Volume 4, Reading 28, Question 9 in CFA Materials solution, really

Swanand

Does anyone have any clue how they got the answer to be 5,072,000. I read the solution and I am still unsure what they were really doing.

homie

The original bonds par value were worth $10.0MM, however their value today would be worth $10.0MM x 100.40625 /100 = $10,040,625
The dollar duration on these bonds is worth:
$10,040,625 x 4.53 / 100 = $454,840.32
The question wants us to calculate the amount of 10yr bonds that would result in our dollar duration staying the same. So we work backwards…
The total $ amount of the new bonds that we would need to purchase would be:
$454,840.32 = P x 8.22 / 100
P = $454,840.32/.0822 = $5,533,337.14
Remember, however, that this is the current price and the question is asking for the par value. So we need to take the total investment amount and divide it by the premium:
$5,533,337.14/1.0909375 = $5072,093.62
Hope this helps,
TheChad