Question

a) 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 96.5 percent of par. What coupon rate should Warson Motors set on its bonds?

b) The 7.2 percent bond of Blackford, Inc. has a yield to maturity of 7.3 percent. The bond matures in seven years, has a face value of $1,000, and pays semiannual interest payments. What is the amount of each coupon payment?

Answer 1

Answer to Question A:

Face Value of Bonds = $2,000,000

Issue Value of Bonds = 96.50% * Face Value of Bonds
Issue Value of Bonds = 96.50% * $2,000,000
Issue Value of Bonds = $1,930,000

Annual YTM = 6.30%
Semiannual YTM = 3.15%

Time to Maturity = 20 years
Semiannual Period = 40

Let Semiannual Coupon be $C

$1,930,000 = $C * PVIFA(3.15%, 40) + $2,000,000
$1,930,000 = $C * (1 - (1/1.0315)^40) / 0.0315 + $2,000,000 / 1.0315^40
$1,930,000 = $C * 22.564394 + $578,443.177743
$1,351,556.822257 = $C * 22.564394
$C = $59,897.767

Semiannual Coupon = $59,897.767

Semiannual Coupon Rate = Semiannual Coupon / Face Value of Bonds
Semiannual Coupon Rate = $59,897.767 / $2,000,000
Semiannual Coupon Rate = 0.029949 or 2.9949%

Annual Coupon Rate = 2 * Semiannual Coupon Rate
Annual Coupon Rate = 2 * 2.9949%
Annual Coupon Rate = 5.99%

Answer to Question B:

Face Value of Bonds = $1,000

Annual Coupon Rate = 7.20%
Semiannual Coupon Rate = 3.60%

Semiannual Coupon = 3.60% * $1,000
Semiannual Coupon = $36

So, amount of each coupon payment is $36