Consider afn) Ten-year, 14.5 percent annual coupon bond with a face value of $1,
ID: 2821587 • Letter: C
Question
Consider afn) Ten-year, 14.5 percent annual coupon bond with a face value of $1,000. The bond is trading at a rate of 115 percent a. What is the price of the bond? b. If the rate of interest increases 1 percent what will be the bond's new price? c. Using your answers to parts (a) and (b), what is the percentage change in the bond's price as a result of the 1 percent increase in interest rates? (Negative value should be indicated by a minus sign.) d. Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16) a. Price of the bond b. Bond's new price C. Percentage change d. Bond's new price Percentage changeExplanation / Answer
Answer a.
Face Value = $1,000
Annual Coupon Rate = 14.50%
Annual Coupon = 14.50% * $1,000
Annual Coupon = $145
Annual YTM = 11.50%
Time to Maturity = 10 years
Price of Bond = $145 * PVIFA(11.50%, 10) + $1,000 * PVIF(11.50%, 10)
Price of Bond = $145 * (1 - (1/1.115)^10) / 0.115 + $1,000 / 1.115^10
Price of Bond = $1,173.03
Answer b.
Face Value = $1,000
Annual Coupon = $145
Annual YTM = 12.50%
Time to Maturity = 10 years
Price of Bond = $145 * PVIFA(12.50%, 10) + $1,000 * PVIF(12.50%, 10)
Price of Bond = $145 * (1 - (1/1.125)^10) / 0.125 + $1,000 / 1.125^10
Price of Bond = $1,110.73
Answer c.
Change in Price = ($1,110.73 - $1,173.03) / $1,173.03
Change in Price = -5.31%
Answer d.
Face Value = $1,000
Annual Coupon = $145
Annual YTM = 9.50%
Time to Maturity = 10 years
Price of Bond = $145 * PVIFA(9.50%, 10) + $1,000 * PVIF(9.50%, 10)
Price of Bond = $145 * (1 - (1/1.095)^10) / 0.095 + $1,000 / 1.095^10
Price of Bond = $1313.94
Change in Price = ($1,313.94 - $1,173.03) / $1,173.03
Change in Price = 12.01%