Using
the NPV Rule (Chapter 6)
COMPUTING
CASHFLOWS FOR CAPITAL BUDGETING
·
What
you discount in capital budgeting: project’s incremental net cashflows
(net
cashflows with the project – net cashflows without the project)
o
Why
cashflows and not net income?
·
Initial
version of net cashflows:
REVENUES
-
COSTS
-
DEPRECIATION
-
INTEREST
=
EBT
-
TAX
=
NET INCOME
+
DEPRECIATION
=
OPERATING CASHFLOW
-
CAPITAL
INVESTMENT
=
NET CASHFLOW
·
Convention
followed in computing cashflows for capital budgeting –
Assume project is 100%
equity financed (ignore interest). Effect
of debt financing is accounted for separately.
·
Other
things to remember:
o
Use
tax depreciation, not reported depreciation
REPORTED
VERSION
TAX VERSION
(straight
line depreciation)
(accelerated
depreciation)
1000
EBDT
1000
- 200
DEP
- 400
= 800
EBT
= 600
- 280
TAX (35%)
- 210
= 520
N.I.
= 390
+ 200
DEP
+ 400
= 720
OCF
= 790
Net
Income looks better with straight line depreciation. Actual cashflows are
higher with accelerated depreciation (higher dep. reduces taxes).
So most firms use a different depreciation method in their financial statements
and a different method for tax purposes.
Cashflows depend on actual taxes paid. So we always use the tax
depreciation, not the reported depreciation.
o
Account for working capital
§ deduct
initial
working capital
§
deduct
increase in
WC each year
§ add
back recovery
of working capital in
the last year
e.g. You are
evaluating a 4 year project. Working
capital requirements will be $200 for the first year, $250 for the second
year, $275 for the third year and $320 for the last year. What are the corresponding net cashflows?
§
What
you need for a given year, has to be provided at the beginning of the year
§
Recovery
of WC comes at the end of the last year
o
Include
all incidental effects (how new project affects cashflows of existing business)
§
If the project increases the cashflows of the existing
business, that increase should be added to the project’s cashflows
§
If the project decreases the cashflows of the existing
business, that decrease should be subtracted from the project’s cashflows
o
Include
opportunity costs
§
If unused assets you own are used for a project, you charge
the project for the assets
§
Amount charged = current market value of the assets
§
That’s your opportunity cost of using the assets.
If you didn’t use them for the project, you could sell them today and
get this much. So this is the
amount you forego when you use them for the project
o
Ignore
sunk costs
§
They
are the same with or without the project, hence
there’s no incremental cashflow from taking the project
§
But typically most costs are partly sunk and partly
recoverable => ignore what is sunk component; include what is recoverable
e.g.
An investment of $45,000
was made in a project one year ago. A
change in market conditions makes you re-evaluate the project.
If the project is abandoned, you will recover 70% of the investment.
When you compute the NPV of the project today, how should you treat last
year’s investment?
Ignore the sunk cost = .3*45,000 = 13,500
Charge
the recoverable amount = 0.7*45,000 = 31,500
This is
the opportunity cost of continuing with the project, the amount you would
recover today if you dropped the project.
o
Ignore
allocated overheads (same with or without the project)
§ include only project’s incremental
overheads
o
Include
after-tax salvage cost
§ Tax is paid on the capital gain = sale price –
book value
·
Final
version of net cashflows:
REVENUES
-
COSTS
-
TAX
DEPRECIATION
=
EBT
-
TAX
=
NET INCOME
+
TAX DEPRECIATION
-
INCREASE IN WC
=
OPERATING CASHFLOW
-
CAPITAL
INVESTMENT
=
NET CASHFLOW
Remember
to:
·
Ignore
interest
·
Use
tax depreciation
·
Include
Working capital
·
Follow
the other rules
·
In
practice, net cashflows never grow at inflation rate (i.e., it is never helpful to do
capital budgeting in real terms)
o
Just
because you have 2% inflation doesn't mean all costs increase at this rate.
2% is the average inflation rate. Some costs increase more, some costs increase
less. E.g. labor costs may grow faster than raw materials. Your total
expenses will usually not increase at the inflation rate.
o
Revenues
will usually not increase at the inflation rate.
§
Your sales price may increase more or less than the inflation
rate
§
Number of units sold also usually increases over time
o
Even
if by some coincidence, revenue and expenses grow at the inflation rate,
depreciation does not grow with inflation at all.
So cashflows will still not grow at the inflation rate
EXAMPLE
After
$15,000 has been invested in a project at time –1, a change in market
conditions forces you to re-evaluate the project today (time 0).
60% of the amount already invested can be recovered if the project is
abandoned. Continuing with the
project will require an additional investment of $30,000 today.
The net income statement for time 1 is as follows:
Revenue
23,000
Manufacturing Cost -
11,000
Depreciation
- 2,400
Interest
- 3,200
PBT
6,400
Tax (@ 35%)
- 2,240
N.I.
4,160
The
working capital required for the first year is $2,500.
The working capital requirement for the second year will be 10% higher.
The income statement assumes straight line depreciation; the tax
depreciation for the year will be $3,600.
When
you re-evaluate the project today,
a)
What is the net cashflow at time 0?
b)
What is the net cashflow at time 1?
UNEQUAL
LIVES
·
You have to choose between two machines which produce the
same output.
A will cost $125, will last 3
years, and have after-tax operating expenses of $30/year.
B will cost $125, last 4 years, and
have after-tax operating expenses of $36/year.
If the required return is 10% which
machine is better?
·
If we compute PV of
costs for each machine, we get PVA =
199.61, PVB = 239.12
·
Cannot choose by comparing these numbers (PVA is
the cost of producing for 3 years, PVB is the cost of producing for 4
years)
·
We have to compute equivalent annual cost for each machine (EAC)
·
When we use machine A, the PV of all the costs over the 3
years is 199.61. When we compute
the EAC of the machine, we are asking: this is equivalent to spending how much
each year for 3 years? In other
words, EACA is the solution to the equation
EACA/(1+r) + EACA/(1+r)2
+ EACA/(1+r)3 = 199.61
Solving, we get EACA = 80.27
Buying A and operating it for 3
years and incurring costs with a PV of 199.61 is equivalent to renting it for 3
years at an after-tax rental of $80.27 per year. EAC is the fair rental value of the machine, or
the after-tax cost of using it per year
Similarly, EACB/(1+r) +
EACB/(1+r)2 + EACB/(1+r)3 + EACB/(1+r)4
= 239.12
=> EACB =
·
Implicit assumptions:
o
Firm
plans
to be in business indefinitely
o
If you choose machine
A today, then every 3 years you replace it by a new machine A.
Similarly, if you pick B today, then every 4 years you replace it by a
new machine B.
o
Cashflows for both
machines remain constant over time. (This
is reasonable only for real cashflows; nominal cashflows would grow over time
due to inflation => These problems can only be done using real cashflows and
the real discount rate)
=>
No
matter how many years you produce your product, if you choose A, it will cost
you $80.27/year forever. If
you choose B, it will cost you $ /year forever.
REPLACEMENT
DECISION
·
Not whether to replace, but when to replace
·
You have an existing machine that will last 3 more years.
It will produce the following after-tax operating cashflows (in real
terms): 450 today at time 0, 375 at time 1, 300 at time 2 and 200 at time 3.
A new machine will cost $1,500 to buy, will last 4 years and generate
after-tax operating cashflows (in real terms) of $723 per year. The real discount rate is 10%.
·
NPV of new machine = $791.81
Equivalent annual cashflow =
$249.79
(buying this machine, and
generating an NPV of 791.81 over its four year life is like getting $250 at the
end of each year for 4 years)
·
Today’s cashflow of $450 has already been earned.
Whether you replace the machine today or not only affects cashflows from
time 1 onwards:
0
1
2
3
4
a) Replace at time 0
450 250
250
250
250
b) Replace at time 1
450 375
250
250
250
c) Replace at time 2
450 375
300
250
250
d) Replace at time 3
450 375
300
200
250
clearly b is better than a, and c
is better than b. c is also better
than d
=> replace at time 2.
o
Replacing the machine
means that from the next year you start getting $250 from the new machine
instead of the actual cashflows of the old machine.
o
As long as the old
machine generates more than 250, don’t replace it.
o
For
the first two years the old machine generates more than $250, so you do not
replace.
o
The
third year it generates less than $250, so you replace it at the beginning of
the third year (i.e. time 2)
FLUCTUATING
LOAD FACTORS
·
When there are seasonal fluctuations in demand, you don't
produce at a uniform rate throughout the year
·
In this situation, if you have two identical machines to
replace, there are two obvious choices:
o
Replace
both
o
Replace
none
· But there’s a less
obvious third choice: replace just one machine. And, interestingly, due to the seasonal fluctuation in
production, you may be better off replacing one machine instead of both.
· There are 2 existing machines. The production capacity of each machine is 1000 units/year.
In fall/winter the machines produce at 100% of capacity (500 each).
In spring/summer, they produce at 50% of capacity (250 each).
The machines have an indefinite life.
Operating cost is $12 per unit.
·
New machines are available.
They would cost $50,000, would have the same production capacity, an
indefinite life and an operating cost of $8 per unit.
·
Required return is 5%
Keep old machines:
Annual operating cost = 2*750*12 =
18,000
PV of operating costs = 18,000/0.05
= 360,000
Replace both machines:
Initial investment = 2*50,000 =
100,000
Annual operating cost = 2*750*8 =
12,000
PV of operating costs = 12,000/0.05
= 240,000
Total PV of new machines = 100,000
+ 240,000 = 340,000
Replace just one machine:
The
new machine is cheaper per unit ($8 versus $12). In spring/summer you'll
use only the new machine to get the 500 units you need. In fall/winter
you'll both machines to get the 1000 units you need.
Output of new machine = 1,000;
output of old machine = 500
Initial investment = 50,000
Annual operating cost = 1000*8 +
500*12 = 14,000
PV of operating costs = 14,000/0.05
= 280,000
Total PV = 50,000 + 280,000 =
330,000
=> best to replace just one
machine.
This happens because you don’t
use both machines equally. If you
replace both machines, the marginal production of the second new machine is only
500 units, which is not cost-effective.
OPTIMAL
TIMING
·
With any project, there is an implicit choice: take the
project today or wait and take it in the future. Depending on how the NPV from taking it next year compares
with the NPV from talking it now, it may be better to wait.
·
You own a tract of timber.
You can harvest the trees today, or let them grow one more year and
harvest them next year, or the following year, etc. If the required return is 10%, when should you harvest?
Harvest
Date
0
1
2
3
4
NPV from harvesting
100 120
138 152
159
E(R) from waiting
20% 15% 10.1%
4.6%
If you wait for one year, you give
up an NPV of 100 today, in return for an NPV of 120 tomorrow.
100 today is the opportunity cost of earning the 120 tomorrow => 20%
return.
As long as E(R) from waiting >
required return, it’s better to wait.
=> harvest at time 3.
You could also compute
the PV today of the future NPVs you get by waiting:
Harvest Date
0
1
2
3
4
NPV from harvesting
100
120
138
152
159
PV0(future NPV)
109.09 114.05
114.20 108.60
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