Question

Problem 7-13
Price and yield

An 7% semiannual coupon bond matures in 4 years. The bond has a face value of $1,000 and a current yield of 7.4538%.

a.What is the bond's price? Round your answer to the nearest cent.
$   

b.What is the bond's YTM? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answers to two decimal places.
   %

Answer 1

a) We have,

Current Yield = (Interest per annum / Current market price)*100

7.4538 = (($1,000 * 7%) / Current market price) *100

Current market price = 70 / .074538

= $939.12

bond's current market price = $939.12

b) We have,

YTM = (Interest per annum + average other cost per annum*) / average fund employed**

*average other cost per annum = (Redemption price - current market price) / life remaining to mature

= (1000 - 939.12)/4

= $15.22

**average fund employed = (Redemption price + current market price) / 2

= (1000+939.12) / 2

= $969.56

YTM = (Interest per annum + average other cost per annum*) / average fund employed**

= (70+15.22) / 969.56

= 0.0879

= 8.79 %

Note: You can confirm YTM by discounting the future cash flow at 8.79%, you will get current market price.