Practice of capital budgeting  Monty Hall game  Incremental cash flows  Puts and calls

Demonstration: Monty Hall  A prize is behind one of three doors.  Contestant chooses one.  Host opens a door that is not the chosen door and not the one concealing the prize. (He knows where the prize is.)  Contestant is allowed to switch doors.

Solution  The contestant should always switch.  Why? Because the host has information that is revealed by his action.

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

Practice of Capital Budgeting Finding the cash flows for use in the NPV calculations

Topics:  Incremental cash flows  Real discount rates  Equivalent annual cost

Incremental cash flows  Cash flows that occur because of undertaking the project  Revenues and costs.

Focus on the decision  Incremental costs are consequences of it  Time zero is the decision point -- not before

Application to a salvage project  A barge worth 100K is lost in searching for sunken treasure  Sunken treasure is found in deep water.  The investment project is to raise the treasure  Is the cost of the barge an incremental cost?

The barge is a sunk cost (sorry)  It is a cost of the earlier decision to explore.  It is not an incremental cost of the decision to raise the treasure.

Sunk cost fallacy is  to attribute to a project some cost that is  already incurred before the decision is made to undertake the project.

Product development sunk costs  Research to design a better hard drive is sunk cost when …  the decision is made to invest in production facilities and marketing.

Market research sunk costs  Costs of test marketing plastic dishes in Bakersfield is sunk cost when …  the decision to invest in nation-wide advertising and marketing is made.

Opportunity cost is  revenue that is lost when assets are used in the project instead of elsewhere.

Example:  The project uses the services of managers already in the firm.  Opportunity cost is the hours spent times a manager’s wage rate.

Example:  The project is housed in an “unused” building.  Opportunity cost is the lost rent.

Side effects:  Halo  A successful drug boosts demands for the company’s other drugs.  Erosion  The successful drug replaces the company’s previous drug for the same illness.

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.

Real and nominal interest rates:  Money interest rate is the nominal rate.  It gives the price of time 1 money in dollars of time 0.  A time-1 dollar costs 1/(1+r) time-0 dollars.

Roughly:  real rate = nominal rate - inflation rate  4% real rate when bank interest is 6% and inflation is 2%.  That’s roughly, not exactly true.

Real interest rate  How many units of time-0 goods must be traded …  for one unit of time-1 goods?  Premium for current delivery of goods  instead of money.

Inflation rate is i  Price of one unit of time-0 goods is one dollar  Price of one unit of time-1 goods in time-1 dollars is 1 + i.  One unit of time-0 goods yields one dollar  which trades for 1+r time-1 dollars  which buys (1+r)/(1+i) units of time-1 goods

Real rate is R  One unit of time-0 goods is worth (1+R) units of time-1 goods  1+R = (1+r)/(1+i)  R = (1+r)/(1+i) - 1  Equivalently, R = (r-i)/(1+i)

Real and nominal interest Time zeroTime one Money Food

Upshot

Discount  nominal flows at nominal rates  for instance, 1M time-t dollars in each year t.  real flows at real rates.  1M time-0 dollars in each year t.  (real generally means in time-0 dollars)

Why use real rates?  Convenience.  Simplify calculations if real flows are steady.  Examples pages

Valuing “machines”  Long-lived, high quality expensive versus …  short-lived, low quality, cheap.

Equivalent annual cost  EAC = annualized cost  Choose the machine with lowest EAC.

Costs of a machine

Equivalent annuity at r =.1

Overlap is correct

Compare two machines  Select the one with the lowest EAC

Review  Count all incremental cash flows  Don’t count sunk cost.  Understand the real rate.  Compare EAC’s.

No arbitrage theory  Assets and firms are valued by their cash flows.  Value of cash flows is additive.

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 75.  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 = 75 S = 80, call = 4 S = 70, call = 0 Pr. =.5 Value of call =.5 x 4 = 2

Definition of a put option  A put 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.

Example  A share of IBM sells for 75.  The put has an exercise price of 76.  The value of the put seems to be 1.  In fact, it is more than 1 and in our example equal to 3.

t = 0 t = 1 S = 75 S = 80, put = 0 S = 70, put = 6 Pr. =.5 Value of put =.5 x 6 = 3

Put-call parity  S + P = X*exp(-r(T-t)) + C at any time t.  s + p = x + c at expiration  In the previous examples, interest was zero or T-t was negligible.  Thus S + P=X+C  75+3=76+2  If not true, there is a money pump.

Puts and calls as random variables  The exercise price is always X.  s, p, c, are cash values of stock, put, and call, all at expiration.  p = max(X-s,0)  c = max(s-X,0)  They are random variables as viewed from a time t before expiration T.  X is a trivial random variable.

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 (time T) 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 in market prices  Put call parity already holds by definition in expiration values.  If the relation does not hold, a risk-free arbitrage is available.

Money pump  If S - Xe -r(T-t) = C – P + , then S is overpriced.  Sell short the stock and sell the put. Buy the call.  You now have Xe -r(T-t) +  Deposit the Xe -r(T-t) in the bank to complete the hedge. The remaining  is profit.  The position is riskless because at expiration s + p = X + c. i.e.,  s+max(0,X-s) = X + max(0,s-X)

Money pump either way  If the prices persist, do the same thing over and over – a MONEY PUMP.  The existence of the  violates no arbitrage pricing.  Similarly if inequality is in the other direction, pump money by the reverse transaction.

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