Question

What is the percentage change in price for a zero coupon bond if the yield changes from

8.5​%

to

5.5​%?

The bond has a face value of

​$1,000

and it matures in

19

years. Use the price determined from the first​ yield,

8.5​%,

as the base in the percentage calculation.

Answer 1

Given

Face value of a Zero Coupon bond = $ 1000

Yield rate = 8.5%

We know that Price of ZCB is nothing but the present value of the future cash flows at yield rate

For Zero Coupon bond there is only one Cash flow. i.e Redemption amount.

We know that Present value = Future Value / ( 1+i)^n

Here I = Rate of interest

n = No.of Years

Present value = $ 1000/ ( 1+0.085)^19

. = $ 1000/( 1.085)^19

= $1000/4.711563

= $ 212.24

Hence Price of a Zero Coupon Bond is $ 212.24

Computation of Price of a ZCB if the yield rate is 5.5%

Present value = Future Value / ( 1+i)^n

= $ 1000/( 1+0.055)^19

= $ 1000/( 1.055)^19

= $ 1000/2.765647

= $ 361.58

Hence Price of a Zero Coupon Bond is $ 361.58

% Change in Price of a ZCB =[ ( New price -Old price ) /Old price ]*100

= [ ($ 361.58-$ 212.24)/$ 212.24]*100

= [ $ 149.34/$ 212.24] *100

= 70.36%

Due to change in Yield rate price of ZCB is increased by 70.36%

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