Question

Problems/Short Answer (Points as noted) 1. Use the table below for the questions that follow. Bond Duration A Coupon Rate 6 % Zero coupon Y ield 4.5% 6.25% Maturity 3 years 7 years B (a) Compute the duration of each bond, assuming annual interest payments for the coupon bonds. Show your work below. (4 points) (b) What is the duration predicted price change for each bond for a 1% increase in rates? Show your work below. (6 points) cash flows 2.5% CO ligo loco 126 1180

Answer 1

Part (a)

Bond A: Duration= 2.83695 Years.

Details as follows:

B F G A 1 2 Face Value 3 Coupon rate 4 Term (No. of years) 5 Frequency 6 YTM $1,000 6% Annual interest= B2*B3/F5 = $60.00 3 Annual No. of times a year (k) 4.50% Discount rate (r)= B6/F5 = 0.045 7 Total 8 Period (Half year) (0) 2 3 9 Interest $60.00 $60.00 $60.00 10 Redemption $1,000 11 Total cash flow (CF) $60.00 $60.00 $1,060.00 12 Present value 13 Formula CF/(1+r)^i CF/(1+r)^; CF/(1+r)^i 14 Cell reference B11/(1+F6)^BE C11/(1+F6)^C8 D11/(1+F6)^D8 15 value 57.41626794 54.94379707 928.8744003 16 17 Proportion of PV Cell ref B15/H15 C15/H15 D 15/H15 19 Value 0.055142497 0.052767939 0.892089564 20 21 Time*proprtion of PV 0.055142497 0.1055358792.676268692 22 Duration (Years) =G21/F5= 2.836947068 1041.23447 18 2.83694707

Bond B: For a zero coupon bond, duration is equal to term to maturity. Hence the duration of this bond is its term to maturity, ie., 7 years

Part (b)

Duration predicted price change for a 1% increase in rate is 1% decrease in price for every year of duration.

For Bond A, Duration= 2.83695 years. Hence for 1% increase in rate, price will decrease by 2.83695%

For Bond B, Duration =7 years. Therefore, for 1% increase in rate, price will decrease by 7%