Pembroke Co. wants to issue new 15-year bonds for some much-needed expansion pro

Question

Pembroke Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 8 percent coupon bonds on the market that sell for $1,090, make semiannual payments, and mature in 15 years.

What coupon rate should the company set on its new bonds if it wants them to sell at par? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Pembroke Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 8 percent coupon bonds on the market that sell for $1,090, make semiannual payments, and mature in 15 years.

Explanation / Answer

Given that
Compounding = semi annually
Par Value = 1000
Market Rate = 8%=0.08
YTM= 0.08/2=0.04
Market Price = 1090
N = (15 years) (semiannual)=15*2=30
Coupon rate is annual payout as a percentage of the bond at par value.
Here we use formula

Coupon Rate Formula
Coupon Rate = 2( (Market Price - Par Value x PVIF(ytm%, n) ) / ( Par Value x PVIFA(ytm%, n) ) )
PVIFA(0.04, 30) = 17.29
PVIF(0.04, 30) = 0.3083
You can find PVIFA calculator at following link
http://www.thecalculator.co/finance/PVIFA-Calculator-478.html

You can find PVIF calculator at following link
http://www.miniwebtool.com/pvif-calculator/?r=4&n=30

Then Coupon Rate Calculation will be as follows:
Coupon Rate =2((1090 - 1000 * 0.3083 ) / ( 1000 * 17.29 ))
Coupon Rate =0.0904222093696

Hence coupon rate is 9.04%

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