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Watters Umbrella Corp. issued 10-year bonds 2 years ago at a coupon rate of 8.7 percent....

Watters Umbrella Corp. issued 10-year bonds 2 years ago at a coupon rate of 8.7 percent. The bonds make semiannual payments. If these bonds currently sell for 108 percent of par value, what is the YTM?

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Answer #1

maturity of bond, n = 8 years

coupon rate = 8.7% = 0.087

par value = M = $1000 ( assumed)

coupon value , c = coupon rate*M = 0.087*1000 = 87

semi-annual coupon , C = c/2 = 87/2 = 43.5

no. of semi-annual periods , = 2n = 2*8 = 16

price of bond , P = 108% of par value = 1.08*1000 = 1080

semi-annual YTM = (87/2 + (1000 - 1080 )/2*8)/(0.4*1000+0.6*1080)

semi-annual YTM = (43.5 - 5) / (400 + 648) = 38.5 / 1048 = 0.036736641 = 3.6736641% ( per half year /semi annual ) = 3.67%

Annual YTM = Annual percentage rate = 2 * 0.036736641 = 0.073473282 = 7.35%

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