Free Cash Flows in
Finance
Calculate future cash flows
Financial management: lecture 7
Today’s agenda


Review what we have learned in the last
week
How to calculate the cash flows in the future
Financial management: lecture 7
Some points to remember in
calculating free cash flows






Depreciation and accounting profit
Incremental cash flows
Change in working capital requirements
Sunk costs
Opportunity costs
Forget about financing
Financial management: lecture 7
Cash flows, accounting profit
and depreciation



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
Financial management: lecture 7
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.
Financial management: lecture 7
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
. )
Financial management: lecture 7
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)
Financial management: lecture 7
Forget about financing


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
Financial management: lecture 7
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
Financial management: lecture 7
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
Financial management: lecture 6
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?
Financial management: lecture 7
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?
Financial management: lecture 7
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?
Financial management: lecture 7
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
Financial management: lecture 7
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
Financial management: lecture 7
Inflation
Example - nominal figures
Year
Cost Flow
PV @ 10%
1
8000
8000
1.10
2
8000x1.03 = 8240
3
8000x1.03 2 = 8240
4
8000x1.033 = 8487.20
8240
1.102
8487.20
1.103
8741.82
1.104
 7272.73
 6809.92
 6376.56
 5970.78
$26,429.99
Financial management: lecture 7
Inflation
Example - real figures
Year
Cost 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
Financial management: lecture 7
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.
Financial management: lecture 7
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
Financial management: lecture 7
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
Financial management: lecture 7
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
Financial management: lecture 7
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.
Financial management: lecture 7
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)
Financial management: lecture 7
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
Financial management: lecture 7
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
Financial management: lecture 7
3,039