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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.)

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practice of capital budgeting
Practice of capital budgeting
  • Monty Hall game
  • Incremental cash flows
  • Puts and calls
demonstration monty hall
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
Solution
  • The contestant should always switch.
  • Why? Because the host has information that is revealed by his action.
representation
Representation

switch and win

or

stay and lose

guess wrong

Nature’s move,

plus the contestant’s

guess.

pr = 2/3

pr = 1/3

guess right

switch and lose

or

stay and win

practice of capital budgeting5

Practice of Capital Budgeting

Finding the cash flows

for use in the NPV calculations

topics
Topics:
  • Incremental cash flows
  • Real discount rates
  • Equivalent annual cost
incremental cash flows
Incremental cash flows
  • Cash flows that occur because of undertaking the project
  • Revenues and costs.
focus on the decision
Focus on the decision
  • Incremental costs are consequences of it
  • Time zero is the decision point -- not before
application to a salvage project
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
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
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
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
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
Opportunity cost is
  • revenue that is lost when assets are used in the project instead of elsewhere.
example
Example:
  • The project uses the services of managers already in the firm.
  • Opportunity cost is the hours spent times a manager’s wage rate.
example16
Example:
  • The project is housed in an “unused” building.
  • Opportunity cost is the lost rent.
side effects
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
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
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
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
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
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
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)
slide24

Real and nominal interest

Time zero

Time one

Money

Food

discount
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
Why use real rates?
  • Convenience.
  • Simplify calculations if real flows are steady.
  • Examples pages 171-174.
valuing machines
Valuing “machines”
  • Long-lived, high quality expensive versus …
  • short-lived, low quality, cheap.
equivalent annual cost
Equivalent annual cost
  • EAC = annualized cost
  • Choose the machine with lowest EAC.
compare two machines
Compare two machines
  • Select the one with the lowest EAC
review
Review
  • Count all incremental cash flows
  • Don’t count sunk cost.
  • Understand the real rate.
  • Compare EAC’s.
no arbitrage theory
No arbitrage theory
  • Assets and firms are valued by their cash flows.
  • Value of cash flows is additive.
definition of a call option
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.
example37
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.
slide38

S = 80, call = 4

Pr. = .5

S = 70, call = 0

Pr. = .5

t = 1

t = 0

S = 75

Value of call = .5 x 4 = 2

definition of a put option
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.
example40
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.
slide41

S = 80, put = 0

Pr. = .5

S = 70, put = 6

Pr. = .5

t = 1

t = 0

S = 75

Value of put = .5 x 6 = 3

put call parity
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
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
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
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
No arbitrage pricing impliesput 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
Money pump
  • If S - Xe-r(T-t) = C – P + e, then S is overpriced.
  • Sell short the stock and sell the put. Buy the call.
  • You now have Xe-r(T-t) +e. Deposit the Xe-r(T-t) in the bank to complete the hedge. The remaining e 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
Money pump either way
  • If the prices persist, do the same thing over and over – a MONEY PUMP.
  • The existence of the e violates no arbitrage pricing.
  • Similarly if inequality is in the other direction, pump money by the reverse transaction.