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1. Bond J has a coupon rate of 5.5 percent. Bond S has a coupon rate of 15.5 per

ID: 2821019 • Letter: 1

Question

1. Bond J has a coupon rate of 5.5 percent. Bond S has a coupon rate of 15.5 percent. Both bonds have eight years to maturity, make semiannual payments, a par value of $1,000, and have a YTM of 12 percent.


If interest rates suddenly rise by 3 percent, what is the percentage price change of these bonds? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

If interest rates suddenly fall by 3 percent instead, what is the percentage price change of these bonds? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

2. Bond P is a premium Bond with a coupon rate of 8.2 percent. Bond D is a discount Bond with a coupon rate of 4.2 percent. Both Bonds make annual payments, have a YTM of 6.2 percent, a par value of $1,000, and have seven years to maturity.


What is the current yield for Bond P? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Current yield             %

What is the current yield for Bond D? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Current yield             %

If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Capital gains yield             %

If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond D? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Capital gains yield             %

Percentage
change in price Bond J % Bond S %

Explanation / Answer

Answer to Question 1:

Bond J:

Face Value = $1,000

Annual Coupon Rate = 5.50%
Semiannual Coupon Rate = 2.75%
Semiannual Coupon = 2.75% * $1,000
Semiannual Coupon = $27.50

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

If YTM is 12%:

Annual YTM = 12%
Semiannual YTM = 6%

Price of Bond = $27.50 * PVIFA(6%, 16) + $1,000 * PVIF(6%, 16)
Price of Bond = $27.50 * (1 - (1/1.06)^16) / 0.06 + $1,000 / 1.06^16
Price of Bond = $671.56

If YTM is 15%:

Annual YTM = 15%
Semiannual YTM = 7.5%

Price of Bond = $27.50 * PVIFA(7.5%, 16) + $1,000 * PVIF(7.5%, 16)
Price of Bond = $27.50 * (1 - (1/1.075)^16) / 0.075 + $1,000 / 1.075^16
Price of Bond = $565.78

Change in Price = ($565.78 - $671.56) / $671.56
Change in Price = -15.75%

If YTM is 9%:

Annual YTM = 9%
Semiannual YTM = 4.5%

Price of Bond = $27.50 * PVIFA(4.5%, 16) + $1,000 * PVIF(4.5%, 16)
Price of Bond = $27.50 * (1 - (1/1.045)^16) / 0.045 + $1,000 / 1.045^16
Price of Bond = $803.40

Change in Price = ($803.40 - $671.56) / $671.56
Change in Price = 19.63%

Bond S:

Face Value = $1,000

Annual Coupon Rate = 15.50%
Semiannual Coupon Rate = 7.75%
Semiannual Coupon = 7.75% * $1,000
Semiannual Coupon = $77.50

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

If YTM is 12%:

Annual YTM = 12%
Semiannual YTM = 6%

Price of Bond = $77.50 * PVIFA(6%, 16) + $1,000 * PVIF(6%, 16)
Price of Bond = $77.50 * (1 - (1/1.06)^16) / 0.06 + $1,000 / 1.06^16
Price of Bond = $1,176.85

If YTM is 15%:

Annual YTM = 15%
Semiannual YTM = 7.5%

Price of Bond = $77.50 * PVIFA(7.5%, 16) + $1,000 * PVIF(7.5%, 16)
Price of Bond = $77.50 * (1 - (1/1.075)^16) / 0.075 + $1,000 / 1.075^16
Price of Bond = $1,022.85

Change in Price = ($1,022.85 - $1,176.85) / $1,176.85
Change in Price = -13.09%

If YTM is 9%:

Annual YTM = 9%
Semiannual YTM = 4.5%

Price of Bond = $77.50 * PVIFA(4.5%, 16) + $1,000 * PVIF(4.5%, 16)
Price of Bond = $77.50 * (1 - (1/1.045)^16) / 0.045 + $1,000 / 1.045^16
Price of Bond = $1,365.11

Change in Price = ($1,365.11 - $1,176.85) / $1,176.85
Change in Price = 16.00%