Review

Principle of separation  Present discounted value the real investment. (equivalence).  Decide whether to undertake it (optimization).  Select the appropriate financial investment or disinvestment (optimization).

Representation Nature’s move, plus the contestant’s guess. pr = 2/3 guess wrong guess right pr = 1/3 switch and win or stay and lose switch and lose or stay and win

No arbitrage condition:  Price of bond = price of zero-coupon bond + price of stripped coupon.  Otherwise, a money machine, one way or the other.  Riskless increase in wealth

Pie theory  The bond is the whole pie.  The strip is one piece, the zero is the other.  Together, you get the whole pie.  No arbitrage pricing requires that the values of the pieces add up to the value of the whole pie.

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?

Definition of a call option  A call option is the right but not the obligation to buy 100 shares of the stock at a stated exercise price on or before a stated expiration date.  The price of the option is not the exercise price.

Example  A share of IBM sells for 74.  The call has an exercise price of 76.  The value of the call seems to be zero.  In fact, it is positive and in one example equal to 2.

t = 0 t = 1 S = 74 S = 80, call = 4 S = 70, call = 0 Pr. =.5 Value of call =.5 x 4 = 2

Definition of a put option  A call option is the right but not the obligation to sell 100 shares of the stock at a stated exercise price on or before a stated expiration date.  The price of the option is not the exercise price.

“Real” options  The option to abandon is a put option.  Deciding to delay or not, the firm exercises or not its call on the project.

Value of options  rises with risk …  because options are like insurance, that is …  a put insures the investor who owns a stock and fears it might fall, and …  a call insures an investor who believes a stock will rise and fears it will fall instead.

Review item  What is the interest rate?

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

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.

No arbitrage principle  Market prices must admit no profitable, risk-free arbitrage.  No money pumps.  Otherwise, acquisitive investors would exploit the arbitrage indefinitely.

Example  Coupons sell for 450  Principal sells for 500  The bond MUST sell for 950.  Otherwise, an arbitrage opportunity exists.  For instance, if the bond sells for 920…  Buy the bond, sell the stripped components. Profit 30 per bond, indefinitely.  Similarly, if the bond sells for 980 …

Confirmation in an excel spread sheet.

Incremental cash flows  Cash flows that occur because of undertaking the project  Not sunk barges … oops, I mean costs.  Opportunity cost  Side effects  Working capital

Net working capital  = cash + inventories + receivables - payables  a cost at the start of the project (in dollars of time 0,1,2 …)  a revenue at the end in dollars of time T-2, T-1, T.

Puts and calls before expiration  S, P, and C are the market values at time t before expiration T.  Xe -r(T-t) is the market value at time t of the exercise money to be paid at T  Traders tend to ignore r(T-t) because it is small relative to the bid-ask spreads.

Put call parity at expiration  Equivalence at expiration s + p = X + c  Values at time t in caps: S + P = Xe -r(T-t) + C  Write S - Xe -r(T-t) = C - P

No arbitrage pricing implies put call parity  If the relation does not hold, a risk-free arbitrage is available.  If S - Xe -r(T-t) > C – P, then  Sell the stock short, and also sell the put. Use the proceeds to buy the call and a bond paying X at expiration. The position is riskless. It nets the arbitrageur a positive sum. That violates no arbitrage pricing.  Similarly if inequality is in the other direction.

Internal rate of return  Definition: IRR is the discount rate that makes NPV = 0 That is, IRR is the r such that

IRR’s at r=1 and r=2. NPV r 100% 200%

Scale problems in IRR

Decision Tree for Stewart Pharmaceutical Do not test Test Failure Success Do not invest Invest The firm has two decisions to make: To test or not to test. To invest or not to invest.NPV = $3.4 B NPV = $0 NPV = –$91.46 m

The Option to Abandon: Example The firm has two decisions to make: drill or not, abandon or stay. Do not drill Drill Failure Success: PV = $575 Sell the rig; salvage value = $250 Sit on rig; stare at empty hole: PV = $0. Traditional NPV analysis overlooks the option to abandon. - $300

Covariance  It measures the tendency of two assets to move together.  Variance is a special case -- the two assets are the same.  Variance = expectation of the square of the deviation of one asset.  Covariance = expectation of the product of the deviations of two assets.

 RfRf E[R M ] Security market line 1 Rate of return expected by the market E[R j ]

Example of beta and NPV  Wingmar Inc. has a beta of 2.  The Market risk premium is 8.5%  The risk-free rate is 4%.  Wingmar has a project with cash flows - 100, 60, 80.  The project is typical of Wingmar’s core business.  Should the project be undertaken?

The Long-Term Financial Deficit (2002) Sources of Cash Flow (100%) Internal cash flow (retained earnings plus depreciation) 97% Long-term debt and equity 3% Uses of Cash Flow (100%) Capital spending 98% Net working capital plus other uses 2% Internal cash flow External cash flow Financial deficit

EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 Bust Normal Boom 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%

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

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

Channels $ of operating cash flows TCTC Corporate taxes 1-T B (1-T C )(1-T S ) TBTB TSTS Personal taxes Debt channel Equity channel

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

Summary: APV, FTE, and WACC APVWACCFTE Initial Investment AllAllEquity Portion Cash FlowsUCFUCFLCF Discount Rates r 0 r WACC r S PV of financing YesNoNo Which is best?  Use WACC and FTE when the debt ratio is constant  Use APV when the level of debt is known.

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?

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.

Beta measures risk  How much risk is added depends on the relation of  AM and     Define beta

Capital asset pricing model T-bill rate is known. Market premium is known, approximately 8.5%. Estimate beta as in the project

Security Market Line Expected return on security (%) Beta of security RmRm RfRf 1 M. 0.8 S. T. Security market line (SML) S is overvalued. Its price falls T is undervalued. Its price rises...

Event Studies: Dividend Omissions Efficient market response to “bad news” S.H. Szewczyk, G.P. Tsetsekos, and Z. Santout “Do Dividend Omissions Signal Future Earnings or Past Earnings?” Journal of Investing (Spring 1997)

Relationship among Three Different Information Sets All information relevant to a stock publicly available information past prices

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.