1. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Cash Flows
Chapter 8 introduced valuation techniques
based on discounted cash flows.
This chapter develops criteria for properly
identifying and calculating cash flows.

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Identifying Cash Flows:
Cash Flow vs. Accounting Income
Discount actual cash flows, not necessarily net income.
Using accounting income, rather than cash flow, could
lead to erroneous decisions.

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NPV: Accounting Income -
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 flows to the NPV using accounting income.
Year 1 Year 2
Cash Inflow $1,500 $ 500
Depreciation -$1,000 -$1,000
Accounting Income +$ 500 - $ 500
+ + - =
Apparent NPV = 0 500 500 $41.32
2
1.10 (1.10)

5. 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 flows to the
NPV using accounting income.
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NPV: Cash Flows-Example
Today Year 1 Year 2
Cash Inflow $1,500 $ 500
Project Cost -$2,000
Free Cash Flow -$2,000 +$1,500 + $500
Cash NPV= - $2,000 + $1,500 + $500 = -
$223.14
2
(1.10) (1.10)
Which is correct?

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Incremental Cash Flows
 Discount Incremental Cash Flows
 Include All Indirect Effects
 Forget Sunk Costs
 Include Opportunity Costs
 Recognize the Investment in Working Capital
 Beware of Allocated Overhead Costs
 Remember Shutdown Cash Flows
Incremental
Cash Flow
Cash Flow
with Project
Cash Flow
= - without Project

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Inflation and Discounting Cash
Flows
DDiissccoouunnttiinngg RRuullee:: Real cash flows must be discounted at
a real discount rate, nominal cash flows at a nominal rate.
1 + real interest rate = 1+nominal interest rate
1+inflation rate

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Inflation Example:
Nominal Rates
Example
You own a lease that will earn you $8,000 next year, increasing at 3%
a year for 3 additional years (4 years total). If discount rates are 10%
what is the present value of the lease?
Year Cash Flow PV @ 10%
0 $ 8,000 $8,000
1 $ 8,000 x 1.03 1 = $ 8,240 8240
$7, 491
1.10
1
2 $ 8,000 x 1.03 2 = $ 8,487 8487
$7,014
1.10
2
3 $ 8,000 x 1.03 3 = $ 8,742 8742
$6,568
3
1.10
=
=
=
$29,073

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Inflation Example:
Real Rates Example (ctd)
You own a lease that will earn you $8,000 next year, increasing at 3% a year
for 3 additional years (4 years total). If discount rates are 10%, what is the
present value of the lease?
Year Cash Flow PV @ 6.80%
0 $ 8,000 $ 8,000
1 $ 8,000 $7,491
2 $ 8,000 $7,014
3 $ 8,000 $6,568
8,000
1.068
1
8,000
1.068
8,000
1.068
2
3
=
=
=
$29,073

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Include all Indirect Effects
IInnddiirreecctt EEffffeecctt RRuullee:: You must include all
indirect effects in your analysis.

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Sunk Costs
Sunk Cost
– A cost that cannot be recovered
SSuunnkk CCoosstt RRuullee:: Always ignore sunk costs.

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Opportunity Costs
Opportunity Cost – Benefit or cash flow foregone as a
result of an action.
OOppppoorrttuunniittyy CCoosstt RRuullee:: Be sure to recognize
the opportunity cost (that which is foregone).

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Investments in Working Capital
WWoorrkkiinngg CCaappiittaall RRuullee:: Investments in
working capital, just like investments in
plant and equipment, result in cash
outflows.
Common ways working capital is overlooked:
1. Forgetting about working capital entirely.
2. Forgetting that working capital may change during the life of the project.
3. Forgetting that working capital is recovered at the end of the project.

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Additional Considerations
1) Remember Terminal Cash Flows
2) Beware of Allocated Overhead Costs
3) Separation of Investment &
Financing Decisions

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Final Thought:
Incremental Cash Flows
Ask the following question:
Would the cash flow still exist if the project
does not exist?
If yes, do not include it in your analysis.
If no, include it.

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Calculating Cash Flows
Cash flows are made up of three separate parts.
Total cash flow =
+ cash flows from capital investments
+ cash flows from changes in working
capital + operating cash flows

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Calculating Cash Flows
Capital Investments
Changes in Working Capital
Operating Cash Flows  Operating cash flow =
Revenue – Costs – Taxes

18. Operating Cash Flow (OCF) = After-tax Profit + Depreciation
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Cash Flow from Operations:
Three Methods of Calculation
• Method 1: Dollars in Minus Dollars Out
Operating Cash Flow = Revenue - Cash Expenses - Taxes
• Method 2: Adjusted Accounting Profits
• Method 3: Tax Shields
OCF = (Revenue Cash Expenses) (1 Tax R - ´ - ate)+(Tax Rate´Depreciation)

19. 99--1199
Calculating Cash Flow: Example
Year 0 Year 1 Year 2 Year 3 Year 4
Fixed Assets
Purchase of Factory (sale in 4 years) -$100,000 $ 0 $ 0 $ 0 $ 50,000
Total Cash Flow from Fixed Assets -$100,000 $ 0 $ 0 $ 0 $ 50,000
Working Capital
CF from Inventory (- buildup,+ sell off) $ 0 -$ 20,000 -$ 10,000 $ 10,000 $ 20,000
CF from Accounts Receivable $ 0 -$ 35,000 -$ 25,000 $ 30,000 $ 30,000
Total Cash Flow from Working Capital $ 0 -$ 55,000 -$ 35,000 $ 40,000 $ 50,000
Operations
Revenues $ 0 $120,000 $125,000 $150,000 $150,000
Expenses $ 0 $ 60,000 $ 61,250 $ 70,000 $ 70,000
Depreciation $ 0 $ 12,500 $ 12,500 $ 12,500 $ 12,500
Pre-Tax Profits $ 0 $ 47,500 $ 51,250 $ 67,500 $ 67,500
After-Tax Profits (tax rate = 35%) $ 0 $ 30,875 $ 33,313 $ 43,875 $ 43,875
Total Cash Flow from Operations $ 0 $ 43,375 $ 45,813 $ 56,375 $ 56,375
Total Cash Flow -$100,000 -$11,625 $10,813 $ 96,375 $156,37
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