Wing Hang Bank has EBIT of $500m and no growth. It has a cost of equity of 20%. It is currently 100% equity funded. It has an optimal capital structure of 50% debt (at 5% after-tax cost) and 50% equity (at 20% cost). What is the standalone value of Wing Hang? What is the value of control?

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BlackTom AI · Accepted Answer

First, restate the question to anchor the discussion: Wing Hang Bank has EBIT of 500m with no growth, cost of equity is 20%, currently 100% equity financed. The optimal capital structure is 50% debt (after-tax cost 5%) and 50% equity (cost of 20%). We are asked for the standalone value of Wing Hang and the value of control.

Option-by-option analysis:

Option 1: "$2,500m; $1,500m"
- Standalone value 2,500m: When a firm has no growth and is currently all-equity financed, a common approach is to value the firm using the unlevered cost of equity as the discount rate. With EBIT of 500m and cost of equity 20%, the value equals 500 / 0.20 = 2,500m. This aligns with the idea that the firm’s value at the unlevered cost of capital is 2,500m.
- Value of control 1,500m: If the levered value (under the 50/50 target structure) exceeds the standalone value, the difference is often interpreted as the value created by the levered capital structure (including tax shields). A 1,500m control value implies a levered firm value of 4,000m and thus an incremental 1,500m from leverage. To reach 4,000m from an unlevered base of 2,500m, the PV of the tax shield must be 1,500m. This would require a sufficient tax shield given the debt level (50% of firm value) and the tax rate implied by the after-tax debt cost. While plausible, it hinges on the implied tax rate and the perpetuity assumptions; the calculation details (e.g., the exact tax rate that makes PV of the tax shield equal 1,500m when D = 0.5V) are not given explicitly here.

Option 2: "$2,500m; 30%"
- Standalone value 2,500m is as above, but the second part asks for a control value of 30% (which would imply levered value of 3,250m if the equity value is the base). That would require a PV of tax shields of 750m. Whether this aligns with the 50% debt and 5% after-tax cost depends on the tax rate; a 30% control premium seems inconsistent with the straightforward tax shield calculation under the given 50/50 target, unless a specific tax rate yields exactly 750m of tax shields. Without explicit tax-rate data, this option introduces an incongruent figure relative to the stated after-tax debt cost.

Option 3: "$4,000m; $2,000m"
- Standalone value 4,000m: This would imply a levered value of 4,000m even before considering the tax shield, which contradicts the standard approach where the unlevered value is 2,500m and leverage adds value via tax shields. With no growth and the given EBIT, jumping to 4,000m as the base standalone figure is inconsistent with the basic calculation (unless a large, explicit tax shield is assumed). Therefore, this seems unlikely given the problem setup.
- Value of control 2,000m: If true levered value were 4,000m, the control value would be 1,500m more than the standalone base of 2,500m; here it’s stated as 2,000m, which again doesn’t align with the straightforward interpretation of the tax-shield-driven levered value.

Option 4: "$4,000m; 20%"
- Standalone value 4,000m: As with Option 3, setting the standalone value at 4,000m conflicts with the very first calculation (2,500m) derived from EBIT and unlevered cost of capital. Without a growth assumption or different EBIT, this contradicts the basic unlevered valuation.
- Value of control 20%: A 20% figure for the control value is also unusual given a 50/50 target capital structure; the control premium (or the levered benefit) would typically reflect the tax shield, not simply an identical percentage to the equity cost. This option thus appears internally inconsistent with the information provided.

Synthesis across options:
- The standalone value of 2,500m emerges directly from the no-growth EBIT and the unlevered cost of equity (500 / 0.20). None of the other standalone values (4,000m) align with the basic unlevered valuation under the stated assumptions, making them less plausible unless additional growth or different EBIT were specified.
- The value of control depends on the tax shield created by debt in the levered structure. The problem states a 50% debt target with an after-tax debt cost of 5%, which signals a nontrivial tax shield contribution. The exact control value (whether 1,500m or another figure) hinges on the implicit tax rate that yields the PV of tax shields needed to reach the levered value. Since the question provides only the after-tax cost and the debt fraction, the clean, conventional result would be to add the PV of the tax shield to the unlevered value to obtain the levered (total) value, and then subtract the initial baseline to obtain the value attributed to financing (the control value).

Note on consistency and interpretation:
- If we take the unlevered value as 2,500m and suppose the levered value ends up at 4,000m (to reflect a substantial tax shield from debt), the PV of the tax shield would be 1,500m, implying a debt-based uplift of 1,500m. This aligns with the idea that leverage creates value via tax shields, but the exact calculation requires the tax rate or the explicit PV shield figure. The simplest, commonly cited pairing under these numbers is 2,500m standalone and a 1,500m control premium (option 1).

Conclusion through option-by-option reasoning: evaluating the above, option 1 presents a coherent standalone value given EBIT and no growth, and a plausible control value derived from the levered structure via tax shields, whereas the other options introduce inconsistencies with the basic valuation framework or rely on unexplained tax-rate implications. Therefore, option 1 appears to be the most consistent choice given the data and typical interpretation of standalone value and control value in a levered structure.

Wing Hang Bank has EBIT of $500m and no growth. It has a cost of equity of 20%. It is currently 100% equity funded. It has an optimal capital structure of 50% debt (at 5% after-tax cost) and 50% equity (at 20% cost). What is the standalone value of Wing Hang? What is the value of control?

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