Answer:
3.33% increase in the price of bond.
Explanation:
Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Price of the bond is calculated by following formula:
According to given data
Price at par means the the bond have face equal to par which is $1,000 and the yield to maturity is also equals to the the coupon rate.
Coupon payment = C = $1,000 x 11.2 = $112 annually = $56 semiannually
Number of periods = n = 2 x 4 years = 8 periods
As the interest rate rises by 3%
Revised discount rate = r = 11.2% + 3% = 14.2 annually = 7.1% semiannually
Price of the Bond = $56 x [ ( 1 - ( 1 + 7.1% )^-8 ) / 7.1% ] + [ $1,000 / ( 1 + 7.1% )^8 ]
Price of the Bond = 455.63 + $577.68 = 1,033.31
Change in price = $1,033.31 - $1,000 = $33.31
Percentage change = $33.31 / $1,000 = 0.03331 = 3.33%
Answer:
Bond Bill = (value of bond - par value) / par value
= ( 910.78 - 1000) / 1000 = -0.0892 = -8.92%
Bond Ted = ( $800 - $1000 ) / $1000 = -0.1994 = -19.94%
Explanation:
The value of coupon rate for both bonds = 11.2 %
when there is an increase of 3% coupon rate = 14.2%
percentage change in the value of the bonds =
( value of bond - par value) / par value
value of bond = present value of coupon + present value of face value
the semiannual coupon payments = (1000 * 11.20) / 2 = $56
semi-annual coupon rate when increased = 14.20% / 2 = 7.10%
number of payments for Bond bill = 4 years * 2 = 8
number of payments for Bond Ted = 21 years * 2 = 42
value of Bond Bill = $56 * ( PVIFA*7,10% *8 ) + $1000 * (PVIFA*7.10%*8 )
= $910.78
Value of Bond Ted = $56 * (PVIFA*7.10%*42 ) + $1000 * ( PVIFA * 7.10%*42)
= $800.58
calculate the individual percentage change in value of each bonds
Bond Bill = (value of bond - par value) / par value
= ( 910.78 - 1000) / 1000 = -0.0892 = -8.92%
Bond Ted = ( $800 - $1000 ) / $1000 = -0.1994 = -19.94%
