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?

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

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%