Question

8. Coupon Rates [LO2] McConnell Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $1,045. The bonds make semiannual payments. What must the coupon rate be on these bonds?

10. Valuing Bonds [LO2] Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 4.8 percent. What is the price of the bond?

Answer 1

8. 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 =$1,045

C = coupon payment or semi-annual interest payment =?

n = number of payments = 14.5 *2 = 29

i = yield to maturity (YTM) = 5.3% per annum or 5.3%/2 =2.65% semiannual

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

Therefore,

$1,045 = C * [1 – 1 / (1+2.65%) ^29] /2.65% + $1,000 / (1+2.65%) ^29

OR C = ($1045 - $468.37)/ ([1 – 1 / (1+2.65%) ^29] /2.65%)

OR C = $576.63 / 20.061 = $28.74

Annual coupon payment = $28.74 *2 = $57.49

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

= $57.49 / $1,000

= 5.749% or 5.75% per year

10. 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 =?

M = value at maturity, or par value = $2000

C = coupon payment or semi-annual interest payment = 4.4% * $2000 = $88 or $88/2 = $44 semiannual payments

n = number of payments = 13 *2 = 26

i = yield to maturity (YTM) = 4.8% per annum or 4.8%/2 =2.4% semiannual

Therefore,

P = $44 * [1 – 1 / (1+2.4%) ^26] /2.4% + $2,000 / (1+2.4%) ^26

= $843.77 + $1,079.52

= $1,923.29

Therefore the price of the bond is $1,923.29.