Question

Both Bond A and Bond B have 7 % coupons, are priced at par value, and make semiannual payments. Bond A has 5 years to maturity, whereas Bond B has 15 years to maturity.

A) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond A?

B) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond B?

C) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond A be then? D) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond B be then?

Answer 1

Answer A:

Bond A

Face Value = $1,000

Semiannual coupon =1000* 7%/2 = $35

Time to maturity = 5 years = 10 semiannual periods

Current Price = Priced at par = $1000

Current interest rate = 7%

Interest rates suddenly rise by 4 percent = 7% +4% = 11%

Price will be = PV (rate, nper, pmt, fv, type) = PV (11%/2, 10, -35, -1000, 0) = $849.25

Percentage change in price = (849.25 - 1000) / 1000 = -15.08%

Percentage change in price = -15.08%

Answer B:

Bond B

Face Value = $1,000

Semiannual coupon =1000* 7%/2 = $35

Time to maturity = 15 years = 30 semiannual periods

Current Price = Priced at par = $1000

Current interest rate = 7%

Interest rates suddenly rise by 4 percent = 7% +4% = 11%

Price will be = PV (rate, nper, pmt, fv, type) = PV (11%/2, 30, -35, -1000, 0) = $709.33

Percentage change in price = (709.33 - 1000) / 1000 = -29.07

Percentage change in price = -29.07%

Answer C:

Bond A

Interest rates suddenly fall by 4 percent = 7% - 4% = 3%

Price will be = PV (rate, nper, pmt, fv, type) = PV (3%/2, 10, -35, -1000, 0) = $1184.44

Percentage change in price = (1184.44 - 1000) / 1000 = 18.44%

Percentage change in price = 18.44%

Answer D:

Bond B

Interest rates suddenly fall by 4 percent = 7% - 4% = 3%

Price will be = PV (rate, nper, pmt, fv, type) = PV (3%/2, 30, -35, -1000, 0) = $1480.32

Percentage change in price = (1480.32 - 1000) / 1000 = 48.03%

Percentage change in price = 48.03%