Question

Kiss the Sky Enterprises has bonds on the market making annual payments, with 19 years to maturity, and selling for $830. At this price, the bonds yield 11.0 percent. What must the coupon rate be on the bonds? Grohl Co. issued 7-year bonds a year ago at a coupon rate of 8 percent. The bonds make semiannual payments. If the YTM on these bonds is 11 percent, what is the current bond price? Ashes Divide Corporation has bonds on the market with 18 years to maturity, a YTM of 9.2 percent, and a current price of $1,156.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

Answer 1

1. Kiss the Sky Enterprises has bonds on the market making annual payments, with 19 years to maturity, and selling for $830. At this price, the bonds yield 11.0 percent. What must the coupon rate be on the bonds?

The bond price or coupon rate can be calculated with the help of following formula

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

Market price of the bond, P0 =$830

C = coupon payment or annual interest payment =?

n = number of payments or time remaining for the maturity of bond = 19

i = yield to maturity (YTM) = 11% per annum

M = value at maturity, or par value = $ 1000 (assumed)

Therefore,

$830 = C * [1 – 1 / (1+11%) ^19] /11% + $1,000 / (1+11%) ^19

OR C = ($830 - $137.68)/ ([1 – 1 / (1+11%) ^19] /11%)

OR C = $692.32 / 7.84 = $88.314

Therefore coupon rate = Coupon payment / Par value of bond

= $88.314 / $1,000

= 8.8314%

2. Grohl Co. issued 7-year bonds a year ago at a coupon rate of 8 percent. The bonds make semiannual payments. If the YTM on these bonds is 11 percent, what is the current bond price?

The bond price can be calculated with the help of following formula

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Market price of the bond, P0 =?

C = coupon payment or annual interest payment = 8% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 8%/2 of $1000 = $40

n = number of payments or time remaining for the maturity of bond = 12 (6*2 for semiannual payments)

i = yield to maturity (YTM) = 11% per annum or 5.5% per semiannual

M = value at maturity, or par value = $ 1000

Therefore,

Price of bond P0 = $40 * [1 – 1 / (1+5.5%) ^12] /5.5% + $1,000 / (1+5.5%) ^12

= $344.74 + $525.98

= $870.72

3. Ashes Divide Corporation has bonds on the market with 18 years to maturity, a YTM of 9.2 percent, and a current price of $1,156.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

The bond price or coupon rate can be calculated with the help of following formula

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

Market price of the bond, P0 =$1,156.50

C = semiannual coupon payment or semiannual interest payment =?

n = number of payments or time remaining for the maturity of bond = 18 *2 = 36 semiannual payments

i = yield to maturity (YTM) = 9.2% per annum or 4.6% per semiannual

M = value at maturity, or par value = $ 1000 (assumed)

Therefore,

$1,156.50 = C * [1 – 1 / (1+4.6%) ^36] /4.6% + $1,000 / (1+4.6%) ^36

OR C = ($1,156.50 - $198.09)/ ([1 – 1 / (1+11%) ^19] /11%)

OR C = $958.41/ 17.43 = $54.98

Semiannual coupon payment = $54.98, therefore annual coupon payment = 2* $54.98 = $109.95

Therefore annual coupon rate = annual Coupon payment / Par value of bond

= $109.95 / $1,000

= 10.995%