Both bond A and bond B have 8 percent coupons and are priced at par value. Bond

Question

Both bond A and bond B have 8 percent coupons and are priced at par value. Bond A has 5 years to maturity, while bond B has 18 years to maturity.

a.  
If interest rates suddenly rise by 2.4 percent, what is the percentage change in price of bond A and bond B? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
  
      
Bond A   %
Bond B   %

b.  
If interest rates suddenly fall by 2.4 percent instead, what would be the percentage change in price of bond A and bond B? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

      
Bond A   %
Bond B   %

Explanation / Answer

Before proceeding to answer the question, please note that:

1. In case the bond price = par value, coupon rate = Yield to Maturity (YTM). Thus, in this case, YTM of both the bonds = 8%

2. There is inverse relationship between price of bond and movement in interest rates.

3. Changes in interest rates affect bond with longer time to maturity much more than bonds with shorter time to maturity if coupon rates are same.

With respect to the question,

Current price = $1000 (Assuming par value = $1000)

Annual coupon on both the bonds = 8% * $1000 = $80

Current YTM = 8%

If interest rates rise by 2.4%, YTM = 8% + 2.4% = 10.40%

If interest rates decline by 2.4%, YTM = 8% - 2.4% = 5.60%

a) If interest rates rise by 2.4%, new price of:

Bond A = 80 * PVIFA (10.40%,5) + 1000 * PVF (10.40%,5)

= 80 * 3.75 + 1000 * 0.60975

= 300 + 609.75

= 909.75

Bond B = 80 * PVIFA (10.40%,18) + 1000 * PVF (10.40%,18)

= 80 * 8 + 1000 * 0.16848

= 640 + 168.48

= 808.48

Change in price of Bond A = (1000 - 909.75) / 1000

= 9.02%

Change in price of Bond B = (1000 - 808.40) / 1000

= 19.16%

b) If interest rates decline by 2.4%, new price of:

Bond A = 80 * PVIFA (5.60%,5) + 1000 * PVF (5.60%,5)

= 80 * 4.26 + 1000 * 0.76151

= 340.80 + 761.51

= 1102.31

Bond B = 80 * PVIFA (10.40%,18) + 1000 * PVF (10.40%,18)

= 80 * 11.16 + 1000 * 0.37501

= 892.80 + 375.01

= 1267.81

Change in price of Bond A = (1000 - 1102.31) / 1000

= -10.23%

Change in price of Bond B = (1000 - 1267.81) / 1000

= -26.78%

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