Dr. Faulk's Outdoor Market wants to raise $2 million by selling 20-year coupon bonds at par. Comparable bonds in the market have a coupon rate of 6.3 percent, semiannual payments, 20 years to maturity, and are selling at 96.5 percent of par. What coupon rate should the company set on its bonds

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%