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.

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.)

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.)

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WorksheetDifficulty: 2 MediumSection: 10.4 Interest Rate Risk and Malkiels Theorems

Problem 10-17Learning Objective: 10-03 Interest rate risk and Malkiels theorems.

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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.

Explanation / Answer

a. Current Yield to Maturity of Bond A = 8%

If Interest Rate rise by 2.40% than new Yield to Maturity = 8 + 2.40 = 10.40%

New Price: Bond Price = Par Value x Coupon Rate x 1 - (1+r) -mxn / r + Par Value / (1+r)mxn

r = Yield to Maturity = 10.40%, m = Payment in a Year = 1, n = Number of Years = 5

Bond Price = 1,000 x 8% x 1- (1+10.40%) -1x5 / 10.40% + 1,000 / (1+10.40%) 1x5

New Bond Price = $910

Percentage Change in Price = -90/1,000 = -9%

Current Yield to Maturity of Bond B = 8%

If Interest Rate rise by 2.40% than new Yield to Maturity = 8 + 2.40 = 10.40%

New Price: Bond Price = Par Value x Coupon Rate x 1 - (1+r) -mxn / r + Par Value / (1+r)mxn

r = Yield to Maturity = 10.40%, m = Payment in a Year = 1, n = Number of Years = 18

Bond Price = 1,000 x 8% x 1- (1+10.40%) -1x18 / 10.40% + 1,000 / (1+10.40%) 1x18

New Bond Price = $808

Percentage Change in Price = -192/1,000 = -19.20%

b. Current Yield to Maturity of Bond A = 8%

If Interest Rate fall by 2.40% than new Yield to Maturity = 8 - 2.40 = 5.60%

New Price: Bond Price = Par Value x Coupon Rate x 1 - (1+r) -mxn / r + Par Value / (1+r)mxn

r = Yield to Maturity = 5.60%, m = Payment in a Year = 1, n = Number of Years = 5

Bond Price = 1,000 x 8% x 1- (1+5.60%) -1x5 / 5.60% + 1,000 / (1+5.60%) 1x5

New Bond Price = $1102

Percentage Change in Price = 102/1,000 = 10.20%

Current Yield to Maturity of Bond B = 8%

If Interest Rate fall by 2.40% than new Yield to Maturity = 8 - 2.40 = 5.60%

New Price: Bond Price = Par Value x Coupon Rate x 1 - (1+r) -mxn / r + Par Value / (1+r)mxn

r = Yield to Maturity = 5.60%, m = Payment in a Year = 1, n = Number of Years = 18

Bond Price = 1,000 x 8% x 1- (1+5.60%) -1x18 / 5.60% + 1,000 / (1+5.60%) 1x18

New Bond Price = $1268

Percentage Change in Price = 268 /1,000 = 26.80%

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