# Example ```Other Investment Criteria
and Free Cash Flows in
Finance
Capital Budgeting
Decisions
Fin351: lecture 5
Today’s agenda




Net Present Value (revisit)
Other two investment rules
Free cash flows calculation
A specific example
Net Present Value rule (NPV)



NPV is the present value of a project
minus its cost
If NPV is greater than zero, the firm
should go ahead to invest; otherwise
A hidden assumption: there is no budget
constraint or money constraint.
NPV (continue)
In other words:
Managers can increase shareholders’
wealth by accepting all projects that are
worth more than they cost.
Therefore, they should accept all
projects with a positive net present value
if there is no budget constraint.
Net Present Value
NPV = PV - required investment
C1
C2
Ct
NPV  C0 

...
1
2
(1  r )
(1  r )
(1  r ) t
Net Present Value
Example
You have the opportunity to
purchase an office building.
You have a tenant lined up
that will generate \$16,000 per
year in cash flows for three
years. At the end of three
years you anticipate selling the
building for \$450,000. How
much would you be willing to
pay for the building?
Net Present Value
\$466,000
Example - continued
\$450,000
\$16,000
\$16,000
\$16,000
0
1
2
3
Net Present Value
\$466,000
\$450,000
Example - continued
Present Value
14,953
14,953
380,395
\$409,323
0
\$16,000
\$16,000
1
2
\$16,000
3
Net Present Value
Example - continued
If the building is being
offered for sale at a price
of \$350,000, would you
generated by your
purchase and
management of the
building?
Net Present Value
Example - continued
If the building is being offered for sale at a price of
\$350,000, would you buy the building and what is the
management of the building?
16,000 16,000 466,000
NPV  350,000 


1
2
3
(1.07 ) (1.07 )
(1.07 )
NPV  \$59,323


An oil well, if explored, can now produce
100,000 barrels per year. The well will produce
forever, but production will decline by 4% per
year. Oil prices, however, will increase by 2%
per year. The discount rate is 8%. Suppose
that the price of oil now is \$14 for barrel.
If the cost of oil exploration is \$12.8 million, do
you want to take this project?
Solution

Visualize the cash flow patterns
C0=1.4, C1=1.37, C2=1.34, C3=1.31
What is the pattern of the cash flow?



• g=C1/C0 -1 =-0.0208=-2.1%
• PV( the project) =C0+C1/(r-g)=15
• NPV=PV( the project ) -12.8&gt;0
Two other investment rules


IRR rule
Payback period rule
IRR rule
Internal Rate of Return (IRR) – Single discount
rate at which NPV = 0.
IRR rule - Invest in any project offering a IRR
that is higher than the opportunity cost of
capital or the discount rate.
IRR rule
Example
You can purchase a building for \$350,000. The
investment will generate \$16,000 in cash flows
(i.e. rent) during the first three years. At the
end of three years you will sell the building for
\$450,000. What is the IRR on this investment?
Internal Rate of Return
Example
You can purchase a building for \$350,000. The investment will
generate \$16,000 in cash flows (i.e. rent) during the first three
years. At the end of three years you will sell the building for
\$450,000. What is the IRR on this investment?
16,000
16,000
466,000
0   350,000 


1
2
3
(1  IRR )
(1  IRR )
(1  IRR )
Internal Rate of Return
Example
You can purchase a building for \$350,000. The investment will
generate \$16,000 in cash flows (i.e. rent) during the first three
years. At the end of three years you will sell the building for
\$450,000. What is the IRR on this investment?
16,000
16,000
466,000
0   350,000 


1
2
3
(1  IRR )
(1  IRR )
(1  IRR )
IRR = 12.96%
Internal Rate of Return
200
150
IRR=12.96%
NPV (,000s)
100
50
0
-50
0
5
10
15
20
-100
-150
-200
Discount rate (%)
25
30
35
What’s wrong with IRR?
Pitfall 1 - Mutually Exclusive Projects
 IRR sometimes ignores the magnitude of the project.
 The following two projects illustrate that problem.
Example
You have two proposals to choose between.
The initial proposal (H) has a cash flow that
is different from the revised proposal (I).
Using IRR, which do you prefer?
Internal Rate of Return (1)
Example
You have two proposals to choose between. The initial
proposal (H) has a cash flow that is different from the revised
proposal (I). Using IRR, which do you prefer?
Project
H
I
C0
-350
-350
C1
400
16
C2
C3
16
466
IRR
14.29%
12.96%
NPV@7%
\$ 24,000
\$ 59,000
Internal Rate of Return
NPV  350 
16
1
(1  IRR)

16
(1  IRR)
2
IRR  12.96%
NPV  350 
IRR  14.29%
400
(1  IRR)1
0

466
(1  IRR)
3
0
What’s wrong with IRR (2)?
Pitfall 2 - Lending or Borrowing?
Example
project
C0
C1
IRR (%)
NPV at 10%
J
-100
+150
+50
+\$36.4
K
+100
-150
+50
-\$36.4
What’s wrong with IRR (3)?
Pitfall 3 - Multiple Rates of Return



Certain cash flows can generate NPV=0 at two
different discount rates.
The following cash flow generates NPV=0 at both (50%) and 15.2%.
Example
• A project costs \$1000 and produces a cash
flow
of \$800 in year 1, a cash flow of \$150 every year
from year 2 to year 5, and a cash flow of -150 in
year 6.
Payback period rule


Payback period is the number of
periods such that cash flows recover
the initial investment of the project.
The payback rule specifies that a
project be accepted if its payback
period is less than the specified cutoff
period. The following example will
demonstrate the absurdity of this rule.
Payback period rule
The following example shows that all the three projects have
a payback period of 2. If the payback period used by the
firm is 2, the firm can take project C and lose money.
Prj.
A
B
C
Cash Flows
C0
C1
C2
C3
-2000 +1000 +1000 +10000
-2000 +1000 +1000
0
-2000
0 +2000
0
Payback
2
2
2
NPV@10%
7,429
-264
- 347
Some points to remember in
calculating free cash flows
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Depreciation and accounting profit
Incremental cash flows
Change in working capital requirements
Sunk costs
Opportunity costs
Cash flows, accounting profit
and depreciation


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Discount actual cash flows
Using accounting income, rather than
cash flows, could lead to wrong
investment decisions
Don’t treat depreciation as real cash
flows
Example

A project costs \$2,000 and is expected
to last 2 years, producing cash income of
\$1,500 and \$500 respectively. The cost
of the project can be depreciated at
\$1,000 per year. Given a 10% required
return, compare the NPV using cash flow
to the NPV using accounting income.
Solution (using accounting
profit)
Cash Income
Depreciation
Accounting Income
Year 1
Year 2
\$1500
\$ 500
- \$1000 - \$1000
+ 500
- 500
500  500
Accounting NPV =

 \$41.32
2
1.10 (110
. )
Solution (using cash flows)
Today
Cash Income
Project Cost
- 2000
Free Cash Flow
- 2000
Year 1
Year 2
\$1500
\$ 500
+ 1500
+ 500
1500
500
Cash NPV = -2000 

 \$223.14
1
2
(1.10) (1.10)


When valuing a project, ignore how the
project is financed.
You can assume that the firm is financed
by issuing only stocks; or the firm has no
debt but just equity
Incremental cash flows



Incremental cash flows are the increased
cash flows due to investment
Do not get confused about the average cost
or total cost?
Do you have examples about incremental
costs?
Incremental
Cash Flow
=
cash flow
with project
-
cash flow
without project
Working capital




Working capital is the difference between a
firm’s short-term assets and liabilities.
The principal short-term assets are cash,
accounts receivable, and inventories of raw
materials and finished goods.
The principal short-term liabilities are
accounts payable.
The change in working capital represents
real cash flows and must be considered in
the cash flow calculation
Example

We know that inventory is working
capital. Suppose that inventory at year 1
is \$10 m, and inventory at year 2 is \$15.
What is the change in working capital?
Why does this change represent real
cash flows?
Sunk costs


The sunk cost is past cost and has
nothing to do with your investment
decision
Is your education cost so far at SFSU is
sunk cost?
Opportunity cost


The cost of a resource may be relevant
to the investment decision even when no
cash changes hands.
Give me an example about the
opportunity cost of studying at SFSU?
Inflation rule




Be consistent in how you handle inflation!!
Use nominal interest rates to discount
nominal cash flows.
Use real interest rates to discount real
cash flows.
You will get the same results, whether you
use nominal or real figures
Example
You own a lease that will cost you \$8,000 next
year, increasing at 3% a year (the forecasted
inflation rate) for 3 additional years (4 years
total). If discount rates are 10% what is the
present value cost of the lease?
1  real interest rate =
1+ nominal interest rate
1+inflation rate
Inflation
Example - nominal figures
Year Cash Flow
PV @ 10%
1
8000
8000
1.10
2
8000x1.03 = 8240
8240
1.102
8487 .20
1.103
8741.82
1.104
3
4
2
8000x1.03 = 8240
3
8000x1.03 = 8487.20
 7272.73
 6809.92
 6376.56
 5970.78
\$26,429.99
Inflation
Example - real figures
Year
Cash Flow
PV@6.7961%
1
8000
1.03
= 7766.99
7766.99
1.068
 7272.73
2
8240
1.032
8487.20
1.033
8741.82
1.034
= 7766.99
7766.99
1.0682
7766.99
1.0683
7766.99
1.0684
 6809.92
3
4
= 7766.99
= 7766.99
 6376.56
 5970.78
= \$26,429.99
How to calculate free cash
flows?

Free cash flows = cash flows from
operations + cash flows from the change
in working capital + cash flows from
capital investment and disposal
• We can have three methods to calculate cash
flows from operations, but they are the exactly
same, although they have different forms.
How to calculate cash flows
from operations?

Method 1
• Cash flows from operations =revenue –cost
(cash expenses) – tax payment

Method 2
• Cash flows from operations = accounting
profit + depreciation

Method 3
• Cash flows from operations =(revenue –
cost)*(1-tax rate) + depreciation *tax rate
Example
-
revenue
Cost
Depreciation
Profit before tax
Tax at 35%
Net income
1,000
600
200
200
70
130
Given information above, please use three methods to calculate
Cash flows
Solution:

Method 1

Method 2

Method 3
• Cash flows=1000-600-70=330
• Cash flows =130+200=330
• Cash flows =(1000-600)*(1-0.35)+200*0.35
=330
A summary example ( Blooper)

Now we can apply what we have
learned about how to calculate cash
flows to the Blooper example, whose
information is given in the following
slide.
Blooper Industries
Year 0
Cap Invest
1
2
3
4
5
6
10,000
WC
1,500
4,075
4,279
4,493
4,717
3,039
0
Change in WC
1,500
2,575
204
214
225
 1,678
 3,039
Revenues
15,000
15,750
16,538
17,364
18,233
Expenses
10,000
10,500
11,025
11,576
12,155
Depreciation
2,000
2,000
2,000
2,000
2,000
Pretax Profit
3,000
3,250
3,513
3,788
4,078
.Tax (35%)
1,050
1137
,
1,230
1,326
1,427
Profit
1,950
2,113
2,283
2,462
2,651
(,000s)
Cash flows from operations for
the first year
Revenues
15,000
- Expenses
10,000
 Depreciation
2,000
= Profit before tax
3,000
.-Tax @ 35 %
1,050
= Net profit
1,950
+ Depreciation
2,000
= CF from operations
3,950 or \$3,950,000
Blooper Industries
Net Cash Flow (entire project) (,000s)
Year 0
1
2
3
4
5
6
- 2,575
- 204
- 214
- 225
1,678
3,039
CF from Op
3,950
4,113
4,283
4,462
4,651
Net Cash Flow -11,500
1,375
3,909
4,069
4,237
6,329
Cap Invest
Change in WC
-10,000
-1,500
NPV @ 12% = \$3,564,000
3,039
```