In: Finance
Ann purchased a treasury bond with exactly six years until maturity, which pays coupon annually. The bond has a par value of $1,000, a 5% annual coupon rate, and a current yield to maturity (YTM) of 6%. After exactly three years Ann sold the bond to another investor, with the yield to maturity of 4%. She was always able to re-invest all her coupon income at a return of 3%. All rates are annual. What is her ANNUALIZED holding period return over the 3-year period?
Par value of Bond= $1000
Annual coupon Payment = $1000*5% = $50
Current YTM = 6%
n= no of years to maturity = 6
Calculating the Current price:-
Price = $ 245.865 +$ 704.96
Price = $ 950.83
Now, after 3 years the YTM is 4%
& n will be 3 years
Calculating the Price after 3 years :-
Price = $ 138.755 +$ 889
So, Price after 3 years= $ 1027.76
- During the 3 year period all coupon will be re-invested at 3%:-
Calculating the future accumulated value of Coupon payment with interest after 3 years:-
Where, C= Periodic Payments = $50
r = Periodic Interest rate = 0.03
n= no of periods=3
Future value = $ 154.55
Now, we will Calculate the Annualized Holding period Return(AHPR):-
where, n= no of years = 3
Income = $ 154.55
P0 =Current price = $ 950.83
P1 =Price after 3 years= $ 1027.76
So, AHPR over 3 years is 7.53%
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