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Derivatives. Lecture 7. Bond Prices. Example If today is October 2001, what is the value of the following bond? An IBM Bond pays \$115 every Sept for 5 years. In Sept 2006 it pays an additional \$1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%) Cash Flows

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Derivatives

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## Derivatives

Lecture 7

### Bond Prices

Example

If today is October 2001, what is the value of the following bond?

An IBM Bond pays \$115 every Sept for 5 years. In Sept 2006 it pays an additional \$1000 and retires the bond.

The bond is rated AAA (WSJ AAA YTM is 7.5%)

Cash Flows

Sept 0203040506

1151151151151115

### Bond Prices

Example continued

If today is October 2001, what is the value of the following bond?

An IBM Bond pays \$115 every Sept for 5 years. In Sept 2006 it pays an additional \$1000 and retires the bond.

The bond is rated AAA (WSJ AAA YTM is 7.5%)

Price

Yield

### Yield To Maturity

All interest bearing instruments are priced to fit the term structure

This is accomplished by modifying the asset price

The modified price creates a New Yield, which fits the Term Structure

The new yield is called the Yield To Maturity (YTM)

### Yield to Maturity

Example

A \$1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?

### Yield to Maturity

Example

A \$1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?

C0C1C2C3C4C5

-1078.801051051051051105

Calculate IRR = 8.5%

Price

Yield

### Bond Price Sensitivity

Bond B

YTM = 3.50%

Maturity = 5 years

Coupon = 7% or \$70

Par Value = \$1,000

Price = \$1,158.03

Bond A

YTM = 4.00%

Maturity = 8 years

Coupon = 6% or \$60

Par Value = \$1,000

Price = \$1,134.65

### Bond Price Sensitivity

Bond B

YTM = 4.25%

Maturity = 5 years

Coupon = 7% or \$70

Par Value = \$1,000

New Price =\$1,121.57

Price dropped by 3.15 %

Bond A

YTM = 4.75%

Maturity = 8 years

Coupon = 6% or \$60

Par Value = \$1,000

New Price= \$1,108.61

Price dropped by 2.30 %

Yields increased 0.75%...prices dropped differently

### Problems

• Class examples

Homework

FinCoach

• 5 Bond price problems

• 5 Bond YTM problems