6. A portfolio manager owns $6 million par value of bond ABC. The bond is trading at 80 and has a modified duration of 7. The portfolio manager is considering swapping out of bond ABC and into bond XYZ. The price of this bond is 75 and it has a modified duration of 3.5.

(a) What is the dollar duration of bond ABC per 100-basis-point change in yield?

(b) What is the dollar duration for the $5 million position of bond ABC?

(c) How much in market value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC?

please show calculations and formulas