Question

Both Bond Bill and Bond Ted have 11.2 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 4 years to maturity, whereas Bond Ted has 21 years to maturity. Both bonds have a par value of 1,000. If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds

Answer 1

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 2

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%