Claire purchases an eight-year callable bond with a 10% annual coupon rate payable semiannually. The bond has a face value of 3,000 and a redemption value of 2,800. The purchase price assumes the bond is called at the end of the fourth year for 2,900, and provides an annual effective yield of 10.0%. Immediately after the first coupon payment is received, the bond is called for 2,960. Claire’s annual effective yield rate is i. Calculate i.

12.41%

Explanation:

yield to call = {coupon + [(call value - market value)/n]} / [(call value - market value)/2]

0.05 = {150 + [(2,900 - market value)/8]} / [(2,900 - market value)/2]

0.05 x [(2,900 - market value)/2] = 150 + [(2,900 - market value)/8]

0.05 x (1,450 + 0.5MV) = 150 + 362.5 - 0.125MV

72.5 + 0.025MV = 512.5 - 0.125MV

0.15MV = 440

MV = 440 / 0.15 = $2,933.33

Claire's total returns = $150 (coupon) + ($2,960 - $2,933.33) = $176.67

Claire's return on investment = $176.67 / $2,933.33 = 6.02273%

effective annual yield = (1 + 6.02273%)² - 1 = 12.41%

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