Question

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AB Builders, Inc., has 24-year bonds outstanding with a par value of $2,000 and a quoted...

AB Builders, Inc., has 24-year bonds outstanding with a par value of $2,000 and a quoted price of 97.842. The bonds pay interest semiannually and have a yield to maturity of 6.80 percent. What is the coupon rate?

  1. 9.92%
  2. 5.95%
  3. 6.62%
  4. 13.23%
  5. 6.29%

Solutions

Expert Solution

Solution

Given in question,

Par Value = $2000

Issue Price = 97.842

Yield to maturity = 6.80%

Interest = semi annually

Now,

Coupon rate = Annual Coupon Payment / Bond Par value * 100

so, we first need to calculate the semi-annual coupon payment on the bond using the pmt formula in excel

= pmt(rate,nper,-pv,fv)

here in formula,

Rate = 6.80% / 2 = 3.40% (six month yield to maturity as coupon pays semi annually)

nper = 24 * 2 = 48 (the number of periods to maturity) (years multiplied by 2)

pv = 97.842%*2000=$1956.84 (current price of the bond)

fv = $2000 (Future value of Bond)

= pmt(3.40,48,-1956.84,2000)

pmt=66.164

That means semi annually coupon payment = $66.164

and annual coupon payment would be =  66.164 * 2=$132.33 annually

Coupon rate = Annual Coupon Payment / Bond Par value * 100

                       =132.33 / 2000

                       =6.62%

Therefore, correct answer is Option C.

ekkarill92 answered 2 years ago
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