The APV formula is the sum of the present value of cash flows and present value of tax shield, where Present value of cash flows and tax shield is calculated separately with a different formula. PV of cash Flow calculation involves cash flow, risk rate, asset beta, market return and risk rate. Product of tax rate and PV of tax shield.

Present Value of Tax Shield = Interest Expense * ( Debt Rate / Tax Rate )

Adjusted Present Value (APV) = PV of Cash Flows + Present Value of Tax Shield

The benefits of APV are tax shield from tax deduct-ability and borrowing at sub-market rates.