Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 2 years to maturity, whereas Bond Dave has 12 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?

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(b) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?

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Requirement 2:

(a) If rates were to suddenly fall by 4 percent instead, what would be the percentage change in the price of Bond Sam be then?

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(b) If rates were to suddenly fall by 4 percent instead, what would be the percentage change in the price of Bond Dave be then?

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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 = 11% (because it increases by 4% from 7%) nper = 2 years = 2*2 = 4 semi annual payment, pmt = 0.07*1000 = 70/2 = $35 and FV =1000.

The Price of Bond Sam =PV(0.11/2,2*2,70/2,1000) =$929.90

The Price of Bond Dave =PV(0.11/2,12*2,70/2,1000) = $736.97

Percentage change in Price of Bond Sam = (929.90-1000)/1000 = -7.01(negative)

Percentage change in Price of Bond Dave= (736.97-1000)/1000 = -26.309(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 = 3% (because it decreases by 4% from 6%) nper = 2 years = 2*2 = 4 semi annual payment, pmt = 0.07*1000 = 70/2 = $35 and FV =1000.

The Price of Bond Sam =PV(0.03/2,2*2,70/2,1000) =$1077.09

The Price of Bond Dave =PV(0.03/2,12*2,70/2,1000) = $1400.61

Percentage change in Price of Bond Sam = (1077.09-1000)/1000 =7.709

Percentage change in Price of Bond Dave= (1400.61-1000)/1000 = 40.061

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