Question

Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 5 years to maturity, whereas Bond Dave has 18 years to maturity. (Do not round your intermediate calculations.)

   

Requirement 1:

(a)	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam?
	(Click to select)7.50%-7.34%-7.36%-7.94%8.13%

     

(b)	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Dave?
	(Click to select)-14.60%15.90%18.93%-17.12%-14.62%

     

Requirement 2:

(a)	If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then?
	(Click to select)-7.31%7.50%8.09%8.16%8.11%

     

(b)	If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Dave be then?
	(Click to select)-14.57%18.96%15.90%18.91%18.89%

rev: 09_18_2012

Answer 1

Requirement 1:

a)

Assuming par value to be $1,000

Current price will also be $1,000 since it is priced at par

Current interest rate will also be 10%.

Coupon = 0.1 * 1000 = 100 / 2 = 50

Number of periods = 5 * 2 = 10

Rate = ( 10% + 2%) / 2 = 6%

Price of bond when interest rate rises = Semi annual payment * [ 1 - 1 / ( 1 + r)ⁿ] / r + FV / ( 1 + r)ⁿ

Price of bond when interest rate rises = 50 * [ 1 - 1 / ( 1 + 0.06)¹⁰] / 0.06 + 1000 / ( 1 + 0.06)¹⁰

Price of bond when interest rate rises = 50 * 7.360087 + 558.395

Price of bond when interest rate rises = 926.399

Percentage change in price = [ ( ending price - beginning price) / beginning price] * 100

Percentage change in price = [ ( 926.399 - 1000) / 1000] * 100

Percentage change in price = -7.36%

b)

Assuming par value to be $1,000

Current price will also be $1,000 since it is priced at par

Current interest rate will also be 10%.

Coupon = 0.1 * 1000 = 100 / 2 = 50

Number of periods = 18 * 2 = 36

Rate = ( 10% + 2%) / 2 = 6%

Price of bond when interest rate rises = Semi annual payment * [ 1 - 1 / ( 1 + r)ⁿ] / r + FV / ( 1 + r)ⁿ

Price of bond when interest rate rises = 50 * [ 1 - 1 / ( 1 + 0.06)³⁶] / 0.06 + 1000 / ( 1 + 0.06)³⁶

Price of bond when interest rate rises = 50 * 14.620987 + 122.741

Price of bond when interest rate rises = 853.79

Percentage change in price = [ ( ending price - beginning price) / beginning price] * 100

Percentage change in price = [ ( 853.79 - 1000) / 1000] * 100

Percentage change in price = -14.62%

Requirement 2:

a)

Assuming par value to be $1,000

Current price will also be $1,000 since it is priced at par

Current interest rate will also be 10%.

Coupon = 0.1 * 1000 = 100 / 2 = 50

Number of periods = 5 * 2 = 10

Rate = ( 10% - 2%) / 2 = 4%

Price of bond when interest rate decreases = Semi annual payment * [ 1 - 1 / ( 1 + r)ⁿ] / r + FV / ( 1 + r)ⁿ

Price of bond when interest rate decreases = 50 * [ 1 - 1 / ( 1 + 0.04)¹⁰] / 0.04 + 1000 / ( 1 + 0.04)¹⁰

Price of bond when interest rate decreases = 50 * 8.110896 + 675.564

Price of bond when interest rate decreases = 1,081.11

Percentage change in price = [ ( ending price - beginning price) / beginning price] * 100

Percentage change in price = [ ( 1,081.11 - 1000) / 1000] * 100

Percentage change in price = 8.11%

b)

Assuming par value to be $1,000

Current price will also be $1,000 since it is priced at par

Current interest rate will also be 10%.

Coupon = 0.1 * 1000 = 100 / 2 = 50

Number of periods = 18 * 2 = 36

Rate = ( 10% - 2%) / 2 = 4%

Price of bond when interest rate decreases = Semi annual payment * [ 1 - 1 / ( 1 + r)ⁿ] / r + FV / ( 1 + r)ⁿ

Price of bond when interest rate decreases = 50 * [ 1 - 1 / ( 1 + 0.04)³⁶] / 0.04 + 1000 / ( 1 + 0.04)³⁶

Price of bond when interest rate decreases = 50 * 18.908282 + 243.669

Price of bond when interest rate decreases = 1,189.083

Percentage change in price = [ ( ending price - beginning price) / beginning price] * 100

Percentage change in price = [ ( 1,189.083 - 1000) / 1000] * 100

Percentage change in price = 18.91%