Question

Bond J has a coupon rate of 5 percent. Bond K has a coupon rate of 12 percent. Both bonds have 6 years to maturity, make semiannual payments, and have a YTM of 8 percent.

  

	If interest rates suddenly rise by 5 percent, what is the percentage price change of Bond J?

  

	If interest rates suddenly rise by 5 percent, what is the percentage price change of Bond K?

  

	If interest rates suddenly fall by 5 percent, what is the percentage price change of Bond J?

  

	If interest rates suddenly fall by 5 percent, what is the percentage price change of Bond K?

Answer 1

Bond J:

Face Value = $1,000

Annual Coupon Rate = 5.00%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $1,000
Semiannual Coupon = $25

Time to Maturity = 6 years
Semiannual Period = 12

If Interest Rate is 8.00%:

Annual Interest Rate = 8.00%
Semiannual Interest Rate = 4.00%

Price of Bond = $25 * PVIFA(4.00%, 12) + $1,000 * PVIF(4.00%, 12)
Price of Bond = $25 * (1 - (1/1.04)^12) / 0.04 + $1,000 / 1.04^12
Price of Bond = $859.22

If Interest Rate is 13.00%:

Annual Interest Rate = 13.00%
Semiannual Interest Rate = 6.50%

Price of Bond = $25 * PVIFA(6.50%, 12) + $1,000 * PVIF(6.50%, 12)
Price of Bond = $25 * (1 - (1/1.065)^12) / 0.065 + $1,000 / 1.065^12
Price of Bond = $673.65

Percentage Change in Price = ($673.65 - $859.22) / $859.22
Percentage Change in Price = -21.60%

If Interest Rate is 3.00%:

Annual Interest Rate = 3.00%
Semiannual Interest Rate = 1.50%

Price of Bond = $25 * PVIFA(1.50%, 12) + $1,000 * PVIF(1.50%, 12)
Price of Bond = $25 * (1 - (1/1.015)^12) / 0.015 + $1,000 / 1.015^12
Price of Bond = $1,109.08

Percentage Change in Price = ($1,109.08 - $859.22) / $859.22
Percentage Change in Price = 29.08%

Bond K:

Face Value = $1,000

Annual Coupon Rate = 12.00%
Semiannual Coupon Rate = 6.00%
Semiannual Coupon = 6.00% * $1,000
Semiannual Coupon = $60

Time to Maturity = 6 years
Semiannual Period = 12

If Interest Rate is 8.00%:

Annual Interest Rate = 8.00%
Semiannual Interest Rate = 4.00%

Price of Bond = $60 * PVIFA(4.00%, 12) + $1,000 * PVIF(4.00%, 12)
Price of Bond = $60 * (1 - (1/1.04)^12) / 0.04 + $1,000 / 1.04^12
Price of Bond = $1,187.70

If Interest Rate is 13.00%:

Annual Interest Rate = 13.00%
Semiannual Interest Rate = 6.50%

Price of Bond = $60 * PVIFA(6.50%, 12) + $1,000 * PVIF(6.50%, 12)
Price of Bond = $60 * (1 - (1/1.065)^12) / 0.065 + $1,000 / 1.065^12
Price of Bond = $959.21

Percentage Change in Price = ($959.21 - $1,187.70) / $1,187.70
Percentage Change in Price = -19.24%

If Interest Rate is 3.00%:

Annual Interest Rate = 3.00%
Semiannual Interest Rate = 1.50%

Price of Bond = $60 * PVIFA(1.50%, 12) + $1,000 * PVIF(1.50%, 12)
Price of Bond = $60 * (1 - (1/1.015)^12) / 0.015 + $1,000 / 1.015^12
Price of Bond = $1,490.84

Percentage Change in Price = ($1,490.84 - $1,187.70) / $1,187.70
Percentage Change in Price = 25.52%