A manager wishes to hedge a bond position with a principal of $75 million by selling Treasury bond futures. Suppose that (1) the conversion factor for the cheapest-to-deliver issue is 0.90, (2) the price value of a basis point of the cheapest-to-deliver issue is $0.1335 per $100 of principal, and (3) the modified duration of the bond to be hedged is 12.5. The market price (per $100 of principal) of the cheapest to deliver is $98 while the market price (per $100 of principal) of the bond to be hedged is $101. Finally, the beta of the regression of the yield changes on the bond to be hedged against the yield changes of the CTD bond is equal to 0.95. Answer the below questions.

a) What is the modified duration of the cheapest to deliver bond?

b) What is the price value of a basis point of the cheapest to deliver bond per $10000 of principal?

c) What is the price value of a basis point of the bond to be hedged per $10000 of principal?