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’sguess.

pr =

2/3

guess w

rong

guess right

pr = 1/3

switch and winor

stay and lose

switch and loseorstay 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 zero Time one

Money

Food

1

1

r1

i

r

1

11 R

111

Rri

111

Rri

Upshot

Rr ii

1

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.

Costs of a machine

Time 0 1 2 3Purchase price 100Maintenance cost 20 20 20Salvage value 12

Total cost 100 20 20 8

Equivalent annuity at r = .1

Time 0 1 2 3Cost 100 20 20 8

1/(1+r) t̂ 1 0.909091 0.826446 0.751315PV 100 18.18182 16.52893 6.010518

Total PV 140.7213PVAF(.1,3) 2.486852Equivalent 56.5861 56.5861 56.5861

Overlap is correct

Time 0 1 2 3 4 5 6

Machine 1 100 20 20 8Machine 2 100 20 20 8…EAC1 56.6 56.6 56.6EAC2 56.6 56.6 56.6

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 = 0Pr. = .5

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 = 6Pr. = .5

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 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 + , 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.

.