Sorry but i didn't get your questions.At one point you are saying many rates are used and on other side you had mention only two rates.
Any way, i am trying solve this problem with an assumption that you have the problem with using borrowing rate or discount rate in calculating present value of leasing.
During my Group 3 exam, even i was confused with this and i had made a shortcut to solve this problem. Though i was not cleared with this but i hope this short cut will help you.
Cost of Capital Rate is taken as discounting rate for discounting the Present value of tax shield,Deprecation ,salvaged value etc...
Further, here it is important to note two thing:
1) If borrowing rate is given then you must use the borrowing rate as a discounting rate, only to calculate the PV of lease rental. Whereas for other calculation cost of capital is used.
In simple term Borrowing rate is used for calculating the Present value of Lease rental only.
2) If cost of capital or discounting rate is not mentioned in the problem then you can use the borrowing rate after tax
Please note borrowing rate AFTER TAX.
So borrowing rate is for PV of lease rental and cost of capital and discounting rate is for other.
Modify the above shortcut as per your needs.
Now, the real logic behind this??
Please go through below snapshot of IM Pandey book.This image will answer all your query.
At last, if you still having a problem or if i did not understand your problem properly then feel free to leave a comment here.