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Adjusted present value

Value operations on an all-equity basis and separately price the tax savings and costs of a financing plan.

Adjusted present value (APV) values a business or project as if it were financed entirely with equity, then adds the present value of the benefits and subtracts the present value of the costs of its actual financing plan. In a buyout with scheduled debt repayments, this separates what the business earns from what the borrowing plan contributes as the debt balance falls. Myers, 1974, §V · Jenter, slides 23–28

Start with the business, then price the financing

  1. Value the operations. Forecast free cash flow to the firm after operating taxes and reinvestment, before interest and principal flows. Compute taxes for this baseline without the interest deduction. Discount at the unlevered cost of capital, which reflects the risk of the operating cash flows. For a new project, deduct the initial investment to get the unlevered net present value. Jenter, slides 23–25
  2. Value the tax savings. Use the planned debt balances and interest payments to forecast the interest tax shield when it actually reduces cash taxes. Discount it for its own risk. A predetermined debt schedule with reliable deductions can make that saving relatively predictable. If the firm resets debt to a share of market value, future interest deductions also move with the business. Myers, 1974, §V
  3. Value the other financing effects. Subtract incremental issuance fees and any expected financial distress costs that the operating forecast has yet to capture. For example, if a funding shortfall forces a firm to abandon a profitable investment, the lost value belongs in the comparison of financing plans. Value uncertain costs in the states and periods where they arise. Damodaran, Estimating Expected Bankruptcy Costs and Net Effect · Why Manage Financial Risk? §2.4, full lesson for members

When does the borrowing add value?

A fictional company has an unlevered operating value of USD 100 million. It plans to hold USD 32 million of debt outstanding indefinitely, with interest of 5% paid at each year-end and a net upfront issuance cost of USD 3 million. Assume the company uses the full interest deduction to reduce cash taxes at each year-end at a 25% marginal rate, and the resulting annual saving of USD 0.40 million is discounted at a stipulated 5% annual effective rate. The level saving is worth USD 8 million today. Assume the issuance fee is the only other financing effect. All three values are in USD millions at the valuation date.

APV=100+8−3=105.\mathrm{APV} = 100 + 8 - 3 = 105.

Now suppose the company can use only a quarter of each year's deduction, with no later recovery. Holding the other inputs fixed, the shield is worth USD 2 million and APV is USD 99 million. The break-even tax shield is worth exactly enough to cover the issuance fee.

In the fictional case, a tax shield worth USD 2 million gives an APV of USD 99 million. At USD 3 million the shield just offsets financing costs and APV equals the USD 100 million unlevered value. At USD 8 million APV is USD 105 million.
In the fictional case, a tax shield worth USD 2 million gives an APV of USD 99 million. At USD 3 million the shield just offsets financing costs and APV equals the USD 100 million unlevered value. At USD 8 million APV is USD 105 million.
With financing costs fixed at USD 3 million, the plan adds value only when the tax shield is worth more than USD 3 million.

Reconcile APV with WACC

The after-tax weighted average cost of capital can incorporate the interest tax shield through its debt-cost term. Adding the same shield to an operating value already discounted at that rate counts the saving twice. APV starts with the unlevered rate. A WACC valuation can use period-specific rates if market-value financing weights and required returns change materially. Compare the methods on the same debt policy, tax capacity, risk and other financing effects. The APV above values the financed business as a whole. To reach common equity value, account for debt and other senior claims in the equity bridge. Damodaran, Cost of Capital versus APV Valuation · Jenter, slides 11 and 29
Capital cash flow valuation instead combines operating cash flows and tax shields before discounting when a common rate fits their joint risk.

Sources

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  • corporate finance
  • valuation
  • capital structure
  • tax shields
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