Question

Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 19 years to maturity. (Do not round your intermediate calculations.) Requirement 1: (a) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam? (b) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave? Requirement 2: (a) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then? (b) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

a. If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam?

Price of Bond Sam =PV(rate,nper,pmt,fv) where rate = 12% (because it increases by 4% from 8%) nper = 3 years = 3*2 = 6 semi annual payment, pmt = 0.08*1000 = 80/2 = $40 and FV =1000.

The Price of Bond Sam =PV(0.12/2,3*2,80/2,1000) =$901.65

The Price of Bond Dave =PV(0.12/2,19*2,80/2,1000) = $703.08

Percentage change in Price of Bond Sam = (901.65-1000)/1000 = -9.83%(negative)

Percentage change in Price of Bond Dave= (703.08-1000)/1000 = -29.69%(negative)

b.If interest rates suddenly fall by 4 percent, what is the percentage change in the price of Bond Sam?

Price of Bond Sam =PV(rate,nper,pmt,fv) where rate = 4% (because it decreases by 4% from 8%) nper = 3 years = 3*2 = 6 semi annual payment, pmt = 0.08*1000 = 80/2 = $40 and FV =1000.

The Price of Bond Sam =PV(0.04/2,3*2,80/2,1000) =$1,112.03

The Price of Bond Dave =PV(0.04/2,19*2,80/2,1000) = $1,528.81

Percentage change in Price of Bond Sam = (1112.03-1000)/1000 =11.20%

Percentage change in Price of Bond Dave= (1528.81-1000)/1000 = 52.88%