Question

3. An investment pays 2000 in three years and 4000 at the end of the fourth year. If it was purchased to yield an annual rate of 7.5%, what would be the modified duration? A) 3.35 B) 3.40 C) 3.50 D) 3.65 E) 3.70

Answer 1

F 149 150 Annual Yield (YTM) 7.50% 151 152 | 153 Year 1 2 154 155 Cashflow puf @ 7.5% time weight O 0.930232558 1 O 0.8653326122 2000 0.80496057 4000 0.74880053 Total PV of time-weighted cashflows A] PV of time-weighted cashflows 0 0 4829.763417 11980.80848 16810.57189 4 156 157 Initial Investment [B] 4605.123258 158 159 160 161 162 MACAULAY DURATION [C] = [A]/[B] 3.650406504 163 MODIFIED DURATION [C] / (1+YTM) 3.40

time weight B 149 CALCULATIONS 150 Annual Yield (YTM) 0.075 151 152 Year Cashflow pvf @ 7.5% 153 =1/(1.075)^B153 1 154 =1/(1.075)^B154 2 155 2000 =1/(1.075)^B155 3 156 4000 =1/(1.075)^B156 157 Total PV of time-weighted cashflows [A] 158 159 Initial Investment [B] PV of time-weighted cashflows =C153*D153*E153 =C154%D154*E154 =C155*D155*E155 =C156*D156*E156 =SUM(F153:F156) 13 = (C155*D155)+(C156*D156) 160 MACAULAY DURATION [C] = [A] / [B] =F157/F159 161 162 MODIFIED DURATION [C] / (1+YTM) =F161/(1+C150)