Financial Concepts

Bond Pricing

Student Name:

Instructions

Leave all answers in TWO decimal places.

For the boxes in Question 1 through 5, put calculator input numbers in the second row and your computed answer in the third row.

Question 1 thru 5 cash flow sign conventions: negative PV [assuming we are buying bonds]. Therefore PMT and FV are positive numbers [receiving periodic coupons and receiving face value at maturity].

All bonds have a face value of $1,000.Assume that all coupon payments are made annually unless the problem specifically states otherwise.

Some additional notes and guidance at the end of the document.

1) What is the current value of a 30-year bond with a 4% coupon rate if the current market interest rate is 5.00%?

N

i

PV

PMT

FV

?

?

?

?

= ?

2) A zero coupon bond is sold at a discount and pays no cash interest during its lifetime. At maturity it pays the face value of the bond.What is the current value of a 10-year zero coupon bond if the current market interest rate is 4.00%? monkey2

N

i

PV

PMT

FV

?

?

?

?

= ?

3) What is the current value of a 20-year bond with a coupon rate of 6% (annual) with semi-annual coupon payments if the current market interest rate is 3.0% (annual)? [The coupon frequency is explicitly stated here because we want to compare this PV(bond) to the next question. Everything else being equal, the frequency of coupons DO affect the price of the bond.]

N

i

PV

PMT

FV

?

?

?

?

= ?

4) What is the current value of a 15-year bond with a coupon rate of 5% with quarterly couponpayments if the current market interest rate is 6.0%?

N

i

PV

PMT

FV

?

?

?

?

= ?

5)What is the Yield to Maturity (YTM) and the Yield to Call (YTC) for a bond which is currently priced at $975 if the bond has a coupon of 6%, matures in 10 years but could be called at a price of $1,025 in 5 years? Spring2 Fall2

Calculate YTM:

N

YTM

PV

PMT

FV

?

?

?

?

= ?

Calculate YTC:

N

YTC

PV

PMT

FV

?

?

?

?

= ?

monkey2

6a) In each of the blue cells below, calculate the value of the respective bonds with various combinations of market interest rate, coupon rate, and maturity assumptions:

[assume annual coupons; $1,000 face value]

[you can leave the following bond prices as positive numbers; easier to calculate % change]

Market Interest Rate = 5%

Maturity

10-Yr

30-Yr

Scenario1

2016 Spring2

1% coupon

What value?

What value?

5% coupon

1,000.00

1,000.00

8% coupon

What value?

What value?

Market Interest Rate = 2%

Maturity

10-Yr

30-yr

Scenario2

1% coupon

What value?

What value?

5% coupon

What value?

What value?

8% coupon

What value?

What value?

In each of the red cells below, calculate the respective change in bond value from Scenario1 to Scenario2:

% change in Bond value from Scenario 1 to 2

Maturity:

10-Yr

30-Yr

1% coupon

% change?

% change?

5% coupon

% change?

% change?

8% coupon

% change?

% change?

6b) What do you conclude about the relative sensitivity of bond prices to changes in interest rate?

[Hint: use the above calculated numbers to make comments on the following comparisons with regard to how sensitive are bond price changes when its market interest rate changes]

1)Longer maturities relative to shorter maturities?

Put your response here ....

2)Higher coupon bonds relative to lower coupon bonds?

Put your response here ....