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July 16 Outline

•EAR versus APR•Interest Rates and Bond Valuation

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Effective Annual Rate (EAR)

This is the actual rate paid (or received) after accounting for compounding that occurs during the year

If you want to compare two alternative investments with different compounding periods, you need to compute the EAR and use that for comparison.

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Annual Percentage Rate (APR)

This is the annual rate that is quoted by law on all loans.

By definition: APR = period rate times the number of periods per year

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Computing EARs Example

Suppose you can earn 1% per month on $1 invested today.

What is the APR? 1(12) = 12%

How much are you effectively earning?

FV = 1(1.01)12 = 1.1268Rate = (1.1268 – 1) / 1

= .1268 = 12.68%

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Computing EARs Example (continued)

Suppose you put it in another account and earn 3% per quarter.

What is the APR? 3(4) = 12%

How much are you effectively earning?

FV = 1(1.03)4 = 1.1255Rate = (1.1255 – 1) / 1

= .1255 = 12.55%

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EAR - Formula

Remember that the APR is the quoted rate, and

“m” is the number of compounding periods per year

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EAR and Frequency of Compounding

Interest Rates and Bond Valuation

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Chapter Outline

•Bond Definition•Bond Features•Bond Valuation•Inflation and Interest Rates•Determinants of Bond Yields•Bond Ratings•Bond Markets

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)

Bond Definition

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A bond contains three key items:

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

2. Term of the contract (e.g., maturities ranging from 2-30 years)

3. A coupon interest rate

Bond Features

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• You lend money to the borrower with the expectation that you will get back your original investment plus interest.

• The interest is determined by the coupon interest rate.

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Bond Features

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

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Types of Bonds

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1.Government Bonds2.Zero Coupon Bonds3.Floating-Rate Bonds4.Catastrophe (Cat)

Bonds5.Convertible Bonds

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

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t

t

r)(1

FV

rr)(1

1-1

C 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).

A bond valuation example:

• 5 year bond •14% as the discount rate (YTM)•6% coupon interest rate•$1,000 maturity value21

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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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Excel

Key concepts:

•If the coupon interest rate exactly equals the discount rate, then the bond value today will ALWAYS = the par value ($1,000)•If the coupon interest rate is less (more) than the discount rate, then the bond value today will be greater (less) than the par value ($1,000).•Bond prices are inversely related to discount rates.

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Bond Valuation

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Bond Valuation

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See http://www.bloomberg.com/markets/rates-bonds/government-bonds/us for the current US Treasury Yield Curve.