CHAPTER 11
Cash Flow Estimation
And Chapter 12 Risk







Need to be in class for this ch.
Relevant Cash Flows
New Investment
Replacement Investment
Measuring Risk
Market Risk (Beta)
Project Risk Considerations
10-1
Capital Budgeting Processes

Capital budgeting process consists of the
following steps:



Determine (estimate) the expected cash flows of
available projects
Apply decision criteria such as NPV and IRR
In this class you are given all the
information to forecast cash flows but
they are subject to error

Estimating project cash flows is the most difficult and
error-prone part of capital budgeting
10-3
Example Proposed Project:





Cost: $200,000 + $10,000 shipping +
$30,000 installation. Depreciable cost:
$240,000.
Inventories will rise by $25,000 and
payables by $5,000.
Economic life = 4 years.
Salvage value = $25,000.
MACRS 3-year class.
10-4
Data/Assumptions

Sales: 100,000 units/yr @ $2.

Var. cost = 60% of sales.

Tax rate = 40%.

WACC = 10%.
10-5
Three “categories” of Cash Flow
Initial Cost, including installation and
change in net Working Capital
2. Operating Cash Flows
– Need: Returns/Savings
Tax Depreciation
– Set up a modified income statement
for each year
3. Terminal Cash Flow
– Need to consider taxes and return of
working capital
1.
10-6
Set up, without numbers, a time
line for the project’s cash flows:
0
Initial
Cost
CF0
1
OCF1
CF1
2
3
OCF2
OCF3
CF2
CF3
4
OCF4
+
Terminal
CF
CF4
10-7
Investment at t = 0: (Initial cost)
Equipment
-$200
Installation & Shipping
-40
Increase in inv.
-25
Increase in A/P
5
Net CF0
NWC = $25 - $5 = $20.
-$260
10-8
10-9
What’s the annual depreciation?
Depreciation
Initial Basis: $240,000
year percentage
1
0.33
2
0.45
3
0.15
4
0.07
Total
Depreciation
$ 79,200
$ 108,000
$ 36,000
$ 16,800
$ 240,000
Due to 1/2-yr conv., a 3-yr asset
is depreciated over 4 years.
10-10
Operating cash flows:
Operating Cash Flow
Item
Sales
Variable cost
net returns
less Depreciation
Year 1
$ 200,000
$ 120,000
$ 80,000
$ (79,200)
Year 2
$ 200,000
$ 120,000
$ 80,000
$ (108,000)
Year 3
$ 200,000
$ 120,000
$ 80,000
$ (36,000)
Year 4
$ 200,000
$ 120,000
$ 80,000
$ (16,800)
EBT
Less 40% Tax
$
$
800
(320)
$ (28,000)
$ 11,200
$ 44,000
$ (17,600)
$ 63,200
$ (25,280)
EAT
Dep add back
Operating CF
$
$
$
480
79,200
79,680
$ (16,800)
$ 108,000
$ 91,200
$
$
$
$
$
$
26,400
36,000
62,400
37,920
16,800
54,720
This is an income statement with no interest.
10-11
Net Terminal CF at t = 4:
Salvage Value
Tax on SV (40%)
Recovery of NWC
Terminal CF
$25000
-10000
20000
$35000
Q. Always a tax on SV?
Q. Ever a positive tax number?
Q. How is NWC recovered?
Tax on SV
Do a “side” calculation!
Selling Price
- adjusted basis
= Taxable gain (loss if negative)
x tax rate
= Tax (tax credit if negative)
• The tax basis when you sell an asset is the initial basis less
accumulated depreciation (adjusted basis).
•The sign (negative or positive) can be confusing. You just
have to think.
10-12
10-13
Calculator Workout

Draw the time line for this project and put
the cash flows on the time line (on board).
 Compute the NPV and IRR

Note we are skipping Profitability Index
10-14
IRR = 9.28%
10-15
What’s the Payback Period?
0
1
2
3
4
-260
79.7
91.2
62.4
89.7
-180.3
-89.1
-26.7
63.0
Cumul:
-260
Payback = 3 + 26.7 / 89.7 = 3.3 years.
Numbers slightly rounded to fit onto slide better.
10-16
Should CFs include int. expense?
Dividends?

No. The cost of capital is
accounted for by
discounting at the 10%
WACC, so deducting
interest and dividends
would be “double counting”
financing costs.
10-17
Suppose $50,000 had been spent
last year to improve the building.
Should this cost be included in the
analysis?
No. This is a sunk cost.
Analyze incremental investment.
10-18
Suppose the plant could be leased
out for $25,000 a year. Would this
affect the analysis?

Yes. Accepting the project means
foregoing the $25,000. This is an
opportunity cost, and it should be
charged to the project.
 A.T. opp. cost = $25,000 (1 - T) =
$25,000(0.6) = $15,000 annual cost.
10-19
If the new product line would
decrease sales of the firm’s other
lines, would this affect the analysis?
Yes. The effect on other projects’ CFs
is an “externality.”
 Net CF loss per year on other lines
would be a cost to this project.
 Externalities can be positive or neg.,
i.e., complements or substitutes.

Another Example
10-20

Given the following information, calculate
the NPV and IRR of a proposed project:
Cost = $40,000; estimated life = 3 years;
increase in accounts receivable = $10,000;
estimated salvage value = $10,000; net
income before taxes and depreciation =
$20,000 per year; method of depreciation =
3-year MACRS; tax rate = 40 percent;
required rate of return = 12 percent.

(see spreadsheet key LectExample.xls)
10-21
If this were a replacement rather
than a new project, would the
analysis change?
Yes. The cash flows would be the incremental
cash flow or changes in cash flow.
1. The old equipment would be sold now
2. You would calculate the change in revenue
and expenses.
10-22
3. The relevant depreciation would be
the change with the new equipment.
4. Also, if the firm sold the old machine
now, it would not receive the SV at
the end of the machine’s life.
Replacement Problem
10-23
9-3
Atlantic Control Company purchased a machine two years ago at a cost of
$70,000. At that time, the machine’s expected economic life was six years and its
salvage value at the end of its life was estimated to be $10,000. It is being depreciated
using the straight line method so that its book value at the end of six years is $10,000.
In four years, however, the old machine will have a market value of $0.
A new machine can be purchased for $80,000, including shipping and
installation costs. The new machine has an economic life estimated to be four years.
Three-year MACRS depreciation will be used. During its four-year life, the new
machine will reduce cash operating expenses by $20,000 per year. Sales are not
expected to change. But the new machine will require net working capital to be
increased by $4,000. At the end of its useful life, the machine is estimated to have a
market value of $2,500.
The old machine can be sold today for $20,000. The firm’s marginal tax rate is
40 percent. The appropriate required rate of return is ten percent.
a.
If the new machine is purchased, what is the amount of the initial investment
outlay at Year 0?
b.
What incremental operating cash flows will occur at the end of Years 1 through 4
as a result of replacing the old machine?
c.
What is the terminal cash flow at the end of Year 4 if the new machine is
purchased?
d.
What is the NPV of this project? Should Atlantic replace the old machine?
Problem 9-3 Key
10-24
10-25
Operating Cash flow
Item
1
2
3
4
Cost Savings
$20,000
$20,000
$20,000
$20,000
-Depreciation
change
-16,400
-26,000
-2000
--4400
EBT
3,600
-6000
18,000
24,400
-Taxes (40%)
-1440
--2400
-7200
-9760
EAT
2160
-3600
10,800
14640
Depreciation
add back
16,400
26,000
2000
-4400
Operating
Cash Flow
18560
22400
12800
10240
10-26
Cash Flows and NPV
K=10
10-27
Q.
If E(INFL) = 5%, is NPV biased?
CFt
Re v t  Cost t
NPV  

.
t
t
t  0 1  k 
1  k 
n
A. YES.
k = k* + IP + DRP + LP + MRP.
Inflation is in denominator but not in
numerator, so downward bias to NPV.
Should build inflation into CF forecasts.
10-28
What does “risk” mean in
capital budgeting?


Risk relates to uncertainty
about a project’s future
profitability.
Is NPV, IRR, large? Will taking
on project increase firm’s and
stockholders’ risk?
10-29
Chapter 12

Read chapter 12 for background on the
remaining slides in this set.
 There will not be a usual chapter
homework for chapter 12
 There will be questions on the chapter
handed out in lab.
10-30
Is risk analysis based on
historical data or subjective
inputs?

Can sometimes use historical
data, but generally can’t.
 So, risk analysis is usually based
primarily on subjective
judgment.
10-31
What three types of risk are
relevant in capital budgeting?
1.
Stand-alone risk
2.
Within-firm risk
3.
Market risk
10-32
How is each type of risk
measured, and how do they relate
to one another?
1.
Stand-Alone Risk:
Risk of the project if it were
investor’s only asset. Ignores
diversification. Measured by
the std. dev. or CV of NPV.
10-33
2. Within-Firm (Corporate) Risk:
Reflects the project’s effect on
corporate earnings stability.
Considers firm’s other assets
(diversification within the firm).
 Depends on (1) project’s std. dev.
and (2) its correlation with returns on
other projects.
 Measured by the project’s beta
versus total corp. earnings.

10-34
3. Market Risk:
Project’s risk to a well-diversified
investor. Takes account of firms’
and stockholders’ other assets.
Total diversification.
 Depends on project’s correlation
with the stock market. Stock
market beta.

10-35
How is each type of risk used?

Market risk is theoretically best.
 However, creditors, customers,
suppliers, and employees are
affected by within-firm risk.
 Therefore, within-firm risk is also
relevant.
10-36



Stand-alone risk is easiest to
measure, intuitive.
Core projects correlated with other
assets, so stand-alone risk reflects
within-firm risk; Maybe??
If project is correlated with the
economy, stand-alone risk also may
reflect market risk; Not likely??
10-37
What is sensitivity analysis?



Shows how changes in a
variable such as sales affect
NPV or IRR.
Each variable is fixed except for
one.
Change this one variable to see
effect on NPV or IRR.
10-38
Illustration
Resulting NPV (000):
Change from
Base Level
-30%
-20
-10
0(base)
+10
+20
+30
*Salvage Value
Unit Sales
-$36
-19
-2
15
32
49
66
SV*
$12
13
14
15
16
17
18
k
$34
28
21
15
9
3
-2
10-39
Sensitivity Graph
NPV (000s)
Unit sales
80
60
40
20
SV
0
k
-20
-40
-60
-30
-20
-10
0
10
20
30 % change
from base
Base
10-40


Steeper sensitivity lines show
greater risk. Small changes result
in large declines in NPV.
Unit sales line is steeper than
salvage value or k, so NPV is
more sensitive to changes in unit
sales than in salvage value or k.
10-41
Weaknesses of sensitivity analysis:
1.
2.
Does not reflect diversification.
Does not incorporate info. about
the likelihood of changing variables, i.e.,
steep sales line not a problem if sales
won’t fall.
Why useful?
1.
2.
Gives idea of project risk.
Identifies dangerous variables.
10-42
What is scenario analysis?


Examines several possible
situations, usually worst case,
most likely case, and best case.
Indicates range of possible
outcomes.
10-43
Assume we know all variables except
unit sales, which could range from
75,000 to 125,000 (or 75 to 125). Here
are the scenario NPVs:
Scenario
Probability
NPV (000)
Worst
0.25
-$27.8
Base
0.50
15.0
Best
0.25
57.8
E(NPV) =
(NPV) =
Problem 6 in lab
$15.0
$30.3
10-44
Standard Deviation:
NPV = $30.3
Coefficient of Variation:
CVNPV
 NPV
$30.3


 2 .0
ENPV $15
10-46
Define Monte Carlo simulation.


A type of scenario analysis
which brings in probabilities
of input variables.
Computer selects values for
variables based on probability
distributions.
10-47

NPV and IRR are calculated.

Process is repeated 1,000’s of times.

End result: Prob. distr. of NPV and
IRR.
10-48
Prob. Density
xxxxx
xxxxxxxxx
xxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxx
0
E(NPV)
NPV
10-49
Advantages of simulation
analysis?
•Reflects probability of each input.
•Shows range of NPVs, expected
NPV, NPV, and CVNPV.
•Simulation fairly easy to do with a
spreadsheet (@risk)
10-50
Disadvantages of simulation:

Difficult to specify probability
distributions and correlations. (If you
have historical data there is software
to help)
 If inputs are bad, output will be bad:
GIGO = Garbage In, Garbage Out!
10-51

Sensitivity, scenario, and
simulation analysis all ignore
diversification.
 Thus, they measure only
stand-alone risk.
10-52
Find the project’s market risk and
cost of capital based on the
CAPM, given these inputs:
Target debt ratio = 50%.
kd = 12%
Tax rate = 40%
kRF = 10%
BetaProject = 1.2
Market risk premium = 6%.
10-53

Beta = 1.2, so project has more market risk
than average.
 Project’s required return on equity:
ks  kRF  kM  kRF bp
 10%   6%12
.  17.2%.
WACCP  w dkd 1  T  w ceks
 0.512% 0.6  0.517.2%
 12.2%.
10-54
Project’s market risk vs. the firm’s
overall risk:

Project’s WACC = 12.2% vs.
company WACC = 10%.

Risk adjusted discount rate

So project’s market risk must be
greater than average.
Problem 15, Hudson Furniture in lab
10-55
Estimating project beta:
1.
Pure-play. Find several publicly
traded companies exclusively in
project’s business.
Use average of their betas as
proxy for project’s beta.
Hard to find such companies.
10-56
2. Accounting beta.
•Run regression between “project’s” rate of
return and S&P index rate of return.
•Accounting betas are correlated with market
betas. But hard to get data on projects’ rate
of return before the cap. bud. decision has
been made.
•Usually accounting data for a division of the
company is used for the “project”