A 10-year bond with semi-annual coupons of $70 and redemption value of $1000 was
ID: 2709265 • Letter: A
Question
A 10-year bond with semi-annual coupons of $70 and redemption value of $1000 was purchased for $1270. The coupons (received by the original bond owner) were invested at 8% convertible semiannually.
Two years and six months after purchase, the bond is sold at a price which will yield the original owner 7% (convertible semi-annually).
Assuming the new owner holds the bond to maturity and accumulates a sinking fund with level deposits each six months to replace the premium he paid for the bond, what annual yield rate (convertible semi-annually) does the new owner realize? Assume the sinking fund rate is 9% convertible semiannually. (Answer: 11.3%)
Explanation / Answer
Amount accumulated of coupon invested till 2 1/2 year = semi annual coupon*((1+r)^n-1)/r
semi annual coupon = 70
r ( half yearly interest rate in which it was invested) = 8%
n (no of semi annual period) = 2.5*2 = 5
Amount accumulated of coupon invested till 2 1/2 year = 70*((1+8%)^5 -1)/8%
Amount accumulated of coupon invested till 2 1/2 year = $ 410.66
Total Amount accumulated of Oiginal bond owner till 2 1/2 year = Purchase Price*(1+r)^n
Total Amount accumulated of Oiginal bond owner till 2 1/2 year = 1270*(1+7%)^(2*2.5)
Total Amount accumulated of Oiginal bond owner till 2 1/2 year = $ 1781.24
Sale price of bond by Oiginal bond owner = Total Amount accumulated of Oiginal bond owner till 2 1/2 year - Amount accumulated of coupon invested till 2 1/2 year
Sale price of bond by Oiginal bond owner = 1781.24-410.66
Sale price of bond by Oiginal bond owner = $ 1370.58
Purchase price of new owner = $ 1370.58
Amount accumulated of coupon by new owner till the maturity = semi annual coupon*((1+r)^n-1)/r
semi annual coupon = 70
r ( half yearly interest rate in which it was invested) = 9%
n (no of semi annual period) = (10-2.5)*2 = 15
Amount accumulated of coupon by new owner till the maturity = 70*((1+9%)^15 -1)/9%
Amount accumulated of coupon by new owner till the maturity = $ 2055.26
Redemption Value = 1000
Total Amount accumulated by new owner = 1000+2055.26
Total Amount accumulated by new owner = $ 3055.26
Annual yield rate (convertible semi-annually) does the new owner realize =( (Total Amount accumulated by new owner/Purchase Price)^(1/n) - 1 )*2
Annual yield rate (convertible semi-annually) does the new owner realize =( ( 3055.26/1370.58)^(1/7.5) - 1)
Annual yield rate (convertible semi-annually) does the new owner realize = 11.28%
Annual yield rate (convertible semi-annually) does the new owner realize = 11.3% (approx)
Answer
11.3%
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