Question

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

Answer 1

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%