DMA Corporation has bonds on the market with 18.5 years to maturity, a YTM of 6.

Question

DMA Corporation has bonds on the market with 18.5 years to maturity, a YTM of 6.5 percent, and a current price of $1,048. The bonds make semiannual payments and have a par value of $1,000.

What must the coupon rate be on these bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

DMA Corporation has bonds on the market with 18.5 years to maturity, a YTM of 6.5 percent, and a current price of $1,048. The bonds make semiannual payments and have a par value of $1,000.

Explanation / Answer

Years to maturity = 18.5

Since, coupon payments are done on semiannual basis

Then No. of periods of maturity (n) = 18.5*2 = 37

YTM = 6.5%

So, semiannual Discount rate (R) = 6.5%/2 = 3.25%

Current bond price = $1048

Par value of bonds = $1000

Assume that, semiannual Coupon payment = C

Then

Current price = Present value of all coupon payment + present value of the bond at par value

Current price = C*(1-1/ (1+R) ^n)/R   + 1000/ (1+R) ^n

1048 = C*(1-1/1.0325^37)/.0325   + 1000/1.0325^37

1048=C*21.3463 + 306.2441

C = (1048 - 306.2441) / 21.3463 = $34,748 = $34.75

So, semiannual coupon payment is $34.75 or 3.475 %

Or

Annual coupon payment is $69.5 or 6.95%

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