The Theoretical Foundations of APV and WACC: A Modern Interpretation of Modigliani-Miller Propositions

The rapid tightening of Hong Kong dollar liquidity — the HKMA’s Aggregate Balance stood at HKD 44.8 billion as of 30 September 2025, down from HKD 96.2 billion a year earlier — has forced a re-examination of corporate valuation frameworks. When the risk-free rate moves 150 basis points in 12 months and the HIBOR-OIS spread widens to 28 bps, the traditional preference for a single Weighted Average Cost of Capital (WACC) begins to fray. CFOs of Main Board issuers are increasingly finding that the Modigliani-Miller (MM) propositions, published in 1958 and 1963, provide not a static answer but a diagnostic toolkit. The Adjusted Present Value (APV) method, which separates the value of the unlevered firm from the tax shield of debt, offers a more transparent path when capital structure is expected to change materially. This is not an academic exercise. The HKEX’s 2024 consultation on Chapter 18C — which introduced specialist technology company listing rules — explicitly requires sponsors to justify valuation methodologies in the prospectus (HKEX, “Consultation Conclusions on Listing Regime for Specialist Technology Companies,” March 2024, para. 94). The choice between APV and WACC is now a disclosure risk.

The Modigliani-Miller Propositions: A Framework, Not a Formula

Proposition I: Capital Structure Irrelevance and Its Limits

The foundational insight of MM (1958) is that, in a world without taxes, bankruptcy costs, or asymmetric information, the market value of a firm is independent of its capital structure. The weighted average cost of capital remains constant regardless of the debt-to-equity ratio. For a Hong Kong-listed company with a market capitalisation of HKD 10 billion and debt of HKD 4 billion, MM Proposition I states that the total enterprise value of HKD 14 billion would be identical if the firm were entirely equity-financed.

This proposition holds only under strict assumptions that do not survive contact with the HKMA’s countercyclical capital buffer regime or the SFC’s Code on Takeovers and Mergers. The SFC’s Takeovers Code (SFC, “The Codes on Takeovers and Mergers and Share Buy-backs,” 2024 edition, General Principle 2) requires that all shareholders be treated equally, which introduces frictions when debt restructuring alters control rights. In practice, the irrelevance theorem serves as a null hypothesis. When a CFO observes that a change in leverage has changed firm value, the question becomes: which MM assumption has been violated?

Proposition II: The Cost of Equity and Leverage

MM Proposition II states that the cost of equity rises linearly with leverage. The relationship is:

( r_E = r_U + (D/E)(r_U - r_D) )

Where ( r_E ) is the cost of equity, ( r_U ) is the cost of capital for an unlevered firm, ( r_D ) is the cost of debt, and ( D/E ) is the debt-to-equity ratio.

For a Hong Kong property developer with a debt-to-equity ratio of 1.5x, an unlevered cost of capital of 8.5%, and a pre-tax cost of debt of 5.2%, the implied cost of equity is 13.45%. This calculation is sensitive to the tax treatment of interest. Under the Inland Revenue Ordinance (Cap. 112, s. 16(1)), interest expenses are deductible only if the borrowing is for the production of chargeable profits. A holding company with a BVI intermediate and a Hong Kong operating subsidiary must structure its intra-group debt carefully to preserve the tax shield — a nuance that the simple MM formula does not capture.

The 1963 Correction: Corporate Taxes Change Everything

MM (1963) introduced corporate taxes, demonstrating that the tax deductibility of interest payments creates a value subsidy. The value of the levered firm equals the value of the unlevered firm plus the present value of the tax shield. For a firm paying the Hong Kong profits tax rate of 16.5% (Inland Revenue Ordinance, Cap. 112, s. 14), with perpetual debt of HKD 2 billion at a 5% coupon, the annual tax shield is HKD 16.5 million. Discounted at the cost of debt, the present value of this perpetual shield is HKD 330 million.

This is where the APV and WACC methods diverge. WACC incorporates the tax shield into the discount rate by using an after-tax cost of debt. APV values the tax shield separately. The choice between them depends on whether the firm’s debt policy is fixed in dollar terms (APV) or as a target ratio (WACC).

APV: The Structural Choice for Changing Capital Structures

The Mechanics of Adjusted Present Value

The APV method, formalised by Stewart Myers in 1974, values a project or firm in two steps. First, calculate the present value of the unlevered cash flows, discounted at the unlevered cost of capital. Second, add the present value of the financing side effects — primarily the tax shield of debt, but also the costs of financial distress, issuance costs, and any subsidies.

For a Hong Kong-listed biotech company raising HKD 500 million in a Series B round and planning an IPO under Chapter 18C within 24 months, the capital structure will change from predominantly equity to a mix of equity and debt post-listing. APV handles this naturally. The analyst can model the tax shield only for the period when debt is outstanding, and discount it at a rate appropriate to its risk — typically the cost of debt, not the WACC.

Tax Shield Valuation: Perpetuity vs. Finite Horizon

The classic MM formula assumes perpetual debt. In Hong Kong, where most corporate debt is issued with 3-to-7 year tenors (HKMA, “Hong Kong Debt Market Review 2024,” Table 3.1), the finite horizon matters. For a HKD 1 billion bond issued at 4.8% for 5 years, the annual tax shield is HKD 7.92 million (HKD 1 billion × 4.8% × 16.5%). The present value of these five annual shields, discounted at 4.8%, is HKD 34.4 million — versus HKD 165 million under the perpetual assumption.

This gap of HKD 130.6 million represents a material overvaluation if the analyst uses the perpetual formula without adjustment. The HKEX’s Listing Rule 11.07 requires that valuation reports in circulars disclose all material assumptions. A perpetuity assumption for a 5-year bond would fail this test.

Financial Distress Costs: The Missing Term

APV allows explicit modelling of distress costs, which WACC buries in the discount rate. Empirical work by Almeida and Philippon (2007) estimates that distress costs range from 10% to 23% of firm value. For a Hong Kong-listed real estate investment trust (REIT) with a loan-to-value ratio of 45% and a weighted average debt maturity of 3.2 years, the probability of distress — defined as a covenant breach — can be estimated from the HKMA’s residential mortgage delinquency data, which stood at 0.08% in Q2 2025 (HKMA, “Monthly Statistical Bulletin,” September 2025, Table 4.1). Even a 0.5% probability of distress, with a 15% loss given distress, reduces firm value by 7.5 basis points — small, but not negligible for a HKD 20 billion portfolio.

WACC: The Standard Tool and Its Hidden Assumptions

The Standard WACC Formula

The textbook WACC formula is:

( WACC = (E/V) \times r_E + (D/V) \times r_D \times (1 - T_C) )

Where ( E ) is equity value, ( D ) is debt value, ( V = E + D ), and ( T_C ) is the corporate tax rate.

For a Hong Kong utility with HKD 5 billion in equity and HKD 3 billion in debt, an equity cost of 9.2%, a pre-tax debt cost of 4.5%, and a tax rate of 16.5%, the WACC is 6.98%. This single number is then used to discount all future cash flows, regardless of the year in which they occur.

The Circularity Problem

WACC requires the market values of equity and debt as inputs, but these values are themselves the output of the valuation. This circularity is manageable for a stable, publicly traded firm with a constant debt-to-value ratio. For a private company or a firm undergoing a leveraged buyout, it is not. The analyst must iterate: estimate equity value, compute WACC, discount cash flows, and re-estimate equity value until convergence.

The SFC’s “Guidelines for the Valuation of Private Companies” (SFC, March 2023, para. 3.2.4) explicitly warns against using WACC without adjusting for the capital structure at the valuation date. A sponsor who uses the target capital structure of 30% debt without verifying that the current structure is 10% debt is misrepresenting the discount rate.

The Constant Leverage Assumption

WACC assumes the firm maintains a constant debt-to-value ratio over the projection period. For a Hong Kong-listed company that plans to deleverage from 40% debt to 20% over five years, the WACC will change each year as the equity cost adjusts under MM Proposition II. Using a single WACC overstates the value of the tax shield in the early years and understates it in the later years.

The magnitude of this error can be estimated. For a firm with an unlevered cost of capital of 10%, a debt cost of 5%, and a tax rate of 16.5%, the WACC at 40% debt is 8.23%. At 20% debt, it is 9.02%. Discounting a HKD 100 million annual cash flow stream for five years at 8.23% yields HKD 396.8 million. Discounting the same stream at the year-specific WACC yields HKD 393.1 million — a difference of HKD 3.7 million, or 0.9% of the value. This is not large, but in a competitive IPO book-building process where pricing is set to the nearest HKD 0.10 per share, it matters.

Choosing Between APV and WACC: A Decision Framework

When APV Dominates

APV is superior in three situations. First, when the capital structure is expected to change significantly — a leveraged buyout, a deleveraging plan, or a project financed with a specific debt facility. Second, when the tax shield is risky — for example, a company with volatile earnings that may not generate sufficient taxable profits to utilise the interest deduction. Under the Inland Revenue Ordinance (Cap. 112, s. 61A), the Commissioner can disallow interest deductions if the arrangement is tax-avoidance motivated. APV allows the analyst to discount the tax shield at a rate reflecting this risk.

Third, when the financing side effects are complex — including government subsidies, issuance costs, or the value of debt guarantees. The Hong Kong Mortgage Corporation’s guarantee programme for small and medium enterprises, which covers up to 80% of loan principal, creates a financing subsidy that APV can value explicitly.

When WACC Remains Appropriate

WACC is appropriate for firms with a stable target capital structure and a long history of maintaining that structure. A Hong Kong-listed integrated utility with a 25% debt-to-total-capital ratio for the past decade, and no plan to change it, can be valued with WACC without material error. The cost of the additional complexity in APV — estimating the unlevered cost of capital, modelling the tax shield separately — exceeds the benefit.

The choice also depends on the audience. For a prospectus filed under HKEX Listing Rule 11.07, where the sponsor must disclose the valuation methodology and all material assumptions, APV provides a clearer audit trail. The regulator can verify the unlevered cash flows, the tax shield calculation, and the distress cost assumption independently. WACC, being a single blended number, obscures these components.

The Practical Test: A Hong Kong Case Study

Consider a Hong Kong-listed retailer with HKD 2 billion in revenue, HKD 300 million in EBITDA, and HKD 800 million in debt at 5.5%. The company plans to reduce debt to HKD 400 million over three years. The unlevered cost of capital is 9.5%, and the tax rate is 16.5%.

Under WACC, using the average debt-to-value ratio of 25%, the WACC is 8.67%. The enterprise value, discounting five years of unlevered free cash flow at HKD 180 million per year and a terminal value of HKD 2.5 billion, is HKD 2.47 billion.

Under APV, the unlevered value is HKD 2.23 billion. The tax shield in year one is HKD 7.26 million (HKD 800 million × 5.5% × 16.5%), declining to HKD 3.63 million in year three. The present value of these shields, discounted at 5.5%, is HKD 14.2 million. The total APV is HKD 2.24 billion — HKD 230 million lower than the WACC value.

The difference arises because WACC assumes the tax shield is as risky as the firm’s assets, while APV discounts it at the debt cost. The WACC value is overstated by 9.3%. For a CFO presenting to a board that must approve a HKD 400 million debt repayment plan, the APV number is more conservative and more defensible.

Closing: Three Actionable Takeaways for Corporate Finance Practitioners

1. Use APV for any valuation where the debt-to-equity ratio is expected to change by more than 10 percentage points over the projection period, as the single-WACC error exceeds 1% of enterprise value in such cases.
2. Verify that the tax shield discount rate matches the risk of the interest deduction being realised — use the cost of debt for low-risk shields and the unlevered cost of capital for shields dependent on volatile earnings.
3. Disclose the choice between APV and WACC in all valuation reports submitted to the HKEX or SFC, with a sensitivity table showing the impact of the tax shield assumption on the final equity value.