Question

Suppose a​ ten-year, $ 1,000 bond with an 8.7 % coupon rate and semiannual coupons is trading for $ 1,035.04.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.1 % ​APR, what will be the​ bond's price?

Answer 1

a.Information provided:

Future value= $1,000

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 8.7%/2= 4.35%

Coupon payment= 0.0435*1,000= $43.50

Present value= $1,035.04

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 43.50

PV= -1,035.04

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.09%.

Therefore, the yield to maturity is 4.09%.for a semi-annual period and 4.09%*2= 8.18% for an annual period.

b.Information provided:

Future value= $1,000

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 8.7%/2= 4.35%

Coupon payment= 0.0435*1,000= $43.50

Yield to maturity= 9.1%/2= 4.55% for a semi-annual period

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 43.50

I/Y= 4.55

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

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

The value obtained is 974.10.

Therefore, the price of the bond is $974.10.

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