Capital Structure II Corporate income taxes

Now with taxes.  No threat of bankruptcy.  Corporate taxes, not personal.  Government gets a piece of the pie.  Debt reduces the government slice.

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 tax shield of 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?  WACC is the discount rate for a project that... ..is like the physical asset of the firm and  is financed like the firm.  r S is the required return on the equity of the firm.  Two different things.

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.

Cash flows

MM I Cash Rewrite cash Sub in MM I for S U

Copying Combine terms Finally

Weighted average cost of capital

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.