What coupon rate should the company set on its new bonds if it wants them to sell at par?

QUESTION

Bond Yields
BDJ Co. wants to issue new 10-year bonds for some muchneeded expansion projects. The company currently has 8 percent coupon bonds on the market that sell for $1,095, make semiannual payments, and mature in 10 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?
Concept: If bond is selling at par value then coupon rate will be equal to discount rate or yield to maturity rate. Current bond price can be calculated by present value of all future cash flows. Current Price of the Bond = Annual Coupon Payment*[1-1/(1 + r)^n]/r + Par Value/(1+r)^n Where r -> Discount Rate or Yield to Maturity n -> Number of Period (Maturity Period) Annual Coupon Payment = Coupon Rate*Par Value For Semi-Annual Payments: Interest Rate -> (r/2)% Number of Period = n*2 Coupon Rate = Annual Coupon Rate/2 Solution: Face Value of bond = $1000 Current Price of BDJ Co. bond = $1095 Maturity Period = 10 Year = 10*2 = 20 (Semi-annual) Coupon Rate = 8% Annual Coupon Payment = 8%*1000 = $80 Semi-annual Coupon Payment = $80/2 = $40 According to Bond Price Formula: $1095 = $40*[1-1/(1+r)^20]/r + $1000/(1+r)^20 We use hit and trial method: Try r = 3.3% Bond Price = $40*[1-1/(1+3.3%)^20]/3.3% + $1000/(1+3.3%)^20 = $1101.31 This price is not equal to $1095. Now try r

= 3.35% Bond Price = $40*[1-1/(1+3.35%)^20]/3.35% + $1000/(1+3.35%)^20 = $1093.65 This price is not equal to $1095. Now try r = 3.34% Bond Price = $40*[1-1/(1+3.34%)^20]/3.34% + $1000/(1+3.34%)^20 = $1095.17 This price is approximately equal to $1095. So,

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