Adjusted Present Value (APV): Formula, Tax Shields and Debt Sizing

The APV formula

Discount unlevered free cash flow at the unlevered cost of capital, rᵤ. Add the value of debt-related tax savings separately. A complete economic APV may also include issuance costs, subsidies and expected distress costs; a tax-shield-only model is a simplification.

APV = Unlevered operating value + PV(tax shields) − PV(financing costs)
Tax shieldₜ = Deductible interestₜ × marginal tax rate

Which discount rate belongs to the tax shield?

Discounting tax shields at the cost of debt, r_d, is a common assumption for a predetermined debt schedule when the shield has debt-like risk. It is not universally correct: a debt policy linked to enterprise value makes future borrowing and shields depend on operating performance. State the debt policy, tax capacity and discount-rate assumptions together.

A company must have sufficient taxable profits and satisfy applicable interest-deduction rules to realize the modeled benefit. PIK interest treatment depends on tax law and instrument terms; a noncash accrual is not automatically an available cash tax saving.

Worked example: operating value plus financing benefits

Suppose unlevered operating value is $80m, annual deductible cash interest is $2m, the tax rate is 25%, and the cost of debt is 8%. Five end-of-year tax shields of $0.5m have a present value of approximately $2.0m. With no terminal financing benefit or other financing costs, APV is approximately $82.0m.

If debt amortizes, calculate each year’s actual interest and shield. Do not carry the first-year shield into perpetuity unless the continuing debt policy supports it.

Debt sizing creates a second dependency

If maximum debt is a percentage of APV, debt changes interest, interest changes tax shields and tax shields change APV. Solve consistently, check convergence and compare the resulting leverage with lender constraints. A mathematical solution is not a financing commitment.

APV versus DCF in diophos

diophos presents APV as unlevered firm value plus tax shields, with cash-interest-based tax benefits and a terminal shield assumption. Its debt cost comes from the debt schedule. Review terminal financing assumptions rather than treating the displayed value as a lender-approved price.

Do not add APV tax shields to an ordinary WACC-based DCF: the after-tax cost of debt already incorporates that financing benefit.