BDJ Co. wants to issue new 21-year bonds for some much-needed expansion projects
ID: 2649547 • Letter: B
Question
BDJ Co. wants to issue new 21-year bonds for some much-needed expansion projects. The company currently has 8.6 percent coupon bonds on the market that sell for $1,126, make semiannual payments, and mature in 21 years.
What coupon rate should the company set on its new bonds if it wants them to sell at par?
BDJ Co. wants to issue new 21-year bonds for some much-needed expansion projects. The company currently has 8.6 percent coupon bonds on the market that sell for $1,126, make semiannual payments, and mature in 21 years.
Explanation / Answer
Before answering the question, please note the relationship that in case coupon rate = YTM, price of the bond would be at par.
The relationship can be used to decide the coupon rate of the new bond by equating it to the YTM of the existing bonds (Because both bonds have 21 years to maturity, the two can be considered comparable)
YTM of existing bonds can be found using the present value relationship between bond price and sum of present values of annuity comprising coupon payments and present value of redemption value
Thus,
Bond price = Present value of coupon payments + Present value of redemption value
Coupon payments are made semi-annually
Each coupon payment = 8.6%/2 * 1000 = $43
Number of coupon payments = 21 * 2 = 42
Thus,
$1,126 = $43 * PVIFA (YTM%/2, 42) + $1000 * PVF (YTM%/2, 42)
where PVIFA is the present value interest factor of annuity
and PVF is present value factor
Using trial and error or microsoft excel
YTM / 2= 3.70%
YTM = 7.40%
Thus, the coupon rate on the new bonds has to be 7.40% for the bonds to sell at par
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