Optimal Capital Structure

Find the debt ratio that minimizes WACC from a given schedule.

Problem Scenario

At 0% debt: Re=11%, Rd=5%. At 30% debt: Re=12%, Rd=5.5%. At 50% debt: Re=14%, Rd=7%. At 70% debt: Re=18%, Rd=10%. Tax=25%.

Given Data

0% debtRe=11%, Rd=5%

30% debtRe=12%, Rd=5.5%

50% debtRe=14%, Rd=7%

70% debtRe=18%, Rd=10%

Tax rate25%

Requirements

Calculate WACC at each level
Identify the optimal structure

Solution

Step 1:

0%: WACC = 1.0×0.11 = 11.00%.

Step 2:

30%: WACC = 0.70×0.12 + 0.30×0.055×0.75 = 8.4% + 1.24% = 9.64%.

Step 3:

50%: WACC = 0.50×0.14 + 0.50×0.07×0.75 = 7.0% + 2.625% = 9.625%.

Step 4:

70%: WACC = 0.30×0.18 + 0.70×0.10×0.75 = 5.4% + 5.25% = 10.65%.

Final Answer

Minimum WACC at 50% debt (9.625%). This is the optimal capital structure.

Key Takeaways

✓Too little debt misses the tax shield
✓Too much debt raises both Re and Rd

Common Errors to Avoid

✗Forgetting to tax-adjust the cost of debt
✗Not testing all levels

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FAQs

Common questions about this problem type

Yes. It shifts with interest rates, tax law changes, and firm risk profile.

More debt means equity holders face higher financial risk because debt payments must be made first. Shareholders demand a higher return to compensate for this increased risk, which is exactly what MM Proposition II predicts.