Review

Review Item  An firm has a project with NPV>0 that costs a lot of money.  It pays off after the owner dies.  Should she invest? In the project? In financial assets? How?

Time zero cash flow Time one cash flow An investment opportunity that increases value. NPV Invest to here Finance to here

Review item  What is the interest rate?

Don’t write  The interest rate is the time value of money.

Do write:  The interest rate is the premium for current delivery of money.  P 0 is the price of current money in current money, namely 1.  P 1 is the price of time-one money in terms of current money, something <1.  P

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Review item  When a firm creates value through a financial transaction, who gets the increase?

Answer  Old equity means the shareholders at the time the decision is made.  Old equity gets the gains.  Why? Old equity has no competitors. Everyone else is competitive and must accept a market return.

Review item  Two assets have the same expected return.  Each has a standard deviation of 2%.  The correlation coefficient is.5.  What is the standard deviation of an equally weighted portfolio?

Answer  Var P =.5x.5x4+.5x.5x4+2x.5x.5x.5x2x2  = 3  Standard deviation = sq. root of 3  =1.732

Review item  A firm has a project with positive NPV.  The project costs 100M to start.  The firm has only 50M.  What should it do?

Answer  Raise the money in the capital market.  It can because NPV is market valuation.

EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 RecessionExpectedExpansion EBIT$1,000$2,000$3,000 Interest Net income$360$1,360$2,360 EPS$1.50$5.67$9.83 ROA5%10%15% ROE3%11%20%

Proposition II of M-M  r B is the interest rate  r s is the return on (levered) equity r 0 is the return on unlevered equity  B is value of debt  S L is value of levered equity  r s = r 0 + (B / S L ) (r 0 - r B )

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

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

Optimal Debt and Value Debt (B) Value of firm (V) 0 Present value of tax shield on debt Present value of financial distress costs Value of firm under MM with corporate taxes and debt VL=VU+TCB=VL=VU+TCB= V=Actual value of firm V U =Value of firm with no debt B* Maximum firm value Optimal amount of debt

Channels OperatingCash Flows=$1 Debt channel Equity channel TCTC (1-T C )(1-T S ) TBTB 1 - T B TSTS

Value as equity Value as debt Operating C.F.’s of the whole economy D of Institutions D of rich investors V* = 1/R B V* = 1/R S as debt as equity Miller: Tax-class clienteles

Value as equity Value as debt Operating C.F.’s of the whole economy tax reform increased debt...

Separation theorem interpreted for dividends (Figure 18.4) C1C1 C0C0 slope=-(1+r) Low-dividendfirm High-dividend firm w Future return or dividendno

Dividend equilibrium $ofoperating cashflows HiDiv value per$1 LoDiv value per$1 mqiliriu oiv E L mEquilibriu HiDiv ub D V*=1/RhRh V*=1/RLRL...

Review item  What is the weighted average cost of capital?

Answer  Give the definitions and the formula.  r B = bond rate  r S = expected return on shares  B = market value of bonds  S = market value of shares  T C = corporate tax rate

Pay-off pitch  r WACC = (S/(S+B))r S + (B/(S+B))(1-T C )r B  Now say that it applies when  (1) the physical project has the same risk as the firm  (2) it is financed like the firm.

Review item  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.