Download Practice of Capital Budgeting

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
Money
Food
1
1
Time one
1 r
1 R
1 r
1 R 
1 i
1 r
1 i
Upshot
1 r
1 R 
1 i
ri
R
1 i
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
Purchase price
Maintenance cost
Salvage value
0
100
Total cost
100
1
2
3
20
20
20
12
20
20
8
Equivalent annuity at r = .1
Time
Cost
1/(1+r)^t
PV
Total PV
PVAF(.1,3)
Equivalent
0
1
2
3
100
20
20
8
1
0.909091 0.826446 0.751315
100
18.18182 16.52893 6.010518
140.7213
2.486852
56.5861 56.5861 56.5861
Overlap is correct
Time
Machine 1
Machine 2
…
EAC1
EAC2
0
1
2
3
4
5
6
100
20
20
8
100
20
20
8
56.6
56.6
56.6
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.
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
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)
 If
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.
.