V = VAT e.g. 0.2 currently
A = Agency commission rate e.g. 0.15
How much the contractor invoices the agency including VAT?
X (1 + V) = 1.2X = £360
How much the agency invoices the client including VAT?
X (1 + A) (1 + V) = X (1.15)(1.2) = 1.38X = £414
How much the agency earns excluding VAT?
AX = 0.15X = £45
How much the agency earns including VAT?
AX (1 + V) = £54
A simple calculator should be developed for this to calculate with different rates quickly.