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Rhiannon Corporation has bonds on the market with 12.5 years to maturity, a YTM of 7.3 percent, a par value of $1,000, and a current price of $1,057. The bonds make semiannual payments. What must the coupon rate be on these bonds

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hyderali230

Answer:

The coupon rate be on these bonds is 8%

Explanation:

The coupon payment is the periodic payment made using the coupon rate and face value of the bond.

Use follwing formula to calculate the coupon payment

Price of the bond = C x ( 1 - ( 1 + r )^-n / r ) + F / ( 1 + r )^n

r = YTM = 7.3% /2 = 3.65%

n = numbers of periods = 12.5 years x 2 = 25 periods

F = Face value = $1,000

Price of the bond = $1,057

C = ?

$1,057 = C x ( 1 - ( 1 + 3.65% )^-25 / 3.65% ) + $1,000 / ( 1 + 3.65% )^25

$1,057 = C x 16.22 + $408.10

$1,057 - 408.10 = C x 16.22

648.90 / 16.22 = C

C = $40 semiannually

C = $40 x 2 = $80 annually

Coupon rate = $80 / $1,000 = 0.08 = 8%

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