Answer:
The coupon rate should be: 6.62%.
Explanation:
* Yield to maturity calculation:
With the comparable bond in the market, we have:
+ Semiannual coupon payment = 2 million x 6.3% / 2 = $63,000
+ Price of the bond = 2,000,000 x 96.5% = $1,930,000
=> 1,930,000 = [ (63,000/YTM) x ( 1 - (1+ YTM)^(-40) ] + [2,000,000/(1+YTM)^40] <=> YTM = 3.31%.
* Coupon rate calculation:
To raise $2 million with the duration for 20-year, the present value of the coupon streams from the Bond the company offers plus the present value of the face value repayment in 20 years time; discounting at YTM, should equal to $2 million:
we have:
2,000,000 = [ (Coupon payment/3.31%) x ( 1 - 1.0331^(-40) ] + [2,000,000/1.0331^40] <=> Coupon payment = $66,200.
=> Coupon rate = Semiannual coupon payment / Face value x 2 = 66,200/2,000,000 x 2 = 6.62%
