## Optimal Capital Structure: Minimising Composite Cost of Capital

A firm's optimal capital structure is the debt-equity mix that minimises the Weighted Average Cost of Capital (WACC). As debt increases:

Initially, WACC falls (cheap debt replacing expensive equity)
Beyond a point, WACC rises (rising cost of both debt and equity due to financial risk)
The optimal point is the debt level where WACC is lowest

### Procedure

1. For each debt-equity mix, compute: WACC = (Debt% × Kd) + (Equity% × Ke)

2. Identify the mix with the minimum WACC

3. This is the optimal capital structure

### Why both Kd and Ke rise with debt

Kd rises: More debt → higher financial risk → lenders demand higher interest
Ke rises: Higher debt → higher variability in EPS → equity investors demand higher return (financial leverage risk)

### Reverse WACC problems

If WACC and Kd are known, find Ke:

```

WACC = (Wd × Kd) + (We × Ke)

Ke = (WACC − Wd × Kd) / We

```

If debt-equity ratio = 2:1 → Wd = 2/3, We = 1/3

Worked example

### Example 1

Q58 – Optimal Debt-Equity Mix

Debt%	Equity%	Kd	Ke	WACC
0	100	0	15.0	15.00%
10	90	7.0	15.0	14.20%
20	80	7.0	15.5	13.80%
30	70	7.5	16.0	13.45%
40	60	8.0	17.0	13.40% ← Minimum
50	50	8.5	19.0	13.75%
60	40	9.5	20.0	13.70%

WACC at 40% debt = 0.40×8.0% + 0.60×17.0% = 3.2% + 10.2% = 13.40%

Optimal Debt-Equity Mix = 40:60 (minimum WACC point)

### Example 2

Q59 – Reverse WACC: find Ke

Debt:Equity = 2:1 → Wd = 2/3, We = 1/3

WACC = 12%, Kd(after tax) = 15%(1−0.35) = 9.75%

12% = (2/3 × 9.75%) + (1/3 × Ke)

12% = 6.50% + Ke/3

Ke/3 = 5.50%

Ke = 16.50%

⚠️ Common exam mistakes

Not computing WACC for every mix level — students sometimes check only a few points and miss the true minimum.
Ignoring that both Kd and Ke change as gearing changes — many students keep Ke constant.
For reverse WACC: using the gross interest rate for Kd instead of the after-tax cost.

Reference:

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Optimal Capital Structure — Minimising WACC

Worked example