Question

Problem #5: A 10-year bond has face value (redemption value) $250,000 and quarterly coupons of 390 Consider the time righi after the 12th coupon has been paid, when the yield is 4.4%. (a) What is the price of the bond? (b) Compute the price of the bond if the yield were to increase by 1 basis point (a basis point is l/100 of i%) What is the absolute value of the difference between that price, and your answer to part a)? (c) Would the yield have to increase or decrease in order for the bond to increase in value by $713.54? (d) Based only on your answer to b), approximately how many basis points (bp) would the yield have to move in order for the bond to increase in value by $713.54? Answer as a positive integer.) Problem #5(a) Answer correct to 2 decimals. Problem #5(b) Answer correct to 2 decimals. (A) Decrease (B) Increase Problem #5(c): Select Problem #5(d) Answer as a positive integer

Answer 1

Part-a Part-(b) Yield @ 4.4% Yield @ 5.4% Reqirement-a)& (b) 1.496 [4.496/4; 5.4%/4] Quarterly Yield-to-Maturity, RATE Number of quarters to maturity, NPER Quarterly coupon payments, PMT Bond's maturity value, FV Quarterly compounding type, TYPE Bond's current market price 1.1% 28 28 (10 years x 4)-12 quarters $1,875 $1,875 I$250,000 x 3%/4; Coupon payments are payable on bond's par value onlyl $250,000 $250,000 0 00 if coupon payments occur at the end of each quarter; 1 if coupon payments occur at the beginning of each quarter 229,012.11 $215,218.39 [Ref: NOTE-1] Absalute value of the difference between the price_$13,793.72 1$229,012.11- $215,218.39] NOTE-1: Bond's current market price is calculated using EXCEL FUNCTION PV rate,nper,pmt,f type) where rate=1.1% or 1.4% as applicable); nper-28; pmt=-1875; fv-250000, type-o Here, values for both pmt and fv are input as negative figures as they denote cash inflows, type = 0 because coupon payments are receivable at the end of each quarter only

28 NOTE-2 Number of Quarters left to maturity, NPER [(10 years x 4) - 12 quarters] Quarterly coupon Payment, PMT IS250,000 x 3%/4 Bond's current selling price, PV ($229,012.11+$713.54] Bond's maturity value receivable at the end, FV Quarterly compounding type, TYPE Bond's Quarterly Yield to Maturity [Ref: NOTE-2] Number of Quarters in a year Bond's revised annual yield to maturity $1,875 $229,725.65 Bond's Quarterly Yield to Maturity is calculated using EXCEL FUNCTION RATE(nper,pmt,pv,fv,type) $250,000 0 1.09% per-28; pmt -1875; pv-229725.65; fv-250000; type-0. Here, value for pmt is input as negative figure as it denotes cash inflow; Value for fv is also negative because it denotes cash inflow; type-0 because coupon payments are receivable at the end of each quarter only. 4.3596 [1.2196 x4] It is evident from the above calculation that bond's yield must be DECREASED from 4.4% to 4.35% in order to increase bond's value by $713.54. Requirement-d Bond's initial annual yield rate Bond's revised annual yield to maturity Move in yield rate 4.40% 4.356 [As calculated in Requirement-(c)] 0.05% Therefore, Move in yield rate, in basis points 0.05 [0.0596 x 100]