A bondholder purchased a 5.5% coupon, $1,000 par three-year bond at a 5.5% yield

Question

A bondholder purchased a 5.5% coupon, $1,000 par three-year bond at a 5.5% yield. Interest rates then immediately fell to 3.5% and her bond was called at a price of $1,040. She reinvested her money and earned 3.5% on the $1,040 for three years. What was her three-year rate of return on the original investment to 2 decimal places? % What was the basis point increase or decrease in return resulting from the call? What was the dollar increase or decrease in return resulting from the call to the nearest penny?

Explanation / Answer

SHE INVESTED INITIALLY $1000 IN BOND AND AS A DECREASE IN RESULT, RECEIVED $1040

SHE INVESTES $1040 FOR 3 YEARS @3.5%

SO FV = $1040*(1 +0.035)3 = 1153.07

SO HER 3 YEAR RETURN = (1153.07/1000)(1/3) - 1 = 4.86%

SO BASIS POINT INCREASE = 4.86% - 3.5 % = 1.36% = 136 BASIS POINTS  

IF SHE WOULD HAVE INVESTED $1000 FOR 3 YEARS @3.5%, SHE WOULD HAVE RECEIVED,

FV = $1000*(1 +0.035)3 = $1108.72

SO DOLLAR INCREASE IN RETURN = $1153.07 - $1108.72 = $44.35

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