please answer all parts

Part 1: Problems: Reminder: For problems, be sure to show your work below to receive credit for problems). If you use a financial calculator, please list the steps you used. Module 1: Valuation and Interest Rates and Duration as a Measure of Int. Rate Risk (Chapter 3 of M& E Text; also see lecture notes & review problems) 1. You have a 4 year investment holding horizon, would like to earn a 4% annual compound return each year; you have a choice between two bonds. Whatever money you have to invest will be invested in one type of bond or another. Find the Duration and Modified Duration for each bond (show your work and answer the questions below) Bond 1 has a 4% annual coupon rate, S1000 maturity value, n = 4 years, YTM = 4% (pays a $40 annual coupon at the end of each year for each of the 4 years and $1,000 maturity payment at the end of year 4). Bond 2 is a zero coupon bond with a $1000 maturity value, and n = 4 years; YTM=4%. (pays no coupons; only a $1,000 maturity payment at the end of year 4) a. Price Bond 1_$999.24 Price Bond 2 $854 Interest rate or coupon rate of Bond A=4% Price of Bond 1: n 4 years Yield to maturity =4% Maturity value=S1000 Interest amount Interest rate*Maturity value -4%*$1000 -$40 Price of Bond 1=$40/(1+0.04) 1+$40/(1+0,047 24840/(1+0,04) 3+ (540+$1000)/(1+0.0474 (40/(1.04) 1)-(40/(1.0472)+(40/(1.04) 341040/(1-04Y 4) ={40*0.962)+(40*0.925)+(40*0.890)-1040*0.854) =$38.48+$37+$35.6+$888.16 -$999.24 Price of bond 2: Here Maturity value $1000 Yield to maturity=4% n is the number of years 4 years By substituting the values: Price of Zero-coupon Bond 2-S1000/(1+0.0474 -S1000/1.0414 =S1000*0.854 =$854 b. Duration Bond 1 -4 yearsw _3.78 years Duration Bond 2 Duration of Bondi=1/5999.24 [1*40/(1+0.04) 1+2*40/(1+0.04Y2+3*40/(1+0.04) 3+4* (540+$1000)/(1+0.0474 =(1/8999.24)*[40*0.962+80*0.925+120*0.890+4160*0.855 =(1/$999.24)*[38.48+74+106.8+3556.8] = (1/5999.24)*3776.08 =3.778 or 3.78 years. duration of zero-coupon bond: duration of a zero-coupon bond maturity years= 4 years. c. Modified Duration Bond 1 _3.63 years Modified Duration Bond 2 3.84 years duration of a zero-coupon bond-maturity years 4 years. c. Modified Duration Bond 1 _3.63 years Modified Duration Bond 2 3.84 years (Be sure to show your work for the bond price and duration calculations for credit). Modified Duration of Bond 1=Duration of Bond/(1+YTM) YTM -4% =3.78/(1+0.04) =3.78/(1.04) -3.63 years Modified duration of bond 2: = Duration of Bond/(1+YTM) duration of a zero-coupon bond is 4 years and YTM is 4% =4/(1+0.04) -4/1.04 -3.84 years d. Which of the two bonds should you choose for your 4- year investment horizon to duration match to ensure your desired 4% annual compound yield if you hold the bond to maturity? Explain why. (assume the same default risk for each bond). Bond 2 should be chosen because the price is less e. If interest rates go up by 2%, what will be the % Change in the market value for each Bond's Price? (Hint Change in Price%=- Modified Duration x Change in Rate (expressed as a fraction, i.e..02). f. Which of the 2 bonds has more price risk and which has more reinvestment risk? Explain why