Question

Broke Benjamin Co. has a bond outstanding that makes semiannual payments with a coupon rate of 5.7 percent. The bond sells for $961.87 and matures in 21 years. The par value is $1,000. What is the YTM of the bond?

Answer 1

YTM = 2.99/3%

Explanation:

Given CR= 5.7%, BP= $961.87, FV= $1000, n =21 YTM = ?

The bond is said to make semiannual payments

so calculate n = 21*2= 42

Coupon = 5.7%*1000= $57

semi annual = 57/2=$28.5

YTM = C+F-P/n ÷ F+P/2

=28.5+1000-961.87/42 ÷ 1000+961.87/2

=0.0299/3%

This makes sense for the YTM to be above the the coupon rate because the bond is trading below par value

Answer 2

the the YTM of the bond is 6%

Explanation:

Given:

• Coupon rate of 5.7 percent => Coupon payment = 5.7%*1000 = 57
• Par value is $1,000 (F)
• n =21 years
• Price of bond: $961.87 (P)

As we know that, the formula to find out YTM is:

YTM = [C + (F-P/n) ] / (F+ P) / 2

<=> YTM = [ 57 + (1000 -
`(961.87)/(21)` )] / (1000 + 961.87)/2

<=> YTM = (57 + 1.87 ) / 980.935

<=> YTM = 0.06* 100% = 6%

So the the YTM of the bond is 6%