Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 5 years to maturity, whereas Bond Dave has 19 years to maturity.

Requirement 1:
(a)   If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam?
(b)   If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Dave?

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?
(b)   If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Dave be then?
      

Answer 1

Bond Dave:

Face Value = $1,000

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 19
Semiannual Period to Maturity = 38

If bond is selling at par, then current interest rate is equal to the coupon rate

So, current interest rate is 9.00%

If interest rate increases by 2%:

Annual Interest Rate = 11%
Semiannual Interest Rate = 5.50%

Price of Bond = $45 * PVIFA(5.50%, 38) + $1,000 * PVIF(5.50%, 38)
Price of Bond = $45 * (1 - (1/1.055)^38) / 0.055 + $1,000 / 1.055^38
Price of Bond = $841.95

Percentage Change in Price = ($841.95 - $1,000) / $1,000
Percentage Change in Price = -15.81%

If interest rate decreases by 2%:

Annual Interest Rate = 7%
Semiannual Interest Rate = 3.50%

Price of Bond = $45 * PVIFA(3.50%, 38) + $1,000 * PVIF(3.50%, 38)
Price of Bond = $45 * (1 - (1/1.035)^38) / 0.035 + $1,000 / 1.035^38
Price of Bond = $1,208.41

Percentage Change in Price = ($1,208.41 - $1,000) / $1,000
Percentage Change in Price = 20.84%

Bond Sam:

Face Value = $1,000

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 5
Semiannual Period to Maturity = 10

If bond is selling at par, then current interest rate is equal to the coupon rate

So, current interest rate is 9.00%

If interest rate increases by 2%:

Annual Interest Rate = 11%
Semiannual Interest Rate = 5.50%

Price of Bond = $45 * PVIFA(5.50%, 10) + $1,000 * PVIF(5.50%, 10)
Price of Bond = $45 * (1 - (1/1.055)^10) / 0.055 + $1,000 / 1.055^10
Price of Bond = $924.62

Percentage Change in Price = ($924.62 - $1,000) / $1,000
Percentage Change in Price = -7.54%

If interest rate decreases by 2%:

Annual Interest Rate = 7%
Semiannual Interest Rate = 3.50%

Price of Bond = $45 * PVIFA(3.50%, 10) + $1,000 * PVIF(3.50%, 10)
Price of Bond = $45 * (1 - (1/1.035)^10) / 0.035 + $1,000 / 1.035^10
Price of Bond = $1,083.17

Percentage Change in Price = ($1,083.17 - $1,000) / $1,000
Percentage Change in Price = 8.32%