KING company wants to issue new 10-years bonds to finance some needed expansion. The company currently has an 8 percent coupon bond ($1,000 par value) on the market that sell for $1,080, make semiannual payments and mature in 10 years. What annual coupon rate should the company set on its new bonds if it wants them to sell at par? g

Coupon rate is 7.41%

Explanation:

Using the price formula , the yield to maturity can be calculated first of all:

Bond price=coupon interest /yield to maturity

Bond price is $1080

coupon interest is 8%*$1000=$80

$1080=$80/yield to maturity

$1080*yield to maturity=$80

yield to maturity=$80/$1080

                         =7.41%

However if the price of the bond becomes the par value, the coupon rate can be calculated thus:

$1000=coupon payment/7.41%

coupon payment =$1000*7.41%

coupon payment=$74.1

coupon rate=$74.1/100=7.41%

Annual coupon rate should be: 6.88%

Explanation:

* Yield to maturity (YTM) in semiannual format calculation:

+ Semi annual coupon payment = 1,000 x 8% /2 = $40;

+ The YTM is the discount rate that brings the present value of coupon streams and face value repayment from the bond equals to its current price. So, we have:

  1,080 = [ (40/YTM) x ( 1 - (1+YTM)^(-20) ] + 1,000/(1+YTM)^20 <=> YTM = 3.44%

* Coupon rate calculation:

If the company wants to sell at par ( meaning they wants to gets $1,000), the coupon rate should be equal to the YTM, which is calculated above at 3.44% semiannual.

=> Annual coupon rate = 3.44% x 2 = 6.88%.

So, the answer is 6.88%.

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