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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Year 1 Year 2

Cash Inflow $1,500 $ 500

Depreciation -$1,000 -$1,000

Accounting Income +$ 500 - $ 500

2

500 500Apparent NPV = 0 $41.32

1.10 (1.10)

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.

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Today Year 1 Year 2

Cash Inflow $1,500 $ 500

Project Cost -$2,000

Free Cash Flow -$2,000 +$1,500 + $500

2

$1,500 $500Cash NPV= $2,000 $223.14

(1.10) (1.10)

NPV: Cash Flows-Example

Which is correct?

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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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

Discounting Rule:Discounting Rule: 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 rate1+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?

1

2

3

1 82401.10

2 84871.10

3 87421.10

Year Cash Flow PV @ 10%

0 $ 8,000 $8,000

1 $ 8,000 x 1.03 = $ 8,240 $7,491

2 $ 8,000 x 1.03 = $ 8,487 $7,014

3 $ 8,000 x 1.03 = $ 8,742 $6,568

$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?

1

2

3

8,000

1.068

8,000

1.068

8,000

1.068

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

$29,073

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Include all Indirect Effects

Indirect Effect Rule:Indirect Effect Rule: You must include all indirect effects in your analysis.

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Sunk CostsSunk Cost– A cost that cannot be recovered

Sunk Cost Rule: Sunk Cost Rule: Always ignore sunk costs.

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Opportunity Costs

Opportunity Cost – Benefit or cash flow foregone as a

result of an action.

Opportunity Cost Rule: Opportunity Cost Rule: Be sure to recognize the opportunity cost (that which is foregone).

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Investments in Working Capital

Working Capital Rule:Working Capital Rule: 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

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Cash Flow from Operations: Three Methods of Calculation

• Method 1: Dollars in Minus Dollars Out

• Method 2: Adjusted Accounting Profits

• Method 3: Tax Shields

Operating Cash Flow = Revenue - Cash Expenses - Taxes

Operating Cash Flow (OCF) = After-tax Profit + Depreciation

OCF = (Revenue Cash Expenses) (1 Tax Rate)+(Tax Rate Depreciation)

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Calculating Cash Flow: ExampleYear 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 $156,375