Practice of capital budgeting

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Practice of capital budgeting - PowerPoint PPT Presentation

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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Presentation Transcript
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

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 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
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 zero

Time one

Money

Food

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 171-174.
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.
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.

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
• 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.

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
• 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
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 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
• 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
• 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.