al. You have purchased a bond for $973.02. The bond has a coupon rate of 6.4%,pa

Question

al. You have purchased a bond for $973.02. The bond has a coupon rate of 6.4%,pays interest annually, has a face value of $1,000, 4 years to maturity, and a yield to maturity of 72%. The bond's duration is 3.6481 years. You expect that interest rates will fall by .3% later today i). Use the modified duration to find the approximate percentage change in the bond's price. Find the new price of the bond from this calculation. (7 Marks) m i). Use your calculator to do the regular present value calculations to find the bond's new price at its new yield to maturity. (5 Marks) iii). What is the amount of the difference between the two answers? Why are your.: , (3 Marks) answers different?

Explanation / Answer

Price 973.02 Coupon rate 6.40% Annual Face Value 1000 Maturity 4 Years YTM 7.2% Duration 3.6481 Change in interest rate -0.30% (i) MD = D/(1+YTM) 3.6481/(1+0.072) 3.403078358 MD shows change in price if there is 1% change in interest rate Change in price = 973.02 x (3.4031 x -0.3%) -9.93378991 New price = 973.02 - 9.9338 963.0862101 (ii) New YTM = 7.2 -0.3 = 6.9% Coupon = 1000 x 6.4% = 64 Redumption value = 1000 PVAF(6.9%,4) = 3.3949 PVIF(6.9%,4) = 0.7658 New price = Coupon x PVAF + Redumption x PVIF =64 3.3949 + 1000 x 0.7658 983.02564 (iii) Difference in two prices = 983.0256 - 963.0862 19.9394 The formula of MD is designed considering a straight line but in actual the curve is not straight but is convex. Therefore the difference is due to convexity. Please provide feedback…. Thanks in advance…. :-)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.