Question

Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The nominal required rate of return on these bonds is currently 10 percent (Kd), and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond. What is the annual coupon interest rate??

Answer 1

F = Face value =	$1,000.00
C = Coupon rate = Semi-annual = Coupon /2 =	?
R = Rate = Required rate of return = Yield semi-annual = 10% / 2 =	5.00%
N = Number of remaining coupon payments till maturity = 5 years x 2 = 10 =	10
PV = Present value =	768
Formula for bond price:
PV = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
768 = C x 1000*(1-(1+5%)^-10)/5%+1000/(1+5%)^10
C x 1000*(1-(1+5%)^-10)/5% = 768 - 1000/(1+5%)^10
7721.73493 x C = 768 - 613.91325
C = Coupon rate - Semi-annual =	1.99549%
Convert Semi-annual coupon rate to Annual Coupon rate = C x 2 =	3.99%

Hence, Annual coupon rate is ~ 3.99% (rounded to two decimal places)