Capital Structure II

Corporate income taxes

Review question

Describe the two basic capital budgeting decisions.

Answer

Project acceptance: each project is independent of others. Each is accepted or rejected.

Choice between mutually exclusive projects. Of two or more projects, only one can be undertaken.

MM II without taxes

Facts and derivation. Fact 1: Leverage does not change

market value Fact 2: All cash flows are accounted

for.

BSS LU

BrSrSr BLSU 0

MM I

Cash

BrSrBSr BLSL )(0

BrBSrSr BLLS )(0

BrBSrSr BLLS )(0

BrrSrSr BLLS )( 00

LBS S

Brrrr )( 00

MM Proposition II no tax

Debt-to-equityratio (B/S)

Cost of capital: r(%)

.r0

rS

rWACC

rB

LBS S

Brrrr )( 00

Weighted average cost of capital

The cost to the firm of undertaking a project.

Here independent of leverage … because leverage doesn’t matter.

Now with taxes.

No threat of bankruptcy. Corporate taxes, not personal. Government gets a piece of the pie. A smaller piece if the firm has debt.

MM I with taxes

VU = market value of the unlevered firm VL = market value of the levered firm B = market value of bonds TC = corporate tax rate VL = VU + TC B

Why?

Why isn’t the bond rate in the formula? The bond is a perpetuity. Market rB is the right discount rate for

the perpetuity.

Short derivation

Each year the tax shield is rBTCB

Value of tax shield is rBTCB/rB = TCB

MM II (with taxes)

Corporate taxes, not personal rB = interest rate rS = return on equity r0 = return on unlevered equity B = value of debt SL = value of levered equity Previously, without taxes

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

Effect of tax shield

Increase of equity risk is partly offset by the tax shield

rS = r0 + (1-TC)(r0 - rB)(B/SL) Leverage raises the required return less

because of the tax shield.

MM II and WACC

Debt-to-equityratio (B/S)

Cost of capital: r

(%)

.r0

rS

rB.. rWACC

.

WACC not equal to r0. Why?

r0 is the return on unlevered equity.

WACC is for risk like that of the physical asset of the firm.

Adding debt reduces risk of the asset of the firm.

Adding debt reduces WACC. The levered firm is in a lower risk

category.

WACC declines with leverage.

Why? Because the project is producing bigger

interest tax shields, and the tax shields are a relatively safe

asset.

rS increases with leverage. Why?

Leverage raises risk … and is only partly offset by the tax

shield.

A little derivation

Again. Market value equation. Cash flow equation. The latter is a version of WACC.

BTSBS CUL

BrTSrBrSr BCUBLS 0

MM I

Cash

BrBrTSrSr BBCULS 0

BrBrT

BTBSrSr

BBC

CLLS

)(0

Rewrite cash

Sub in MM I

BrBrT

BTBSrSr

BBC

CLLS

)(0

)1(

)1(00

CB

CLLS

TBr

TBrSrSr

))(1( 00 BCL

S rrTS

Brr

Copying

Combineterms

Finally

Review question

Does a good project have IRR greater than the hurdle rate, or less?

Answer

IRR is the discount rate that makes NPV(IRR) = 0.

The hurdle rate is the market rate for the risk-class.

Investing means cash flows are first negative, then positive.

Financing (in this context) means cash flows are first positive, then negative.

More answer

Other sign patterns, IRR is not useful. Investing, a good project has IRR >

hurdle rate. Financing, a good project has hurdle

rate > IRR.