Capital Structure: Part 1 - University of Manitoba

[Pages:10]Capital Structure: Part 1

For 9.220, Term 1, 2002/03 02_Lecture19.ppt Student Version

Outline

1. Introduction 2. Theories of Capital Structure

a) Modigliani and Miller ? No tax b) M&M with Corporate Tax

3. Summary and Conclusions (so far)

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Introduction

Dfineafinncitiiaolns:eCcuarpititieasl Sutsreudcttuorefinisanthcee mthiex foirfm. Our goal is to see if there is an optimal way for firms to finance.

Should a firm have a higher or lower D/E ratio. What factors affect the optimal D/E choice? In order to optimize the D/E ratio, our overall goal is to maximize the total value of the firm and thus maximize expected shareholder wealth.

Modigliani and Miller ? No Tax Case

M&M began looking at capital

structure in a very simplified world so that we would know what does or does not matter.

Assume no taxes No transaction costs

Including no bankruptcy costs Investors can borrow/lend at the same rate (the same as the firm).

No information asymmetries A fixed investment policy by the firm

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M&M No Tax: Result

A change in capital structure does not matter to the overall value of the firm. The total cash flows produced athree cthaeshsaflmowe,s tihsutshethseamtoeta.l value of It doesn't matter if the cash flows from the firm to its security holders are called debt or equity cash flows.

M&M ? No Tax Case

Equity, $1,000, 100%

Debt, $300, 30%

Equity, $700, 70%

Equity, $400, 40%

Debt, $600, 60%

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The M&M Propositions I & II (No Taxes)

Proposition I

Firm value is not affected by leverage VL = VU

Proposition II

Leverage increases the risk and return to stockholders

rs = r0 + (B / SL) (r0 - rB)

rB is the interest rate (cost of debt) rs is the return on (levered) equity (cost of equity) r0 is the return on unlevered equity (cost of capital) B is the value of debt SL is the value of levered equity

M&M Proposition I (No Taxes)

The derivation is straightforward: Shareholders in a levered firm receive

EBIT - rB B

Bondholders receive rB B

Thus, the total cash flow to all stakeholders is

(EBIT - rB B) + rB B

The present value of this stream of cash flows is VL Clearly (EBIT - rB B) + rB B = EBIT

The present value of this stream of cash flows is VU

VL = VU

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M&M Proposition II (No Taxes)

The derivation is straightforward:

rWACC

=

B B+

S

? rB

+

S B+

S

? rS

Then set rWACC = r0

B B+S

? rB

+

S B+

S

? rS

=

r0

multiply both sides by B + S S

B+ S

S

?

B B+S

? rB

+

B+S S

?

S B+

S

? rS

=

B+ S

S

r0

B S

? rB

+ rS

=

B+ S

S

r0

B S

? rB

+ rS

=

B S

r0

+ r0

rS

=

r0

+

B S

(r0

- rB )

Exercise

1. CtbSf$nWstsoiohtufe9enuorhteptw0apmduaaapnpeucltmpEoctboonvuai[seftsialsRlrree?dellteeiuvtehoIRhqateeftienuhesfnhritE.eoe=dyfecv[i]fEdrhfR?atbm4[itharledhRe%Wumenesqetebegqauthst]ufiaeoioaesiiottrnidyfttycsmf]cadu.titutl6shirohWsEriv%iefttre[ia1hihenRtee,l8hlenaucseMqt%ettle?]vhuWulyieeicd=.sotAraneyafAetCp1lhtldwl$aiCs4heten3oha?e%eqd0,walquf.tueitmirhiitimstgyieylhltiihttoseoend 2. Redo 1 with $60 million of debt.

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The Cost of Equity & Debt, and the WACC: M&M Proposition II with No Corporate Taxes

Cost of capital: r (%)

rS

=

r0

+

B SL

? (r0

- rB )

r0

rWACC

=

B B+S

? rB

+

S B+S

? rS

rB

rB

Debt-to-equity Ratio B S

M&M with Corporate Taxes

When corporate taxes are introduced, then debt financing causes a positive benefit to the value of the firm. The reason for this is that debt interest payments reduce taxable income and thus reduce taxes.

Tahvauislawbliethtodesbetc,utrhiteyrehoisldmerosre(eaqfuteitry-taanxdcadsehbtf)low than there is without debt. Thus the value of the equity and debt securities combined is greater.

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M&M with Corporate Taxes

TC = 40% in this example

Equity, $600, 60%

Tax, $400, 40%

Equity, $420, 42%

Tax, $280, 28%

Debt, $300, 30%

Equity, $240, 24%

Tax, $160, 16%

Debt, $600, 60%

M&M Proposition I (with Corporate Taxes)

Proposition I (with Corporate Taxes)

Firm value increases with leverage

VL = VU + TC B

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M&M Proposition I (with Corp. Taxes)

Shareholders in a levered firm receive Bondholders receive

(EBIT - rB B) ? (1- TC )

rB B

Thus, the total cash flow to all stakeholders is

(EBIT - rB B) ? (1- TC ) + rB B The present value of this stream of cash flows is VL

Clearly (EBIT - rB B) ? (1- TC ) + rB B =

= EBIT ? (1- TC ) - rB B ? (1- TC ) + rB B

= EBIT ? (1- TC ) - rB B + rB BTC + rB B The present value of the first term is VU

The present value of the second term is TCB VL = VU + TC B

M&M Proposition II (with Corp. Taxes)

Proposition II (with Corporate Taxes)

This proposition is similar to Prop. II in the no tax case, however, now the risk and return of equity does not rise as quickly as the debt/equity ratio is increased because low-risk tax cash flows are saved. Some of the increase in equity risk and return is offset by interest tax shield

rS = r0 + (B/S)?(1-TC)?(r0 - rB)

rB is the interest rate (cost of debt) rS is the return on equity (cost of equity) r0 is the return on unlevered equity (cost of capital)

B is the value of debt S is the value of levered equity

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