Question

A "zero coupon bond" (or just "zero") is a bond, that does not pay any interest, it just pays the face value when it matures. Of course nobody would purchase a bond without interest, that's why zero coupon bonds are sold at a discount.

Suppose you are given the following information about the current prices of zero coupon bonds:

bond:	price
1-year zero, face value $1,000	$909.09
2-year zero, face value $1,000	$826.45
3-year zero, face value $1,000	$718.65

I.e. if you buy 1-year zero, you must pay now $909.09 and you will receive $1,000 as the bond matures in exactly 1 year, or, alternatively, if you buy 3-year zero, you pay today $718.65 and will receive $1,000 in exactly 3 years.

Given the information, find:

1. Yield to maturity for each bond.
2. Using zero-coupon bond yields calculated above, what is the price of 3-year coupon bond, if the coupon payment is $100 ($100 received at the end of each year 1, 2, and 3)?
3. Given the price of 3-year coupon bond calculated above and coupon payment of $100 at the end of each year 1, 2, and 3, calculate coupon bond rate.

Answer 1

Answer: We will use the financial calculator to calculate the below answers

1. Yields to maturity for each bond

1. N = 1, PV = $909.09, FV = $1,000, PMT = 0 and I/Y = 10.00011%

2. N = 2, PV = $826.45, FV = $1,000, PMT = 0 and I/Y = 9.99%

3. N = 3, PV = $718.65, FV = $1,000, PMT = 0 and I/Y = 11.642%

2. what is the price of 3-year coupon bond, if the coupon payment is $100 ($100 received at the end of each year 1, 2, and 3)?

N = 3

PMT = $100

I/Y = 11.642%

FV = $1000

PV = $960.32

3. Given the price of 3-year coupon bond calculated above and coupon payment of $100 at the end of each year 1, 2, and 3, calculate coupon bond rate.

Coupon bond rate = Coupon/Face value

Coupon bond rate = 100/1000

Coupon bond rate = 10%