A 27-year maturity bond making annual coupon payments with a coupon rate of 9% has duration...

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Finance

A 27-year maturity bond making annual coupon payments with acoupon rate of 9% has duration of 11.5 years and convexity of191.2. The bond currently sells at a yield to maturity of 8%.
Required:
(a)
Find the price of the bond if its yield to maturity falls to 7%or rises to 9%. (Round your answers to 2 decimal places.Omit the "$" sign in your response.)
  Yield to maturity of 7% $
  Yield to maturity of 9% $

(b)
What prices for the bond at these new yields would be predictedby the duration rule and the duration-with-convexityrule?(Round your answers to 2 decimal places. Omit the "$"sign in your response.)
Duration rule Duration-with-
convexity rule
  YTM falls to 7% $    $
  YTM increases to 9% $    $

(c) What is the percent error for each rule? (Round youranswers to 3 decimal places. Omit the "%" sign in yourresponse.)

Duration rule Duration-with-
convexity rule
  Percent error for 7% YTM %   %
  Percent error for 9% YTM %   %

(d) What do you conclude about the accuracy of the two rules?

Answer & Explanation Solved by verified expert

3.7 Ratings (430 Votes)

K N Bond Price Annual Coupon1 YTMk Par value1 YTMN k1 K 27 Bond Price 910001001 8100k 10001 810027 k1 Bond Price 110935 a New bond price YTM 7 K N Bond Price Annual Coupon1 YTMk Par value1 YTMN k1 K 27 Bond Price 910001001 7100k 10001 710027 k1 Bond Price 123973 New bond price YTM 9 K N Bond Price Annual Coupon1 YTMk Par value1 YTMN k1 K 27 Bond Price 910001001 9100k 10001 910027 k1 Bond Price See Answer

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Transcribed Image Text

A 27-year maturity bond making annual coupon payments with acoupon rate of 9% has duration of 11.5 years and convexity of191.2. The bond currently sells at a yield to maturity of 8%.Required:(a)Find the price of the bond if its yield to maturity falls to 7%or rises to 9%. (Round your answers to 2 decimal places.Omit the "$" sign in your response.) Yield to maturity of 7%$ Yield to maturity of 9%$ (b)What prices for the bond at these new yields would be predictedby the duration rule and the duration-with-convexityrule?(Round your answers to 2 decimal places. Omit the "$"sign in your response.)Duration ruleDuration-with-convexity rule YTM falls to 7%$ $ YTM increases to 9%$ $ (c)What is the percent error for each rule? (Round youranswers to 3 decimal places. Omit the "%" sign in yourresponse.) Duration ruleDuration-with-convexity rule Percent error for 7% YTM% % Percent error for 9% YTM% % (d)What do you conclude about the accuracy of the two rules?

Required:
(a)	Find the price of the bond if its yield to maturity falls to 7%or rises to 9%. (Round your answers to 2 decimal places.Omit the "$" sign in your response.)

	Duration rule	Duration-with- convexity rule
YTM falls to 7%	$	$
YTM increases to 9%	$	$

	Duration rule	Duration-with- convexity rule
Percent error for 7% YTM	%	%
Percent error for 9% YTM	%	%