Question

Both Bond Bill and Bond Ted have 12.6 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 6 years to maturity, whereas Bond Ted has 23 years to maturity. Both bonds have a par value of 1,000. a.If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?

Answer 1

The correct answer is -7.817 % and -13.163%.

Step-by-step explanation:

According to the scenario, the computation of the given data are as follows:

Par value = $1,000

Coupon rate = 12.6%

So, Semi-annual coupon rate =6.3%

Semi annual coupon payment = 6.3% × $1,000 = $63

If interest rate rise by 2%

Then, the discount rate = 12.6% + 2% = 14.6% p.a.

Discount rate (i) semiannual = 7.3%

PV of Annuity = C× [ ( 1 + i )^t - 1 ) ] ÷ (( 1 + i ) × i )

Where, t = Time period semiannual

C = Coupon payment semiannual

By putting the value,

Price of Bill Bond= $63 × (1.073^12-1) ÷ ((1.073^12) × 0.073) + $1,000 ÷ (1.073^12)

= $921.83

So, Percentage change in Bill Bond = (($921.83 - $1,000 ) ÷ $1,000 ) × 100

= -7.817 %

Price of Ted Bond = $63 × (1.073^46 - 1 ) ÷ (( 1.073^46 ) × 0.073 ) + $1,000 ÷ (1.073^46)

= $868.37

So, Percentage change in Ted Bond = (( $868.37 - $1,000 ) ÷ $1,000 ) × 100

= -13.163%