Question

What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semiannual coupons if this bond is currently trading for a price of $884? Please show workA. 6.82%B. 6.23%C. 5.02%D. 12.46%

Answer 1

Answer:

A. 6.82%

Explanation:

Yield to Maturity is a discounting rate which equals all the cash outflows related to bond with the present /current market value of bond. YTM is calculated by trial and error method. Since the options are available in the question, we can use those options to find out correct YTM.

First we are taking YTM 6.82%

Semi-annual YTM = 3.41%

Coupon Interest semi annual = 1000*5.2%*1/2

                                                 = $26

No of times interest paid = 10*2

                                          = 20

Present Value of bond

= Coupon Interest*PVIFA (YTM, 20) + Par Value x PVIF (YTM, 20)

= 26*PVIFA (3.41%, 20) + 1000*PVIF(3.41%, 20)

= (26*14.32884) + (1,000*0.511386)

= 372.55 + 511.39

= $884

At YTM 6.82% all the future cash flows of bond is equals to its current value.

Therefore, The correct YTM is 6.82%