Question 26 4 pts (Really worth 9 points) A bondholder purchased a 7.5% coupon,
ID: 2619463 • Letter: Q
Question
Question 26 4 pts (Really worth 9 points) A bondholder purchased a 7.5% coupon, $1,000 par three-year bond at a 7.5% yield. Interest rates then immediately fell to 5.5% and her bond was called at a price of $1,035. She reinvested her money and earned 5.5% on the $1,035 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
Original investment on the bond = $1,000 (Bond’s price will be equal to its par value as coupon rate and yield both are equal at 7.5%)
Bond’s called price = $1,035.
Invested at 5.5% for three years, therefore future value of investment
FV = PV * (1+r %) ^n
Where,
Future value of investment FV =?
Present value of investment PV = $1,035
Interest rate = 5.5% per year
Time period n = 3 years
Therefore
FV = $1,035 * (1 + 5.5%) ^3
= $1,215.34
Her three-year rate of return on the original investment = (investment value after three year – original investment)/ original investment
($1,215.34 - $1,000) / ($1,000)
= 0.2154 or 21.54% for three years
Therefore annual return = (1+ 21.54%) ^ (1/3) - 1
= 1.0672 -1
=0.0672 or 6.72% per year
The basis point decrease in return resulting from call
= Original Yield of bond - three year’s annual return after call
=7.50% - 6.72%
= 0.78% or 78 basis point
Dollar decrease in return resulting from call = Original investment * basis point decrease in return resulting from call
= $1000 * 0.78% = $7.83 per year
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