Both bond A and bond B have 10 percent coupons and are priced at par value. Bond

Question

Both bond A and bond B have 10 percent coupons and are priced at par value. Bond A has 10 years to maturity, while bond B has 20 years to maturity.

Assume if interest rates suddenly rise by 1 percent, what is the percentage change in price of bond A and bond B? (Round your answer to 2 decimal places. Negative answers should be indicated by a minus sign. Omit the "%" sign in your response.)

Assume if interest rates suddenly fall by 1 percent instead, what would the percentage change in price of bond A and bond B? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Both bond A and bond B have 10 percent coupons and are priced at par value. Bond A has 10 years to maturity, while bond B has 20 years to maturity.

Explanation / Answer

Yield to Maturity

Bond A = 10%

Bond B = 10%

If interest rate increases by 1%, then percentage change in price

Bond A = -5.89%

Bond B = - 7.96%

If interest rate decreases by 1%, then percentage change in price

Bond A = 6.42%

Bond B = 9.13%

Bond A

Coupon rate = 10%

Coupon payment = 10

Par Value = $ 100

Time to maturity = 10 years

When the bond is selling at par value (current price), then the yield to maturity is equal to coupon rate. This can be found from the below calculation

Let r by yield to maturity such that

100 = 10 * [(1-(1/(1+r)^10)/r] + 100/(1+r)^10

100 - 10 * [(1-(1/(1+r)^10)/r] - 100/(1+r)^10 = 0

Let r = 10%, RHS is equal to

= 100 - 10 * [(1-(1/(1.10)^10)/0.10] - 100/(1.10)^10

= 100 - 10 * [(1-(1/(2.593742)/0.10] - 100/2.593742

= 100 – 10 * ((1-0.385543)/0.10) - 100 * 0.385543

= 100 – 10 * (0.614457/0.10) - 38.5543

= 100 – 10 * 6.144567 – 38.5543

= 100 – 61.44567 – 38.5543

= 0

If interest rates increase by 1%, that is ytm = 10+1 = 11%, then price of bond

= 10 * [(1-(1/(1.11)^10)/0.11] + 100/(1.11)^10

= 10 * [(1-(1/2.839421)/0.11] + 100/2.839421

= 10 * ((1-0.352184)/0.11) + 100 * 0.352184

= 10 * (0.647816/0.11) + 35.21845

= 10 * 5.889232 + 35.21845

= 58.89232 + 35.21845

= 94.11077 or 94.11

% change in Bond price = ((94.11 – 100)/100) = -5.88923 or -5.89%

If interest rate falls by 1%, then ytm = 10 – 1 = 9%, then the price of the bond

= 10 * [(1-(1/(1.09)^10)/0.09] + 100/(1.09)^10

= 10 * [(1-(1/2.367364)/0.09] + 100/2.367364

= 10 * ((1-0.422411)/0.09) + 100 * 0.422411

= 10 * (0.577589/0.09) + 42.24108

= 10 * 6.417658 + 42.24108

= 64.17658 + 42.24108

= 106.4177 or 106.42 (rounded off)

% change in Price of the bond = ((106.42 – 100)/100)*100 = 6.417658 or 6.42%

Bond B

Yield to Maturity = 10%      

If interest rates increase by 1%, that is ytm = 10+1 = 11%, then price of bond

= 10 * [(1-(1/(1.11)^20)/0.11] + 100/(1.11)^20

= 10 * [(1-(1/(8.062312)/0.11] + 100/8.062312

= 10 * ((1-0.124034)/0.11) + 100 * 0.124034

= 10 * (0.875966/0.11) + 12.40339

= 10 * 7.963328 + 12.40339

= 79.63328 + 12.40339

= 92.03667 or 92.04 (rounded off)

% change in Bond price = ((92.04 – 100)/100) = -7.9633 or -7.96%

If interest rate falls by 1%, then ytm = 10 – 1 = 9%, then the price of the bond

= 10 * [(1-(1/(1.09)^20)/0.09] + 100/(1.09)^20

= 10 * [(1-(1/5.604411)/0.09] + 100/5.604411

= 10 * ((1-0.178431)/0.09) + 100 * 0.178431

= 10 * (0.821569/0.09) + 17.84309

= 10 * 9.128546 + 17.84309

= 91.28546 + 17.84309

= 109.1285 or 109.13 (rounded off)

% change in Price of the bond = ((109.13 – 100)/100)*100 = 9.128546 or 9.13%

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