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Capital Structure2
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.
Capital Structure3
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.
Capital Structure4
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
Capital Structure5
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.
E
D
r
IXE
r
ID
EDV
Dr Er
Capital Structure6
Example 1
Consider a firm with projects that expect to generate £10,000 in perpetuity.
%10
%5
2,000
000,10
E
D
r
r
I
X 40,00005.0
000,2D
80,0001.0
000,8E
120,000 EDV
Now, let I= £5,000100,000
05.0
000,5D
50,0001.0
000,5E
150,000 EDV
What is Wrong?
Capital Structure7
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?
Capital Structure8
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.
Capital Structure9
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
Capital Structure10
Unlevered Firm
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the worls
Ca
sh F
low
CF to Equity
Capital Structure11
Levered Firm with "Safe Debt"
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the World
Cash
Flo
w
CF to Equity
CF to Debt
Capital Structure12
Let denote the value of the geared (or levered) firm and that of the ungeared (or unlevered) firm. We shall show that
LV UV
UL VV
Capital Structure13
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?
UV
LVDE 01.001.001.0
Capital Structure14
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.
Capital Structure15
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.
)( DAAE rrE
Drr
Capital Structure16
Capital Structure17
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
1A
mVU 1125.1
000,050,15.0000,200,15.0
Capital Structure18
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
000,50006.1
000,530D
000,50019.1
000,5205.0000,6705.0
E
UL VEDV 000,000,1
Capital Structure19
Capital Structure20
Capital Structure21
How leverage Affects Risk and Returns
Also the beta of a firm is a weighted average of the betas of the individual securities.
)( DAAE
EDA
E
D
ED
E
ED
D
Capital Structure22
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)?
Capital Structure23
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
7.1000,100
000,170EPS
Capital Structure24
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?
1000,200
000,200EPS
Capital Structure25
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).
UL VV
Capital Structure26
Capital Structure27
Capital Structure28
Capital Structure Does matter:Corporate taxes
The interest that a company pays is tax deductible, while dividends and retained earnings are not.
ToB on d h o ld ers
$ 1
N on e
ToS tock H o ld ers
$ 1 O p era tin g In com e
Corporate tax
Income aftertax
cT
)T-$(1 c
Capital Structure29
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).
Capital Structure30
Example (continued)
Unlevered Levered 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
Capital Structure31
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?.
shield)PV(tax VV UL
DrT dc
Capital Structure32
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?
000,17506.0500,10
DTrDrT
cd
dc Shield)PV(Tax
Shield)PV(Tax VV UL
Capital Structure33
Unlevered Firm with Corporate Taxes
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the World
Cash
Flo
w
CF to Equity
CF to Taxes
Capital Structure34
Levered Firm with "Safe Tax" and Corporate Taxes
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the World
Cash
Flo
w
CF to Equity
CF to Taxes
CF to Debt
I n mi l l i ons
June 30 1997 1998
Assets
Current assets:
Cash and short- term investments $ 8,966 $13,927
Accounts receivable 980 1,460Other 427 502
Total current assets 10,373 15,889
Property and equipment 1,465 1,505
Equity investments 2,346 4,703
Other assets 203 260
Total assets $14,387 $22,357
Liabi l i t ies and stockholders ’ equity
Current l iabi l i t ies:
Accounts payable $ 721 $ 759
Accrued compensat ion 336 359
Income taxes payable 466 915
Unearned revenue 1,418 2,888
Other 669 809
Total current l iabi l i t ies 3,610 5,730
Commitments and cont ingencies
Stockholders’ equity:
Convert ible preferred stock – shares author ized 100;
shares issued and outstanding 13 980 980
Common stock and paid- in capital – shares authorized 8,000;
shares issued and outstanding 2,408 and 2,470 4,509 8,025
Retained earnings 5,288 7,622
Total stockholders ’ equity 10,777 16,627
Total liabilities and stockholders’ equity $14,387 $22,357
Microsoft Balance SheetsS
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Capital Structure36
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.
Capital Structure37
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.
DTVV CUL
Capital Structure38
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...
Capital Structure39
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?
ED rDE
Er
DE
D
WACC
EDc rDEE
rTDE
D
)1(WACC
DC rT )1( Dr
Capital Structure40
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.
)1( CT Dr
Capital Structure41
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.
EDA ED
E
ED
D
EC
DC
CA DTE
E
DTE
DT )1()1(
)1(
Capital Structure42
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.
Er fD rr
Capital Structure43
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.
%15.9or 0915.0
15.05.005.066.05.0
)1( WACC
EDC rED
DrT
ED
D
m43.40915.0
66.0210NPV
Capital Structure44
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
Mr E
2
)05.010.0(05.015.0
)(
E
E
fMEfE rrrr
A E
2.1)34.01(1
2
)1()1(
)1(
A
EC
DC
CA DTE
E
DTE
DT
%1111.0)05.010.0(2.105.0 Ar
Capital Structure45
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?
m211.0
66.0210 equity) NPV(all
DTC
Capital Structure46
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).
2
34.0210
2
debt) 50% with PV(project D
D
m46.446.2223.734.02 APV
Capital Structure47
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
Capital Structure48
Corporate and Personal Taxes
To b on d h o ld ers
$ 1
N on e
To sh areh o ld ers
$ 1 O p era tin g In com e
CT
CT1$
PT )1( CPE TT
PT1$ )1)(1( CPE TT
Corporate tax
Income after corporate tax
Personal tax
Income aftertaxes
Capital Structure49
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.
)1( PD Tr
DTTT
P
PEC
)1(
)1)(1(1
DTTT
VVP
PECUL
)1(
)1)(1(1
CT PT
ET
Capital Structure50
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.
06.0
675.01
)4.01()05.01)(35.01(
1
DD
Capital Structure51
Capital Structure Does matter:The Cost of Financial Distress
Levered Firm with "Risky Debt" and Corporate Taxes
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the World
Cash
Flo
w
CF to Equity
CF to Debt
CF to Taxes
Capital Structure52
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.
Capital Structure53
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.
Capital Structure54
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.
Capital Structure55
Conflict of interestExample
Consider a firm with £ 50 of 1-year debt.
V4040V
E1030FA
D3010NWC
TL100100TA
E5090FA
D5010NWC
BOOK MARKET
Capital Structure56
Incentives for Costly Games
4/50
10-
1/540
Prob.10 ttA) 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.
Capital Structure57
Capital Structure Does matter:The Cost of Financial Distress
Levered Firm with "Risky Debt", Corporate Taxes, and Financial Distress Costs
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12 13
State of the World
Ca
sh F
low
CF to Equity
CF to Debt
CF to Taxes
Financial Distress Cost
Capital Structure58
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.
distress) financial of PV(costs-shield)PV(tax VV UL
Who has to absorb the costs of financial distress?
Of course, when the firm is in financial distress, it is the debtholders that incur the costs.
However, at the time of issuing the debt, it is the shareholdersthat incur the present value of the costs of financial distress.
Capital Structure59
Summary
Debt
Mar
ket V
alue
of
The
Fir
m
Value ofunlevered
firm
PV of interesttax shields
Costs offinancial distress
Value of levered firm
Optimal amount of debt
Maximum value of firm
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