1. London Business School
Capital Structure
Francesca Cornelli
London Business School

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. Firm’s Objective
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)
Why maximizing the firm’s value is the same as maximizing
the equity’s value?

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:
1) the more debt the firm takes the higher is the risk that the firm will not be able to pay its debt, and therefore the cost of debt should be higher.
However, we said that at this point we are not going to consider the possibility of default. That is, we assume that the debt is safe, i.e., the cash that the project generates is above the interest payment in every state of the world.
So this is not the answer.
2) what about the cost of equity? Is the claim of the equity is more risky? The answer is yes, but in this example it is not so obvious because we cannot calculate the return on equity in each state of the world.
Let us see yet another detailed example.
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 m m .53m m m .67m
Bad m m .53m m m .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 m m
Bad m m

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 f 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.
The required return on equity increases with leverage.
M&M II tells us exactly in which way.

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)?
In the good state the EPS is higher for the leveraged firm. It
is only because of the gearing.
In the good state.
Price-earning ratio decreases, since the stock price
remains the same and expected earning per share
increases.
This is an important observation because people use this
ratio to evaluate stocks.

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)
Unlevered Levered
EBIT 200, ,000
Interest ,000
Income 200, ,000
Tax 70, ,500
Net Combined Income 130, ,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): Why not go for 100% debt?
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

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. Under the above conditions, one can either
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.

51. Capital Structure Does matter: The Cost of Financial Distress
CF to Equity
CF to Taxes
CF to Debt

52. Capital Structure Does matter: The Cost of Financial Distress
A firm that is unable to meet its debt obligations or that will be unable to do so at some point in the near future is said to be in Financial Distress.
A firm in financial distress can seek protection from its creditors by filing for Bankruptcy. It is then either liquidated or reorganized.

53. Capital Structure Does matter: The Cost of Financial Distress
In some industries, liquidation value is low (for example software houses), and for some it is high (For example the liquidation value of an airline is very high).
There are also indirect costs of reorganizing a bankrupt firm:
puts severe constraints on the ability of management to conduct business.
Hampers the relations of the firm with its customers and its suppliers.
Leads to loss of human capital and of growth opportunities.
In some cases, indirect costs are estimated to be as high as 20% of the value of the firm.

54. Financial Distress Without Bankruptcy
There are yet more costs to financial distress than those of liquidation or reorganisation.
These costs are borne by firms which are neither bankrupt nor insolvent, as well as by bankrupt firms that are being reorganised.
They arise from the severe conflicts of interest between shareholders and bondholders created by financial distress.
1) Bet the Bank’s Money:
Suppose the company has the opportunity to take a wild and
possibly lousy gamble (looking for gold in Alaska). If it does
not come off, the shareholders will be no worse off. But if the
gamble does succeed, there will be enough to pay the debt
and to live something in the shareholders’ pocket.
In other words, the shareholders got nothing to lose,
therefore
2) Don’t Bet your own money.
Suppose the company has a good investment opportunity
(positive NPV), however the profit from this project is not
sufficient to rescue the firm. The shareholders have have no
interest in that project. In particular, they have no interest in
putting money in the firm.

55. Conflict of interest Example
Consider a firm with £ 50 of 1-year debt.
BOOK
MARKET
This firm is in a financial distress. It cannot meet its
obligation. Notice, however, that the market value of the
equity is not zero. Why

56. Incentives for Costly Games
A) The shareholders of the firm favor risky projects.
B) Shareholders favor high dividends. They gain the full
benefit, but decline in the firm value is shared with
bondholders.
A) This project has negative NPV, but the shareholders find
it attractive. It is not their money that they are betting.
B) Shareholder are concerned with taking money out of the
firm.

57. Capital Structure Does matter: The Cost of Financial Distress
CF to Equity
CF to Taxes
CF to Debt
It’s useful to think of financial distress as “Cash Flow”
consumed by Financial Distress.
Financial Distress Cost

58. Capital Structure Does matter: The Cost of Financial Distress
Increasing leverage increases the probability of default, and with it the PV of the expected costs of financial distress.
Thus, leverage reduces the market value of the firm by increasing the present value of financial distress.
Who has to absorb the costs of financial distress?
Of course, when the firm is in financial distress, it is the debt
holders that incur the costs.
However, at the time of issuing the debt, it is the shareholders
that incur the present value of the costs of financial distress.

59. Summary Market Value of The Firm Debt Maximum value of firm Costs of
financial distress
Market Value of The Firm
PV of interest
tax shields
Value of levered firm
Value of
unlevered
firm
This is an animated slide
1) We have asked ourselves whether capital structure matters. That is, can we increase the value of the firm simply by using debt instead of equity.
2) We have argued that, in the absence of taxes and of the costs of financial distress, financial leverage should not alter the of the firm (M&M I). The key idea was that in perfect market, whatever the firm can do, the individual can do (or undo), and therefore they don’t think that leverage adds value.
The cost of equity increases in response to an increase in leverage. This happens because the shareholders must be compensated for the greater risk the have to bear (M&M II).
3) We have seen that the presence of corporate taxes increases the value of the leveraged firm above that of an all-equity firm that has the same assets. This is because debt provides tax shield.
4) Costs of financial distress and personal taxes moderate the benefit of leverage.
Optimal amount
of debt
Debt 25