Question

Suppose an eight-year, $1000 bond with a 6% coupon rate and semiannual coupons is trading with a yield to maturity 5%.

a. What price is this bond currently trading at?

b. If the yield to maturity of e bond falls to 4% with semiannual compounding what price will the bond trade at?

Answer 1

a.Information provided:

Par value= future value= $1,000

Time= 8 years*2= 16 semi-annual periods

Coupon rate= 6%/2= 3%

Coupon payment= 0.03*1,000= $30

Yield to maturity= 5%/2= 2.50% per semi-annual period

The price of the bond is calculated by computing the present value of the bond.

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

N= 16

PMT= 30

I/Y= 2.5

Press the CPT key and PV to compute the present value.

The value obtained is 1,065.28.

Therefore, the price of the bond is $1,065.28.

b. Information provided:

Par value= future value= $1,000

Time= 8 years*2= 16 semi-annual periods

Coupon rate= 6%/2= 3%

Coupon payment= 0.03*1,000= $30

Yield to maturity= 4%/2= 2% per semi-annual period

The price of the bond is calculated by computing the present value of the bond.

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

N= 16

PMT= 30

I/Y= 2

Press the CPT key and PV to compute the present value.

The value obtained is 1,135.78.

Therefore, the price of the bond is $1,135.78

In case of any further queries, kindly comment on the solution.