Question
In: Finance
Both Bond A and Bond B have 7 % coupons, are priced at par value, and...
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?
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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? |
Solutions
Expert Solution
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%
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