Question

McCurdy Co.'s Class Q bonds have a 12-year maturity, $1,000 par value, and a 8% coupon paid semiannually (4% each 6 months), and those bonds sell at their par value. McCurdy's Class P bonds have the same risk, maturity, and par value, but the p bonds pay a 8% annual coupon. Neither bond is callable. At what price should the annual payment bond sell?

Answer 1

Since Class Q bonds are selling at par.

Price of class Q bond = $ 1000

Its YTM = Annual Coupon rate = 8%

Semi annual ytm = 4%

Effective YTM = (1+ 0.04)^2 -1 =1.0816 - 1 =0.0816 = 8.16%

This will be YTM for class P bond.

Price of a bond = Present value of annual coupon and FV discounted @ 8.16%

Annual coupon amount = 0.08 * 1000 = 80

Price of class P bond = 80/(1+0.0816)^1 +80/(1+0.0816)^2 +80/(1+0.0816)^3 +80/(1+0.0816)^4 +80/(1+0.0816)^5 +80/(1+0.0816)^6 +80/(1+0.0816)^7 +80/(1+0.0816)^8 +80/(1+0.0816)^9 +80/(1+0.0816)^10 +80/(1+0.0816)^11 +80/(1+0.0816)^12 +1000/(1+0.0816)^12

Price = $988.04 Answer

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