Warson Motors 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 6.5 percent of par. What coupon rate should Warson Motors set on its bonds?

He should set coupon rate of 1.98%

Explanation:

Given Data:

Face Value of Bonds = $2,000,000

Coupon rate = 6.3 percent

Issue Value of Bonds = 6.5% * Face Value of Bonds

                                    = 6.5% * $2,000,000

                                    = 0.065 * $2,000,000

                                     = $130,000

Given Annual YTM = 6.30%  

Therefore,

Semiannual YTM = 3.15%

Time to Maturity = 20 years

Semiannual Period = 40

Let Semiannual Coupon be $C

$130,000 = $C * PVIFA(3.15%, 40) + $2,000,000

$130,000 = $C * (1 - (1/1.0315)^40) / 0.0315 + $2,000,000 / 1.0315^40

$130,000= $C * 22.56 + $578,443.2

$448,443.2 = $C * 22.56

$C = $19877.80

Semiannual Coupon = $19877.80

Semiannual Coupon Rate = Semiannual Coupon / Face Value of Bonds

Semiannual Coupon Rate = $19877.80 / $2,000,000

Semiannual Coupon Rate = 0.0099 or 0.99%

Annual Coupon Rate = 2 * Semiannual Coupon Rate

Annual Coupon Rate = 2 * 0.99%%

Annual Coupon Rate = 1.98%

oh

Explanation: