Question

Suppose a​ ten-year,$1,000 bond with an 8.6% coupon rate and semiannual coupons is trading for $1,034.03.

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 9.9% ​APR, what will be the​ bond's price?

Answer 1

(a)

Compute the semi-annual interest, using the equation as shown below:

Semi-annual interest = Face value*Rate of interest/ 2

                                = $1,000*8.6%/ 2

                                  = $43

Hence, the semi-annual interest is $43.

Compute the yield to maturity (YTM), using MS-excel as shown below:

The result of the above excel table is as follows:

Hence, the yield to maturity is 8.10%.

b.

Compute the semi-annual yield, using the equation as shown below:

Semi-annual yield = Annual yield/ 2

                              = 9.9%/ 2

                              = 4.95%

Hence, the semi-annual yield is 4.95%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

Hence, the present value annuity factor is 12.5152138075.

Compute the price of the bond, using the equation as shown below:

Hence, the price of the bond is $918.651110223.