Interest Rate Sensitivity--I have answers show all work formulas A Bond trader p
ID: 2772843 • Letter: I
Question
Interest Rate Sensitivity--I have answers show all work formulas
A Bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediatey after she purchased the bonds interest rates fell to 7%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table: (I have all the answers but must show ALL WORK/Formulas). Show Work!
Price at 8% Price at 7% Percentage Change
10 year, 10% annual coupon
10 year zero
5 year zero
30 year zero
$100 perpetuity
Answers are: 10 year 10% coupon = 6.75%
10 year zero = 9.75%
5 year zero = 4.76%
30 year zero = 32.19%
$100 perpetuity = 14.29%
SHOW ALL WORK ALL FORMULAS.
Explanation / Answer
Answer:
(i) 10-year, 10% annual coupon YTM 8% NPER = 10 PMT = 10 FV = 100 PV =? Solve for PV PV = ($113.42) (ii) 10-year, 10% annual coupon YTM 7% NPER = 10 PMT = 10 FV = 100 PV =? Solve for PV PV = ($121.07) 10-year zero 5-year Zero (i) YTM 8% YTM 8% NPER = 10 NPER 5 PMT = 0 PMT 0 FV = 100 FV 100 PV =? PV Solve for PV Solve for PV PV = ($46.32) PV= ($68.06) (ii) (ii) 10-year zero 5-year Zero YTM 7% YTM 7% NPER = 10 NPER 5 PMT = 0 PMT 0 FV = 100 FV 100 PV =? PV Solve for PV Solve for PV PV = ($50.83) PV= ($71.30) 30-year zero' (i) YTM 8% NPER = 30 PMT = 0 FV = 100 PV =? Solve for PV PV = ($9.94) 30-year zero' (ii) YTM 7% NPER = 30 PMT = 0 FV = 100 PV =? Solve for PV PV = ($13.14) $100 perpetuity (i) Present value of Bonds = $100/YTM YTM 8% PV = 1250 (ii) Present value of Bonds = $100/YTM YTM 7% PV = 1428.571 Percentage change in the price of Bonds after the decline in rates. Price @ 8% Price @ 7% Percentage Change 10-year, 10% annual coupon 113.42 121.07 6.74% 10-year zero 46.32 50.83 9.74% 30-year zero 9.94 13.14 32.19% $100 perpetuity 1,250 1428.57 14.29% 5 year Zero 68.06 71.3 4.76%Related Questions
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