Worked Solution
✓ VerifiedNote on Question Completeness: The question refers to 'the given weighted average cost of all of 8%' and a case scenario for ABC Manufacturing Limited, but the supporting data table (showing various debt-equity ratios with corresponding costs of debt and equity) has not been provided in the question text. The solution below demonstrates the standard methodology a CA student must apply once that data is available.
Concept: Optimal Capital Structure
The optimal debt-equity composition is the combination at which the Weighted Average Cost of Capital (WACC) is minimised (or equals a target rate, here 8%). Beyond this point, increasing debt raises financial risk, pushing up both cost of equity (Ke) and cost of debt (Kd), thereby increasing WACC.
Formula for WACC:
WACC = Kd × [D/(D+E)] × (1 – t) + Ke × [E/(D+E)]
Where: Kd = pre-tax cost of debt, Ke = cost of equity, D = market value of debt, E = market value of equity, t = corporate tax rate.
Step-by-Step Approach to Identify Optimal Composition:
Step 1 – Tabulate data: List each debt-equity ratio option along with the given Kd (post-tax) and Ke for that level of financial risk.
Step 2 – Compute weights: For each option, calculate the proportion of debt [D/(D+E)] and equity [E/(D+E)].
Step 3 – Calculate WACC: Apply the WACC formula for each combination.
Step 4 – Identify target WACC: Locate the debt-equity ratio at which the computed WACC equals 8%. That ratio represents the optimal capital structure.
Step 5 – State conclusion: The optimal composition is the specific Debt : Equity ratio (e.g., 40:60 or 1:1.5) at which WACC = 8%. If two ratios yield WACC close to 8%, the one that also results in the lower WACC is preferred (minimisation principle).
Important Principle: As per the Traditional Theory of Capital Structure, there exists an optimal point where the firm's overall cost of capital is lowest and market value is highest. The firm should target this composition.
Final Answer: To determine the exact optimal debt-equity ratio, the data table (various D/E combinations with corresponding Kd and Ke) from the original case must be applied to the WACC formula as shown above. The ratio yielding WACC = 8% is the optimal debt-equity composition for ABC Manufacturing Limited.
Write it like this
1The skeleton
- Start with the WACC formula on line 1 — write WACC = Kd(1–t)×[D/(D+E)] + Ke×[E/(D+E)] before anything else, because examiners tick the formula box first and it signals you know the structure.
- Set up a table with columns: D:E ratio | Kd (post-tax) | Ke | Weight of D | Weight of E | WACC — tabular format gets full presentation marks; prose calculations get half.
- Compute WACC row-by-row and circle/bold the row where WACC = 8% — don't just state the answer at the end, show the computation for every option so part-marks are secured even if you slip on one row.
- State the optimal ratio explicitly in a one-line conclusion — write 'The optimal debt-equity ratio is X:Y at which WACC equals 8%' as a standalone sentence; examiners look for a clear concluding statement.
- Anchor the conclusion to the Traditional Theory — one line like 'As per the Traditional Theory, this is the point where WACC is minimised and firm value is maximised' ties your number to theory and picks up the principle mark.
2Examiner-rewarded phrases
3Common trap
Most students use pre-tax Kd in the WACC formula and lose 2 marks silently — always multiply Kd by (1–t) unless the question explicitly says 'post-tax cost of debt is given'. Also, don't just identify the row where WACC = 8% without showing calculations for all rows; examiners need the full table to award step marks.