When valuing an organization, it’s easy to make mistakes if you approach the calculation of Cost of Equity and WACC superficially — because intrinsic value is highly sensitive to these parameters.

In practice, the Unlever & Re-lever procedure is typically based on the following general formula derived from Modigliani–Miller (M&M) Proposition II with Taxes:

However, depending on the specific characteristics of the case, this formula — and consequently the valuation result — can deviate significantly from reality.

🔁 Why do we Unlever and Re-lever?

The purpose of unlevering and relevering — whether for the cost of capital or beta — is to derive a discount rate that accurately reflects the business reality.
Even if we’re valuing a publicly traded company with a published beta, the procedure is still necessary, because the company’s current capital structure may not be optimal and is expected to change.

⚠️ What modifies the general formula?

The key factor that modifies the formula above is how we choose the discount rate for the Interest Tax Shield (ITS).

When using the APV method, we need to discount the tax shield component separately, and this requires selecting an appropriate discount rate.

  • In some cases, the correct rate is the cost of debt (CoD).
  • In others, it’s the unlevered cost of capital (UCoC).
  • And in some situations, it lies somewhere in between.

Even when using the WACC method instead of APV to discount future cash flows, the choice of the ITS discount rate still affects the Cost of Equity, and thus WACC itself.

Here’s the key idea:
If the discount rate for ITS is lower than the unlevered cost of capital, then part of the risk effect introduced by financial leverage on the cost of equity is offset by the value of the tax shield (reflected in the last term of the general formula).

🧠 What determines the discount rate for ITS?

  1. If the absolute amount of debt is relatively insensitive to the company’s operating risk — e.g., the firm holds very little debt or is not growing — then the tax shield behaves more like a low-risk obligation.
    ✅ In this case, ITS should be discounted at the cost of debt (CoD).
  2. If the amount of debt is naturally tied to the company’s asset value, either due to policy or growth dynamics, the ITS becomes riskier and varies with business performance.
    ✅ In this case, the appropriate discount rate is the unlevered cost of capital (UCoC).
  3. To avoid the extremes above, debt can be split into two parts — a stable minimum amount and a growth-linked portion — and the corresponding tax shields can be discounted at different rates.
  4. Even when the company refinances debt to maintain a target capital structure, in reality, this doesn’t happen continuously.
    Typically, D/E is adjusted annually.
    ✅ As such, the tax shield for the first year may be discounted at the cost of debt, and the rest at the unlevered cost of capital.

📐 4 Specific Formulas

Below are four variations of the general cost of equity formula, depending on the assumption we make about the risk of the tax shield (ITS).

🎯 The Moment of Truth Regarding WACC:

The general WACC formula assumes that the ITS is discounted at the cost of debt — yet WACC is exactly what we use when assuming a constant debt-to-value ratio over time.

But if that’s the case, then the tax shield is risky (because D varies with firm value), and discounting it at the cost of debt becomes a contradiction.

So, if the ITS is a material component of firm value — which it usually is — using the standard WACC formula introduces a valuation error.

Here, we present four modified WACC formulas, each adapted to one of the four tax shield risk scenarios described above.

➕ The Same Logic Applies to Beta

The same insights and assumptions carry over to unlevering and relevering beta, where the treatment of tax shield risk directly affects the levered beta result.

Source:
Corporate Valuation: Theory, Evidence and Practice
Mark E. Zmijewski; Robert W. Holthausen, Second Edition