Capital Structure

1. Capital Structure Francesca Cornelli London Business School fcornelli@lbs.ac.uk

2. OUTLINE • Does Capital structure Matter? • No: The Modigliani and Miller propositions. • Yes: • Corporate Taxes • Personal Taxes • Costs of Financial Distress • Agency Costs. • How to take into account corporate taxes when valuing a project: • APV • WACC.

3. Definition • The Capital Structure of a firm is the mix of different securities issued by the firm to finance its projects. Examples of such securities are • bonds • bank debt • common stocks • etc… • Does Capital structure Matter? • We will focus on the consequences of the choice between different proportions of debt and equity in order to finance a given level of assets.

4. Given the firm’s assets and investment plan, find the debt proportion that maximizes firm value Market Value - balance sheet Assets Debt (D) Equity (E) Firm value (V) Firm’s Objective

5. A change in the capital structure of the firm that leaves the assets of the firm unchanged will not change X, the cash flows generated by the assets of the firm. • So, one might be tempted to think that the capital structure of a firm does not alter its value. • Yet, recall that • As and are not equal, the changes in D and E brought about by a change in I will not cancel each other.

6. Example 1 • Consider a firm with projects that expect to generate £10,000 in perpetuity. Now, let I= £5,000 What is Wrong?

7. M&M Proposition I • Modigliani & Miller • Under the following assumptions: • No taxes • No costs of financial distress • Individuals can borrow and lend on the same terms as corporations • No asymmetry of information • The value of a firm is independent of its capital structure • These assumptions are clearly not reasonable. Does that make MMI useless?

8. MM Proposition I • NO • What MMI indicates is that if capital structure matters, as it does indeed, it must be because of taxes, the costs of financial distress or differences in the lending and borrowing terms offered to corporations and individuals. • Other reasons exists for capital structure to matter. These will be discussed later.

9. Example • A firm has assets of £1 million and is 50% debt-financed. Cost of debt is 6%. • State Prob. Assets PBIT Debt Interest PBT Equity • Good 0.5 1.20m .20m .53m 0.03m .17m .67m • Bad 0.5 1.05m .05m .53m 0.03m .02m .52m • The manager thinks he can increase the value of the firm by retiring debt. He thinks some investors might value the resulting decrease in riskiness of the equity. • State Prob. Assets = Equity PBIT = PBT • Good 0.5 1.2m .2m • Bad 0.5 1.05m .05m

10. CF to Equity

11. CF to Equity CF to Debt

12. Let denote the value of the geared (or levered) firm and that of the ungeared (or unlevered) firm. We shall show that

13. Example (continue) • Consider buying 1% of the unlevered firm. The payoff is: • 0.01 of £1.2m= £12,000 in the good state • 0.01 of £1.05m= £10,500 in the bad state • The cost is 0.01 X • Consider buying 1% of the levered firm (1% of its debt and 1% of its equity). The payoff is • 0.01 of £0.67m+0.01 of 0.53m = £12,000 in the good state • 0.01 of £0.52m+0.01 0f 0.53m= £10,500 in the bad state • The cost is • Since the payoff in each state is the same, we conclude that the cost must be the same • Why?

14. No investor would buy a more expensive investment that has the same payoff as a cheaper investment • Thus, the value of the geared firm must equal that of the all-equity firm. • By buying 1% of the geared firm’s equity and 1% of its debt, the investor who chose to do so was able to obtain the same payoffs as those of the investor who chose to buy 1% of the unlevered firm’s equity. • In other words, the investor in the geared firm was able to offset the greater riskiness of the equity of the geared firm by also holding its debt: she unlevered her shares of the geared firm on her own • Because the investor could unlever her shares on her own, there was no need for the firm itself to do so, and therefore no gain for the firm for doing it.

15. How leverage Affects Risk and Returns • Leverage increases the variability and the expected return per share. • M&M I tells us that the price of the share does not change. This is possible if the increase in the expected return is exactly offset by the increase in risk. • Since the expected return on a portfolio is equal to a weighted average of the expected returns on the individual holdings we have: • This is M&M’s proposition II.

17. Example (continued) • The asset beta of the unlevered firm is • As the risk free rate is 6% and the risk premium is 6.5%, the required return on equity is therefore 12.5% • The value of the unlevered firm is

18. The beta of the equity of the geared firm can be shown to be equal to 2, making the required return on equity equal to 19% • The value of the debt is • The value of the equity is • We therefore have

21. How leverage Affects Risk and Returns • Also the beta of a firm is a weighted average of the betas of the individual securities.

22. Leverage and Earning per Share • EPS is profit (or net earnings) divided by number of outstanding shares. • An increase in EPS can be the consequence of an improvement in firm performance (good news). • It can also be achieved, however, by leverage. The expected EPS increases with leverage. It represents only the increased compensation required by shareholders for the additional risk they have bear (no news). • What happens to the price-earning ratio (P/E)?

23. Example (continued) • Suppose the geared firm had 100,000 shares, each selling for £5 (recall that E = £500,000). • Suppose the good state occurs, and profit is £200,000 - £30,000 = £170,000. • We therefore have

24. Now suppose the all-equity firm had retired debt by issuing 100,000 shares at £5 each. • The all-equity firm therefore has a total of 200,000 shares. • In the good state, its PBT is £200,000 and we have • The EPS of the all-equity firm is lower. Is the unlevered firm less valuable?

25. No • We know that . The decrease in EPS is simply a consequence of the decrease in the risk borne by equity. • Furthermore, note that the decrease in gearing not only decreases EPS (actual in the good state and expected), but also increases the price-earnings ratio (the price of a share remains the same, and EPS decreases).

28. Capital Structure Does matter:Corporate taxes • The interest that a company pays is tax deductible, while dividends and retained earnings are not. Corporate tax Income after tax

29. Example • Consider an all-equity firm that has assets of £ 1 million and expected EBIT of £ 200,000 per year. It expects to pay tax of £70,000 (the corporate tax rate is 35%) so it has net income to shareholders of £130,000. • Let the firm issue debt to finance a £ 500,000 repurchase of equity. The debt pays interest of £ 30,000 (6% interest rate).

30. Example (continued) • UnleveredLevered • EBIT 200,000 200,000 • Interest 0 30,000 • Income 200,000 170,000 • Tax 70,000 59,500 • Net Combined Income 130,000 110,500+30,000=140,500 • Debt provides Tax Shield to the shareholders of 30,000 from tax: a saving of 0.35 X 30,000 = 10,500

31. Tax Shield • The value of a levered firm is no longer equal to that of an unlevered firm, but is greater by an amount that represents the present value of the tax shield provided by debt • Every year the tax shield is . • To calculate the present value of the tax shield, which discount rate should we use?.

32. Example (continued): • Assume that the debt is permanent. The yearly tax shield is £10,500, and thus the present value of the tax shield is • In general, when debt is permanent, we have • We have . So leverage increases value. • Why not go for 100% debt?

33. CF to Equity CF to Taxes

34. CF to Equity CF to Taxes CF to Debt

35. Microsoft Balance Sheets Source http://www.microsoft.com/msft/ar98/downloads/msftar98.doc

36. Capital budgeting • Before looking at the effect of personal taxes and costs of financial distress, we want to see how to take into account corporate taxes when valuing a firm or a project • In fact, if in presence of corporate taxes leverage affects value, then we want to see how to take it into account.

37. Adjusted Present Value • The relation • which relates the value of a levered firm to that of an unlevered firm that is otherwise identical to the former suggests that the value of a levered firm can be obtained by • determining the value of the levered firm as if it were unlevered, and • adjusting the obtained value for the presence of the tax shield • Such an approach is called Adjusted Present Value. It is valid for NPV as well as PV.

38. The concept of Adjusted Present Value is very general. • It can be used to account for the value of the tax shields provided by various types of debt, for issuing costs, for the costs of financial distress, etc...

39. Weighted Average Cost of Capital • As an alternative to adjusting the PV of a levered firm for the presence of a tax shield, it is possible to adjust the discount rate that is used to discount the cash flows of the firm. • More specifically, the WACC, which was previously defined as • becomes, in the presence of corporate taxes • is used in place of • Why the lower interest rate in the case of taxes?

40. The factor by which the interest rate is multiplied reflects the fact that interest payments provide a tax shield. • The WACC should be used only in cases where the ratio of debt to the market value of the firm is constant (in addition to the conditions specified in previous lectures). • It is often used as an approximation in the case where the ratio of debt to the market value of the firm is not constant (but the other conditions are nonetheless true). • Under the above conditions, one can either • explicitly account for the value of the tax shield, by using APV, or • use the WACC, in which case no tax shield is to be added.

41. How leverage affects the betas • The relation between assets, equity and debt betas • remains true in the presence of corporate taxes in the case where the risk of the tax shield is equal to the risk of the assets. • It becomes • in the case where the risk of the tax shield is equal to the risk of the debt.

42. EXAMPLE • A firm considers a project that requires an initial investment of £10m and has cash flow of £2m in perpetuity. • The firm has cost of equity =15%, cost of debt =5%, and is 50% debt-financed (debt equals 50% of the value of the firm, equity equals 50%). • The project is in all respects similar to the present operations of the firm, and will also be 50% debt-financed. • NB: When we talk about the value of a company we usually mean its present value. However in this case the firm is considering whether to undertake a project and therefore it is computing the net present value of the project.

43. The WACC of the firm is • The project therefore has NPV • Note that yearly cash flow was not adjusted to account for the presence of the tax shield. • The WACC does so.

44. What if we use the APV? • Let =10%. can therefore be obtained from the CAPM • can now be obtained from by using • We therefore have

45. The NPV of the project assumed to be all-equity financed is • The NPV of the project, with 50% debt, (ie the APV) is given by the NPV(all equity) + PV(Tax Shield) • The present value of the tax shield provided by debt is • But what is D?

46. We know that debt equals 50% of the present value of the project. • The present value of the project equals the sum of the value of the fixed assets of the project, the net present value of the project and the present value of the tax shield. • In other words, we have • The APV therefore equals • which is the same as the NPV obtained with the WACC (save for some rounding errors).

47. Back to the optimal capital structure • Now that we have seen how to take into account corporate taxes, let us go back to see personal taxes and costs of financial distress. • We have already seen that these can be easily taken into account in the APV

48. Corporate and Personal Taxes Corporate tax Income after corporate tax Personal tax Income after taxes

49. Corporate and Personal Taxes • The tax shield (per $1 paid interest rate) is • Corporate tax+personal tax on equity - personal tax (on interest) • In the case of perpetual debt, the present value of the tax shield is (we use as a discount factor): • and • where is the corporate tax rate, is the marginal rate of personal tax, and is effective tax rate on equity.

50. Example • Consider a company who pays no dividends, and its shareholders are top rate taxpayer (personal tax 40%), who do not intend to realize capital gain in the near future. Given the option to defer taxes on capital gains, they view the effective tax rate on capital gain as 5%. The present value of the tax shield is • Leverage now decreases value.