Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, a

Question

Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has five years to maturity, whereas Bond Dave has 16 years to maturity.

If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts 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 rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has five years to maturity, whereas Bond Dave has 16 years to maturity.

Explanation / Answer

Value of Bond = c * PVIFA (Dr . n) + Par value * PVIF (Dr . n)

Being interest payment is half yearly, so discount interest rate and coupon rate gets half and period double.

present value =

Sam = $50 * PVIFA (5% . 5) + $1000 * PVIF (5% . 5) = $50 * 4.329 + $1000 * 0.784 = $1000.45

Dave = $50 * PVIFA (5% . 32) + $1000 * PVIF (5% . 32) = $50 * 15.8027 + $1000 * 0.2099 = $1000.04

If interest rates suddenly rise by 2 percent,

Sam = $50 * PVIFA (6% . 5) + $1000 * PVIF (6% . 5) = $50 * 4.212 + $1000 * 0.747 = $957.60

Dave = $50 * PVIFA (6% . 32) + $1000 * PVIF (6% . 32) = $50 * 14.0840 + $1000 * 0.1550 = $859.20

Change in Prices:

Sam = 1000.45 -957.60 / 1000.45 = -4.28%

Dave = 1000.04 -859.20 / 1000.04 = -14.08%

If rates were to suddenly fall by 2 percent instead,

Sam = $50 * PVIFA (4% . 5) + $1000 * PVIF (4% . 5) = $50 * 4.452 + $1000 * 0.822 = $1044.60

Dave = $50 * PVIFA (4% . 32) + $1000 * PVIF (4% .32) = $50 * 17.8736 + $1000 * 0.2851 = $1178.78

Change in Prices:

Sam = 1000.45 -1044.60 / 1000.45 = 4.41%

Dave = 1000.04 -1178.78 / 1000.04 = 17.87%

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