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Capital Budgeting Part 2:Cash Flow Estimation

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Cash Flow Estimation

For project analysis (i.e., NPV, MIRR, PI), we use future cash flows

But how do we estimate these?

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Cash Flows vs. Accounting Income

Free Cash Flow

Cash flow available for distribution to all investors

Accounting Income

Total revenues minus total expenses

For capital budgeting, which one should we be concerned with?

Free Cash Flows!

Simply say project’s cash flows (CFs)

Key: focus on differences

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Incremental Cash Flows

Project’s incremental cash flow is:

Corporate cash flow with the project

Minus

Corporate cash flow without the project

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Summary of Adjustments to Cash Flows

Don’t adjust for:

Financing costs

Sunk costs

Make adjustments for:

Opportunity costs

Externalities

Depreciation

Net working capital

Inflation

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Proposed Project Data

$200,000 cost + $10,000 shipping + $30,000 installation

Economic life = 4 years

Salvage value = $25,000

Modified Accelerated Cost Recovery System (MACRS) 3-year class

Continued…

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Project Data (Continued)

Annual unit sales = 1,250

Unit sales price = $200

Unit costs = $100

Net working capital:

NWCt = 12% (Salest+1)

Tax rate = 40%

Project cost of capital = 10%

Inflation rate = 3%

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Cash Flow Table

Year 0 | Year 1 | Year 2 | …….. | Year N | |

Init. Cost | |||||

Op. CF | |||||

NWC CF | |||||

Salvage CF | |||||

Net CF | |||||

Fill in this table:

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Annual Sales and Costs

Year 1 | |

Units | 1,250 |

Unit Price | $200 |

Unit Cost | $100 |

Sales | $250,000 |

Costs | $125,000 |

Year 2 |

1,250 |

$206 |

$103 |

$257,500 |

$128,750 |

Year 3 |

1,250 |

$212.18 |

$106.09 |

$265,225 |

$132,613 |

Year 4 |

1,250 |

$218.55 |

$109.27 |

$273,188 |

$136,588 |

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What is an asset’s depreciable basis?

Basis = Cost

+ Shipping

+ Installation

$240,000

Any cost related to making the asset operational:

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Annual Depreciation Expense (000s) Using MACRS

Year | % X | (Initial Basis) | = Deprec. |

1 | 0.33 | $240 | $79.2 |

2 | 0.45 | 108.0 | |

3 | 0.15 | 36.0 | |

4 | 0.07 | 16.8 |

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Operating Cash Flows (Year 1)

Year 1 | |

Sales | $250,000 |

Costs | -125,000 |

Deprec. | -79,200 |

EBIT | $ 45,800 |

Taxes (40%) | -18,320 |

EBIT(1 – T) | $ 27,480 |

+ Deprec. | 79,200 |

Net Op. CF | $106,680 |

We add back depreciation because it does not affect our actual cash flows!

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What if we didn’t account for depreciation tax savings?

Year 1 | |

Sales | $250,000 |

Costs | -125,000 |

Deprec. | -79,200 |

EBIT | $ 45,800 |

Taxes (40%) | -18,320 |

EBIT(1 – T)+ Deprec.Net Op. CF | $ 27,480 79,200 $106,680 |

Year 1 | |

Sales | $250,000 |

Costs | -125,000 |

EBITDA | $125,000 |

Taxes (40%) | -50,000 |

EBITDA(1 – T)Net Op. CF | $ 75,000$ 75,000 |

Accounting for Depreciation

Ignoring Depreciation

Diff = $106,680 – $75,000 = $31,680 = $79,200 x 0.4

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Operating Cash Flows(Years 2, 3, and 4)

Year 2 | Year 3 | Year 4 | |

Sales | $257,500 | $265,225 | $273,188 |

Costs | -128,750 | -132,613 | -136,588 |

Deprec. | -108,000 | -36,000 | -16,800 |

EBIT | $ 20,750 | $ 96,612 | $119,800 |

Taxes (40%) | -8,300 | -38,645 | -47,920 |

EBIT(1 – T) | $ 12,450 | $ 57,967 | $ 71,880 |

+ Deprec. | 108,000 | 36,000 | 16,800 |

Net Op. CF | $120,450 | $ 93,967 | $ 88,680 |

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Cash Flows Due to Investments in Net Working Capital (NWC)

Sales | NWC(% of sales) | CF Due to Investment in NWC | |

Year 0 | $30,000 | -$30,000 | |

Year 1 | $250,000 | 30,900 | -900 |

Year 2 | 257,500 | 31,827 | -927 |

Year 3 | 265,225 | 32,783 | -956 |

Year 4 | 273,188 | 0 | 32,783 |

Additional NWC = 12% of next year’s sales:

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Salvage Cash Flow at t = 4 (000s)

Salvage Value | $25 |

Book Value | 0 |

Gain or loss | $25 |

Tax on SV | 10 |

Net Terminal CF | $15 |

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What if you terminate a project before the asset is fully depreciated?

Basis = Original basis – Accum. deprec.

Taxes are based on difference between sales price and tax basis

Taxespaid

–

Saleproceeds

Cash flowfrom sale

=

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Example: If Sold After 3 Years for $25 ($ thousands)

Original basis = $240

After 3 years, basis = $16.8 remaining

1st 3 years of dep = $223.2

Sales price = $25

Gain or loss = $25 – $16.8 = $8.2

Tax on sale = 0.4($8.2) = $3.28

Cash flow = $25 – $3.28 = $21.72

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Example: If Sold After 3 Years for $10 ($ thousands)

Original basis = $240

After 3 years, basis = $16.8 remaining

Sales price = $10

Gain or loss = $10 – $16.8 = -$6.8

Tax on sale = 0.4(-$6.8) = -$2.72

Cash flow = $10 – (-$2.72) = $12.72

Sale at a loss provides a tax credit, so cash flow is larger than sales price!

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Net Cash Flows

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | |

Init. Cost | -$240,000 | 0 | 0 | 0 | 0 |

Op. CF | 0 | $106,680 | $120,450 | $93,967 | $88,680 |

NWC CF | -$30,000 | -$900 | -$927 | -$956 | $32,783 |

Salvage CF | 0 | 0 | 0 | 0 | $15,000 |

Net CF | -$270,000 | $105,780 | $119,523 | $93,011 | $136,463 |

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NPV= $88,030

0

1

2

3

4

(270,000)

105,780

119,523

93,011

136,463

Project Net CFs Time Line

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What does “risk” mean in capital budgeting?

Uncertainty about a project’s future profitability

Will taking on the project increase the firm’s and stockholders’ risk?

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What three types of risk are relevant in capital budgeting?

Stand-alone risk

The project’s risk if it were the firm’s only asset and there were no shareholders

Corporate risk

Reflects the project’s effect on corporate earnings stability

Market risk

Reflects the project’s effect on a well-diversified stock portfolio

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What is sensitivity analysis?

Shows how changes in a variable such as unit sales affect NPV or MIRR

Each variable is fixed except one

Change this one variable to see the effect on NPV or MIRR

Answers “what if” questions, e.g. “What if sales decline by 30%?”

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-30 -20 -10 Base 10 20 30 (%)

88

NPV

($ 000s)

Unit Sales

r

Sensitivity Graph

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What are the weaknesses ofsensitivity analysis?

Does not reflect diversification

Says nothing about the likelihood of change in a variable, i.e. a steep sales line is not a problem if sales won’t fall

Ignores relationships among variables

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What is scenario analysis?

Examines several possible situations, usually worst case, most likely case, and best case

Provides a range of possible outcomes

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Best scenario: 1,600 units @ $240Worst scenario: 900 units @ $160

Scenario | Probability | NPV(000) |

Best | 0.25 | $279 |

Base | 0.50 | 88 |

Worst | 0.25 | -49 |

E(NPV) = $101.6 | ||

σ(NPV) = 116.6 | ||

CV(NPV) = σ(NPV)/E(NPV) = 1.15 |

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Are there any problems with scenario analysis?

Only considers a few possible out-comes

Assumes that inputs are perfectly correlated—all “bad” values occur together and all “good” values occur together

Focuses on stand-alone risk, although subjective adjustments can be made

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What is a simulation analysis?

A computerized version of scenario analysis that uses continuous probability distributions

Computer selects values for each variabl

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