**What is gearing?**

• The mixture of debt finance relative to equity finance that a company uses to finance its business operations

• Gearing ratios assess financial risk:

• Debt/equity ratio: D/E

• Capital gearing: D/(D+E)

• Market values preferred to book values

• Should D include short-term debt?

**Implications of High gearing**

• Increased volatility of equity returns arises with high gearing since interest must be paid before paying returns to shareholders.

• Increased risk of bankruptcy also occurs.

• Stock exchange credibility falls as investors learn of company’s financial position.

Short-termism moves managers’ focus away from maximisation of shareholder wealth

**Optimal capital structure**

*Key question*:

• Does the mix of debt and equity finance used by a company affect its weighted average cost of capital?

• Is there a mix of debt and equity that will minimise the average cost of capital?

• Minimum cost of capital will maximise market value of company and hence maximise shareholder wealth.

**Simplifying Assumptions**

• No taxes exist.

• Financing choice is between ordinary shares and perpetual debt.

• Capital structure changes incur no cost and entail replacing debt with equity or vice versa.

• All earnings are paid out as dividends.

• Business risk is constant over time.

Earnings and hence dividends are constant

**Traditional approach**

• Cost of equity increases as gearing increases due to rising financial risk and, later, bankruptcy risk.

• Cost of debts rises at high levels of gearing due to bankruptcy risk.

• As company starts to replace expensive equity with cheaper debt, WACC falls.

• As gearing continues to increase, cost of equity and cost of debt increase, offsetting the benefit of cheap debt.

**Miller and Modigliani 1 (1**

^{st}Proposition)• Capital markets are assumed to be perfect.

• No risk of bankruptcy so cost of debt curve is flat.

• Linear increase in cost of equity due to increasing financial risk.

• As company gears up and replaces equity with debt, benefit of cheaper debt is exactly balanced by the increasing cost of equity.

No optimal capital structure is found

**Example**

Assume you own 1% of B’s shares:

(1) Sell your shares for £77.27

(2) Borrow £30 to copy B’s gearing

(3) Buy 1% of A’s shares (surplus of £7.27)

• Return on B’s shares: 11% × £77.27 = £8.50

• Return on A’s shares: 10% × £100 = £10

• Less interest: £30 × 5% = £1.50 leaves £8.50

• Same return but you now have £7.27 surplus

Arbitrage proof using companies A and B:

A B

Net income 1000 1000

Interest at 5%

__Nil____150__Earnings 1000 850

Divide by cost of equity

__10%____11%__MV of equity 10 000 7 727

MV of debt

__Nil____3 000__Total market value

__10 000____10 727__**NB:**

• Selling will cause B’s share price to fall and buying will cause A’s share price to rise.

• Return on B’s shares will rise and return on A’s shares will fall.

• WACC of A (10%) will fall and WACC of B (9.3%) will rise, and WACCs will converge until any arbitrage opportunity is eliminated.

• The claim that identical business risk will have an identical WACC is shown to be true.

**Miller and Modigliani II (2**

^{nd}Proposition)• M&M adjusted their first model to reflect the tax deductibility of interest payments.

• Tax efficiency implies that gearing up by replacing equity with debt gives benefit of a tax shield, increasing the value of company.

• Cost of debt curve falls from before-tax to after-tax level, so WACC curve slopes downwards.

This implies an optimal capital structure does exist: i.e. gear up with as much debt as possible

**Market Imperfection**

• M&M relaxed assumption of perfect capital market by considering corporate taxation.

• If we relax perfect market assumption further by considering bankruptcy risk, an optimal capital structure emerges.

• Companies have to balance the tax efficiency of debt with the risk of bankruptcy.

**Conclusions:**

• Traditional approach: Optimal Capital Structure (OCS) exists

• Miller and Modigliani I: no OCS is found

• Miller and Modigliani II: OCS is 100% debt

• Market imperfections: OCS exists

In practice, rather than one optimal capital structure existing for each firm, a range of optimal capital structures may exist.

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