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Ashes Divide Corporation has bonds on the market with 20 years to maturity, a YTM of...

Ashes Divide Corporation has bonds on the market with 20 years to maturity, a YTM of 8.8 percent, and a current price of $1,166.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

9.07%

10.68%

18.17%

21.20%

10.58%

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Answer #1

Price of a bond is present value of all cashflows associated with the bond - coupon payments as well as maturity value. Mathematically, it is represented as:

where P is the price of a bond, with C as periodic coupons, i is the periodic YTM, M is the maturity value (or face value) and n is the number of periods to maturity.

For our question, semi-annual YTM, i = 8.8%/2 = 4.4%, number of maturity periods, n = 40 semi-annual periods, P = $1,166.50, M = $1,000

1,166.50 = 18.6673C + 178.6406

987.8594 =  18.6673C

C = $52.92 --> Semi-annual coupon

Hence, annual coupon = 2 * $52.92 = $105.84

Hence, Coupon rate = 105.84/1000 = 10.58%. Answer

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