(1FV

rr)(1

1-1C Value Bond

Fisher Effect: (1 + R) = (1 + r)(1 + h) Fisher Effect (approximation): R = r + h

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Key Concepts and Skills

• Bond definition• Computation of bond’s

value• Inverse relationship

between YTM and bond value

• Impact of inflation on bonds• Term structure of interest

rates