An investor owned a 9 percent annual payment coupon bond for six years that was
ID: 2742572 • Letter: A
Question
An investor owned a 9 percent annual payment coupon bond for six years that was originally purchased at a 9 percent required return. She redeemed the bond at par at maturity. What was her annual realized rate of return if she reinvested the coupons and earned 9 percent on each coupon? What was her annual realized rate of return if she did not reinvest any coupons (she kept the money under her mattress)? What was her annual realized rate of return if she did reinvest the coupons but only earned 5 percent on each coupon? Why are your answers in B and C are not equal to the answer in A?Explanation / Answer
A)Annualized realized return will be equal to yield to maturity if coupon are invested at yield rate which is equal to 9%
B)If coupons are not reinvested then annualized return will be equal to coupon rate which is equal to 9% in this case
c)Interest on bond = Par value *coupon rate
= 1000 (assume) *.09 = $ 90
Total interest if coupon is reinvested = 90(1+.05)^5 + 90(1+.05)^4+ 90(1+.05)^3 +90(1+.05)^2+ 90(1+.05)^1+ 90
=114.87+109.40+104.19+99.23+94.5 +90
= 612.19
Total payment received at maturity = 1000 (par value) + interest 612.19 = 1612.19
Rate = (Amount received /amount invested)^1/n -1
= (1612.19/1000)^1/6 -1
= (1.61219)^ .16667 -1
= 1.0829- 1
= .0829 or 8.29%
D)Because in case of part B ,coupons are not reinvested so there is no compounding or return on interest we received .
In case of part C,coupons are reinvested at a rate lower than rate in part A
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