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.

MM I Cash

MM Proposition II no tax Debt-to-equity ratio (B/S) Cost of capital: r (%). r0r0 rSrS r WACC rBrB

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  V U = market value of the unlevered firm  V L = market value of the levered firm  B = market value of bonds  T C = corporate tax rate  V L = V U + T C B

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

Short derivation  Each year the tax shield is r B T C B  Value of tax shield is  r B T C B/r B = T C B

MM II (with taxes)  Corporate taxes, not personal  r B = interest rate  r S = return on equity  r 0 = return on unlevered equity  B = value of debt  S L = value of levered equity  Previously, without taxes r S = r 0 + (B/S L )(r 0 - r B )

Effect of tax shield  Increase of equity risk is partly offset by the tax shield  r S = r 0 + (1-T C )(r 0 - r B )(B/S L )  Leverage raises the required return less because of the tax shield.

MM II and WACC Debt-to- equity ratio (B/S) Cost of capital: r (%). r0r0 rSrS rBrB.. r WACC.

WACC not equal to r 0. Why?  r 0 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.

r S 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.

MM I Cash Rewrite cash Sub in MM I

Copying Combine terms 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.