Question

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?

Answer 1

Answer:

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%