Question

In 2014, AT&T issued 10-year bonds with a coupon that pays $93.75 annually. At the time of issue, the bonds sold at par. Today, bonds of similar risk and maturity must pay an annual coupon of 7.25% to sell at par value. Assuming semi-annual payments and a 7.25% yield to maturity, what is the current price of the firm’s bonds? (please use financial calculator-show work)

Answer 1

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using financial calculator as below :

I/Y = 3.625    (Semiannual YTM of bonds = annual YTM / 2 = 7.25%/2 = 3.625%)

NPER = 8 (4 years remaining until maturity with 2 semiannual coupon payments each year. Total number of semiannual coupon payments = 4 * 2 = 8)

PMT = 46.875 (semiannual coupon payment = annual coupon payment / 2 = $93.75 / 2 = $46.875)

FV = 1000 (face value receivable on maturity)

CPT --> PV

PV is calculated to be $1,072.66

Current bond price = $1,072.66