Week 1 - The Basics of Capital Structure - Modigliani Miller, Taxes, and Bankruptcy Costs

Question 1

Modigliani Miller Safe Debt V2>V1

Answer 1

• Short Sell fraction alpha of firm 2’s shares (Pay alphaX at t = 1), receive alphaV2 at t = 0, by fraction alpha*V2/V1 of firm 1’s debt
• t = 0, investor net cash flow = 0
• t = 1, investor recieves:

(alphaV2/V1)(1+rf)D1 + (alphaV2/V1)(X - (1+rf)D1) = alphaV2/V1X >Alpha *X if V2>V1

pay Alpha *X to close short position - arbitrage opportunity

Question 2

Modigliani-Miller safe debt V1>V2

Answer 2

• Short sell fraction alpha of firm 1’s shares for AlphaE1 -> commit to pay alpha[X - (1+rf)*D1] at t = 1
• Borrow alphaD1 and invest the proceeds in a fraction AlphaV1/V2 of firm 2’s shares
• t = 0, net cash flow = 0
• t = 1, Investor gets alphaV1/V2X, pays interest (1+rf)AlphaD1 and pay alpha[X - (1+rf)D1]

Cashflow: (AlphaV1/V2X - (1+rf)AlphaD1 - alpha[X - (1+rf)D1] = Alpha(V1/V2 - 1)*X >0

Question 3

intuition behind arbitrage

Answer 3

V2>V1 - Arbitrageurs undo firm 1’s leverage by buying its debt and equity in the right proportion

V1>V2 - Arbitrageurs can lever-up firm 2 by borrowing on individual accounts (Homemade leverage)

Question 4

Modigliani-Miller Proposition 1

Answer 4

There is no optimal capital Structure Provided that:

• Competitive and complete markets
• Individuals can borrow and lend at the same rate
• No Taxes, bankruptcy and transaction costs
• Financing decision neither affects cash flows generated by assets nor conveys information

Question 5

Modigliani-Miller Prosposition 2

Answer 5

Capital Structure does not affect firm Value

• A firm’s Cost of equity capital increases as its market value debt/Equity ratio increases as its market value D/E ratio increases. However, the overall cost of capital (WACC) is constant

Intuition: Raising debt makes existing equity more risky hence more costly - the seemingly lower cost of debt capital is an illusion

Question 6

Proof of MM2

Answer 6

WACC = D/Vrd + E/Vre can be written as:

re = WACC + (WACC - rd)*D/E

Using MM1 - WACC is independent of capital structure because:
1+WACC = E[X)/V

Since firm value is uniquely determined by the expected cash flow, WACC is independent of the D/E ratio and re is linear in D/E

Note: typically, WACC > rd and re increases with D/E

Hence, the difference between the cost of debt and equity is compatible with the irrelevance proposition

Question 7

Summary of MM1 and MM2

Answer 7

MM1:
In a frictionless economy, firm value is independent of the firm’s capital structure
- This also means that a firm’s cost of capital does not depend on the D/E mix

MM2:
Whereas the firm’s overall cost of capital (WACC) does not depend on the firm’s D/E mix, the cost of equity is higher when the firm has more debt

Question 8

How do corporate taxes affect the cash flows accruing to debt and equity holders?

Answer 8

The issue is the differential tax treatment between interest and dividends
- In most countries, debt has a tax advantage:
- Interest payments are tax deductible
- Dividends and retained earnings are taxed

Question 9

Tax shield derivation

Answer 9

Payment to equityholders: (1-t)(X - rfD) + rf*D

Can be rewritten as: (1-t)X + trf*D

(1-t)*X is the value of an all equity firm

trfD is the value of the tax shield

Firm can pay this extra to investors as opposed to an all equity firm

Question 10

Tax shields in perpetuity formula

Answer 10

PV(Tax shields) = trfD/rf = t*D

Question 11

Value of levered firm under perpetual tax shields

Answer 11

V(D) = (1-tc)X/ra + tD = V(0) + t*D

Question 12

MM1 with corporate taxes

Answer 12

The value of a levered firm equals that of an unlevered firm + the PV of the interest tax shield

V(D) = V(0) + PV(Tax shield perpetuity)

Question 13

WACC with corporate Taxes

Answer 13

Effective after tax borrowing rate becomes rd(1-t)

WACC = E/Vre + D/Vrd*(1-t)

Intuition: The government pays a fraction t of the firm’s interest expenses. Investors cannot get an equivalent tax break on homemade leverage hence they are ready to pay a premium for levered firms

Question 14

Who benefits from the tax gains?

Answer 14

All the tax gains from leverage accrue to the shareholders

Intution: Debtholders receive a fair return
- Shareholders reap the tax benefits

Question 15

Bankruptcy cost implications on MM

Answer 15

The possibility of bankruptcy does not itself violate MM. For Bankruptcy to matter, it must be costly - deadweight cost

• in a perfect capital market, bankruptcy merely transfers ownership to debtholders without reducing firm value
• In reality, bankruptcy is often a long and complicated process that imposes costs on the firm and investors
• Such bankruptcy costs may offset tax advantage of debt financing

Question 16

Trade-Off Theory of Capital structure

Answer 16

If financial distress has real costs, the optimal debt-equity ratio trades-off tax advantage of debt vs cost of financial distress

Question 17

What are the costs of financial distress

Answer 17

Direct Bankruptcy costs:

• Cost incurred in liquidation and/or reorganisation procedures include:
• Administrative and court cost, legal and advisory fees
• Time and resources spent by management and creditors
• Fire sale of assets
• Mismanagement by bankruptcy judges
• Direct costs represent (on average) some 2-5% of total firm value for large companies and up to 20-25% for small ones
• For capital Structure choice, these ex-post bankruptcy costs must be weighted by the probability of bankruptcy. Lowers expected cost significantly

Question 18

Example of bankruptcy costs

Answer 18

In small firms, bankruptcy cost and legal fees can quickly eat up all assets

Example:
- Estimate of annual default probability: 4%
- Company value at moment of entering bankruptcy: 30% of current value
- Deadweight loss: 20%

Total: 0.24%

For 10 billion dollar firm, ex-ante bankruptcy cost of 24 million. Small relative to tax savings of debt for 10 billion firm in 35% tax bracket

Question 19

How do bankruptcy costs affect different firms?

Answer 19

• For firms with mostly tangible assets, bankruptcy may not be very costly
  -For firms with mostly intangible assets, bankruptcy can be very costly

Question 20

Indirect Bankruptcy costs

Answer 20

Costs that arise before bankruptcy when the probability of bankruptcy is no longer negligible

Ex-Ante costs of financial distress:
- Loss of customers
- Loss of key employees
- Inability to access trade credit with suppliers
- Predatory actions by rivals
- Inability to raise financing for essential capital enhancements