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Homework answers / question archive / You buy an 10% coupon(annually paid), , 5-year maturity bond when its yield to maturity is 9%

You buy an 10% coupon(annually paid), , 5-year maturity bond when its yield to maturity is 9%

Finance

You buy an 10% coupon(annually paid), , 5-year maturity bond when its yield to maturity is 9%. 3-year later, the yield to maturity is 8%. What is the holding period of return over the year?

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Let us suppose the face value of the bond to be $ 1000
First, we need to find the purchases price of the bond
which can be found by using the formula,
Current price=FV of all its coupons+FV of face value to be recd. At maturity----both discounted at its yield to maturity
ie. Price=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)
where,
Price---- we need to find out----??
Pmt.=the annual coupon pmt., ie. 10%*1000= $ 100
r=the yield to maturity(YTM) given as 9%
n= no.of coupon periods, still pending to maturity, ie. 5
FV=Face value, $ 1000
Now, plugging all the values in the formula,
ie. Price=(100*(1-(1+0.09)^-5)/0.09)+(1000/(1+0.09)^5)=
1038.90
 
 
Now, we need to find the price of the bond again,
3-year later, when the yield to maturity is 8%
Using the same formula, as above,
only two changes will be
r=the yield to maturity(YTM), at end of 3 yrs, is 8%
n= no.of coupon periods, still pending to maturity, ie. 5-3=2
so, the price is
ie.Price at end of yr.3=(100*(1-(1+0.08)^-2)/0.08)+(1000/(1+0.08)^2)=
1035.67
 
So, the holding period $ return over the period of 3 years is
Total returns from the investment =Appreciation in price +Coupon interest received
(Price at end yr.3-Purchase price)+( 3 yrs.'Coupon interests)
ie.(1035.67-1038.90)+(100*3)=
296.77
 
so, the holding return % = HPR in $/Initial Investment
ie.296.77/1038.90=
28.57%

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