ch10 measuring cash flow

Chapter 10

MEASURINGCASH FLOW

Alex Tajirian

Capital Budgeting CFs 10-2

© morevalue.com, 1997

1 OBJECTIVE

# We already know criteria for selecting projects (payback, NPV,IRR).

What are the relevant CFs in the analysis of capital budgeting?

# What is involved in calculating NPV?

! # of CF periods (this chapter)

! amount of CFs (this chapter)

! risk of use of CF

# Accounting vs. Financial/Economic Valuation

L Still assume that “k” (cost of financing) is given.

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incremental / additional

The only relevant CFs for a project are incremental CFs. They consist of any and all changes in the firm’s futureCFs that are a direct consequence of taking the project.

2 WHAT ARE A PROJECT’S CFs?

2.1 Basics

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2.2 A CLOSER LOOK AT INCREMENTAL CFs

2.2.1 INCLUDE OPERATING OPPORTUNITY COST

! Definition: CF generated from assets the firm already owns.Distinguish this from financing opportunity cost--"k".

! Example: Opportunity Cost

Suppose company already has extra storage space. Is storagecost for the project = 0?

No, you have to include storage cost, as if you had to go andrent space for the particular project.

! Financial accounting does not consider opportunity cost.

? Should cost be estimated as the market value or purchase price?

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2.2.2 INCLUDE NET WORKING CAPITAL (NWC)

## Definition:

NWC = current assets - current liabilities

= C/A - C/L

## Why include NWC?

! Projects usually require investment in A/R and inventory assales _.

! Investment in C/A is recoverable at end of project as A/R iscollected and inventory sold.

Example: Incremental CFs due to change in NWC

Given the following info from Income Statement:

A/R Jan 95 A/R Dec 95

$50 $80

CF = ?

Solution: 80 - 50 = 30

$30 is cash outflow; as if firm is lending $30.

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2.2.3 Operating Cash Flow (OCF)

## Definitions

!! Revenue = R = (price of product)(Quantity sold)

! Operating Cost = C = fixed cost + variable cost

fixed cost = overhead

variable cost1 = salaries, employee benefits, unsolddefective products, etc.

Example:

Sales 1994 Sales 1995 Incremental CFs in 1995

$120 $200 ? = $200

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2.2.4 FORGET ABOUT SUNK COSTS

# Definition: Costs that cannot be recovered

# Illustrations

! marketing expenditure

! existing railroad tracks

! You spent $2,000 on your old Moscovich car yesterday.Suppose it broke down again today and it would cost you$2,500 to re-fix. If your car was in running condition, it wouldbe worth $2,200. The junkyard would only pay you $200.Repair or scrap?

The $2,000 you spent on the original repair is irrelevant (sunkcost).

# Financial accounting does not consider sunk cost.

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2.2.5 CONSIDER IMPACT ON THE ENTIRE FIRM.side effects / spillovers/ externalities

! Effect on other parts (divisions/projects) of the firmQ negative (cannibalization)

e.g., The introduction of a new software version

Q positive (network effects)e.g., Make your “system” compatible with others.

! General Example: Project Impact on Entire FirmYou own a jazzercise enterprise for women. If you includemen, you will obtain new source of revenue. Should youundertake the project?

New proposal can _ or ` in women patronage.

2.2.6 CONSIDER POTENTIAL OF CREATING NEWPRODUCTS IN THE FUTURE

Note: This is easier said than done. Easy methods toincorporate these effects are not available yet. Theyinvolve game theory and option pricing. However, thisdoes not mean that you should ignore them!

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2.2.7 INTEREST EXPENSE NOT INCLUDED AS CF

! Cost of financing is reflected in the process of discounting theCFs -- k.

! Obviously the higher the cost of financing, the higher the k.Thus, the lower the PV.

! That is why it is possible to separate the investment and thefinancing decisions.

! In practice, firms calculate NPV as if there will be no debtfinancing, then decide on how to best finance the project.

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3 SPECIAL APPLICATIONS: REPLACEMENT & PURCHASE OF NEW ASSETS

3.1 INVESTMENT-RELATED OUTLAYS# Initial (t = 0)

! investment in plant & equipment (I0) ! After-tax value of sale of equipment in asset-replacement

problem.

## Terminal (time = end of project)

! After-tax salvage or sale value of plant and equipment at endof project

3.2 CHANGES IN NET WORKING CAPITAL (NWC); short-term

# Definition

NWC = Current Assets - Current Liabilities

NWC = C/A - C/L

) NWC = ) C/A - ) C/L

) / change in/ additional / incremental change in

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3.3 Operating Cash Flow (OCF)

# Approach 1

OCF = Revenue - Operating Cost - Tax Bill

= R - C - (tax rate) ( R - C - Depreciation) . . . . . . .(*)

= ® - C) - T ® - C) + T x D

= ® - C) (1 - T) + T x D

= (Revenue - Operating Cost)(1 - tax rate) + (tax rate) x (Depreciation)

= after-tax profits + depreciation tax shield

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OCF ' R & C & Tax bill' (R & C)(1 & T) % T × Depreciation' EBIT × (1 & T) % Depreciation

# Approach 2

From equation (*) above

OCF = ® - C) - T® - C - D)

= ® - C) - T® - C - D) + (D - D)

= ® - C - D) - T® - C - D) + D

= EBIT (1 - T) + Depreciation

where,

EBIT = Earnings Before Interest & Taxes

ˆ̂

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CF ' OCF & ) NWC & I' Operating CF & change in Net Working Capital & Inital outlays' cash inflow & cash outflow

Putting all the above components together, we have,

Notes.

! ) NWC > 0 means cash outflow.

! _ in investment outlays is cash outflow.

! Cost of financing a project is not included as a CF. It isreflected in the cost of capital (k).

! if CL _ Y a cash in-flow

! You subtract ) NWC because an _ in NWC is a cash-outflow--short-term investment. Obviously, I is also subtracted --long-term cash outflow.

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Example: Two Approaches to Calculating OCF

Given: tax rate = T = 40%

Project Income Statement

Revenue $100

Depreciation (D) 20

All other operating costs 40

EBIT 40

Solution:

# Approach 1

OCF = ® - C)(1 - T) +(T)(Depreciation)

OCF = ($100 - $40) (.6) + (.4) ($20)

= $36 + $ 8 = 44

# Approach 2

OCF = EBIT(1 - T) + Depreciation

OCF = $40 ( 1 - .4) + 20 = 40 (.6) + 20

= 24 + 20 = 44

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Example: Two Approaches to CF Calculation

Given: For simplicity, assume depreciation = T = 0, capital spending= 0. R = $500, C = $310, and A/R, A/P are given below.

Y only two sources of CFs

# first source: OCF

OCF = ® - C)(1 - T) + Tax x Depreciation

= (500 - 310)(1 - 0) + 0 = 190

# second source: ) NWC

Given ?

Beginning End Change

A/R $880 $910 30

A/P 550 605 55

NWC 330 305 -25

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Solution: Two approaches

# CF = OCF - ) NWC - capital spending = 190 - (-25) - 0 = 215

# Solution based on cash in- and outflows:

cash inflow = Sales - ) A/R = 500 - 30 = 470cash outflow = Cost - ) A/P = 310 - 55 = 255

Net CF = 215

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4 HOW MANY YEARS SHOULD YOU USE?

# In practice, this is very hard to determine. Strategic considerationsare very important. (FI 320)

# Depends on Economic Life of asset in consideration. Thegovernment sets depreciation schedule. Obviously, if salvage valueafter being fully depreciated is zero, then economic life = years ofdepreciation.

# For this class:

! economic life / useful life / # of years of CFs generated byproject

! You will be given this number.

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5 UN-EQUAL LIVES PROBLEM.

5.1 Illustration

You are planning to spend 4 years in Moscow and need to own a car forthe entire duration. After some search, you have narrowed down yourchoices to a Ferrari and a Moscovich. The latter is expected to last onlytwo years. The CFs from the two cars are below. Which car would youbuy?

Net Cash Flow Year Moscovich Ferrari0 ($100,000) ($100,000)1 60,000 33,5002 60,000 33,5003 0 33,5004 0 33,500

Solution with no finance background:at k = 10%, NPVMoscovich = $4,130

NPVFerrari = -$100,000 + $33,500 (PVIFA10%,4) = $6,191

Approach is

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5.2 Solutions to Un-equal Lives Problem:

un-equal lives ] one of the projects is generating CFs over longertime horizon and you need CFs over the entire time Y need to re-purchase short-life asset in the future.

5.2.1 Solution 1:

# Project Moscovich:

! Since the project provides CFs over only 2 years, you need tore-purchase another car after two years.

! Assume that cost of re-purchase and CFs do not change.

0 1 2 3 4

CFs from firstpurchase

-100,000 60,000 60,000

CFs fromre-purchase

-100,000 60,000 60,000

Net CFs -100,000 60,000 -40,000 60,000 60,000

Using above CFs, k = 10% NPVMoscovich = 7,547

# From previous calculation: NPVFerrari = 6,190

ˆ̂ choose Moscovich, since higher NPV

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EAA 'Original NPV

PVIFAk,original life

EAAMoscovich '$4,132

PVIFA10%,2

'$4,1321.7355

' $2,381

EAAFerrari '6,190

PVIFA10%,4

'6,190

3.1699' $1,953

5.2.2 Solution 2: Equivalent Annual Annuity (EAA)

Method is based on continuous replacement (re-purchase). Thistechnique is used to simplify the problem of having to make livesequal.

ˆ̂ choose one withhighest EAA.

YY

Ferrari =

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6 ACCOUNTING vs. FINANCIAL VALUATION

! Accounting ignores CF timing, risk, and operating opportunity cost.

! Also, earnings or income are not good measures of performance asaccounting numbers can be manipulated. An example would bechanging from LIFO to FIFO.

IllustrationRevenue 510Cost 310

Net Income 200

Beginning End ChangeAR 880 1,390 510AP 0 0 0

ˆ̂ Cash inflow = Revenue - )AR = 510 - 510 = 0Cash outflow = Cost - )AP = 310 - 0 = 310Net CF = 0 - 310 = - 310

Thus, although the division is making money in an accounting sense(earnings), it is not in an economic sense.

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7 EXAMPLE: PURCHASE OF A NEW ASSET

Given: Data on Proposed New Asset

MACRS depreciation 3-year

Economic life 4 years

Price $100,000

Freight & Installation $20,000

Salvage Value $30,000 in year 4

Effect on NWC Increase inventories by $10,000

Effect on operating costs Decrease by $50,000 per year

Tax rate 40%

Project cost of capital 10%

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Solution:

periods

0 1 2 . . . N

InitialOutlay

initialoutlays

OCF-

)NWCOCF -))NWC

Terminal Outlays TerminalOutlays

net CFs net CFs

Step 1: Calculate initial Outlay (t=0)Price ($100,000)Freight & installation (20,000)) NWC (10,000)Net initial outlay (130,000)

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1 Depreciation factors depend on the appropriate depreciation schedule. They are givenAppendix. Depreciation includes all costs incurred to bring the purchased asset to an operationalcondition.

2 (33%) x ($120,000)


Example: Purchase Of Asset (Continued) Step 2: Calculate Depreciation1 Schedule (MACRS)

Net cost = price + freight & installation = $120,000

Given Need to Calculate

Year Factor Depreciation =(factor)(Net cost)

Book Value =Net cost - Total Depreciation

1 33% 239,600 120,000 - 39,600

2 45 54,000 120,000 - (39,600 + 54,000)

3 15 18,000 ...

4 7 8,400 0

$120,000

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Step 3: Calculate # of periods: n = 4 years, since economic life = 4, and sold in year 4.

Step 4: Calculate CF =- Initial Outlays + (OCF - )NWC) - Terminal Outlays

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Example: Purchase Of Asset (Continued)

periods

0 1 2 3 4

initial outlay (130,000)

(R-C)(1-T) 30,000 030,000 30,000 0 30,000

(Tax) x (Depreciation) 15,840 21,600 7,200 3,360

OCF 45,840 51,600 37,200 33,360

Salvage value 30,000

tax on salvage value (12,000)

NWC recovery 10,000

Net CF (130,000) 45,840 51,600 37,200 61,360

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NPV ' &130,000 %45,840(1% .1)

%51,600

(1% .1)2% ... % 61,360

(1% .1)4

' &130,000 % 45,850×[PVIF10%,1] % ... % 61,360×[PVIF10%,4]

Step 5: Calculate NPV

= $24,176; IRR = 18.1%

Note:(R-C)(1-T) = (0 - (- $50,000))(1-.4) = $30,000Tax x Depreciation = .4(39,600) = $15,840 in year 1Salvage Value Tax = (Salvage Value - Book Value) (T)

= (30,000 - 0) (.4) = $12,000

Remember to distinguish between the different costs: 7

! investment costs (long-term)

! operating costs (OCF)

! cost of capital (k)

! NWC costs

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1.Varies with the quantity of output produced.

8 Endnotes

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9 QUESTIONS

I. True/False-Explain

1 A NPV > 0 project might end up with NPV < 0 if external financing were to be used.

2 An increase in inventories is a cash outflow.

3 Suppose company X has AR=$90 at the end of 1991. Thus, AR CF is necessarily $90.

4 Quayle Potatos Inc. is a one man "cash and carry business." If revenues are > operatingexpenses, the firm should stay in business.

5 An increase in inventory is a cost to the firm. So is an increase in operating costs. Thus, thereis no compelling reason to distinguish between these two costs. Costs are costs!

6 If the government increases depreciation allowance, it should have no impact on the value of afirm since depreciation is not a cash flow.

7 NPV analysis can be easily applied by managers of the newly "emerging democracies."

8 It does not make sense to use NPV in project analysis, since you never really know how longyou would be using the machine.

9 The source of project finance is irrelevant because it has no impact on a project's CFs.

10 An increase in NWC is a cash outflow.

11 If the acquisition of a new computer reduces the cost of inventory tracking, then undertakingthe project would decrease NWC, other things equal.

12 If sales (# of items sold) from a project increase over time, then it makes sense to anticipate acorresponding increase in NWC.

13 If a project's Revenue increases from $50 to $60, then cash inflows necessarily increase by $10.

14 If a project were to be financed by issuing new equity, then floatation cost have to be includedas part of the project CFs.

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II. NumericalThe purpose of the numerical questions is to ensure that:

a. you understand the different types of costs and how they influence valuation.b. What is and is not a CF.c. you know how to correctly substitute in the NPV equation.

1. Machine PurchaseYou are interested in the purchase of a machine that costs $100,000. The machine has aneconomic life of 4 years, with 3-year MACRS depreciation. However, you expect to sell it after3 years at a salvage value of $8,000. The machine requires an increase in inventory by $10,000.While in operation, the machine will generate $10,000 annually and it would cost $2,000 tooperate. If the corporate tax rate is 40%, and k = 20%, should the machine be purchased?

2. Machine ReplacementYou are considering the replacement of an existing machine that has been fully depreciated. Itcan be sold for $10,000. The cost of the new machine is $100,000.The machine has aneconomic life of 4 years, with 3-year MACRS depreciation. However, you expect to sell it after3 years at a salvage value of $8,000. The machine requires an increase in inventory by $10,000.While in operation, the machine will generate $10,000 in revenue annually and it would cost$2,000 to operate. If the corporate tax rate is 40%, and k = 20%, should the machine bereplaced?

3.H Machine ReplacementYou bought a machine 4 years ago at $100,000 that is being depreciated straight line over its 5-year life. The machine has a salvage value of $30,000. You are now considering its replacementwith a new $110,000 machine, which would reduce annual operating costs from $60,000 to$25,000. The new machine, which requires an additional $10,000 in modification costs, has aneconomic life of 3 years and would be straight line depreciated. On a time line write down therelevant CFs for the replacement analysis, assuming a 40% tax rate.

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4. Given the following end-of-period information (in $000s) on a project, write down the relevantannual CFs.

1989 1990 1991 1992

Cost of machine 14

Machine Modification Costs 1 1

Revenue 10 20 40

Operating Cost 5 10 15

Inventory 1 2 2

Depreciation 8 5 2

Tax rate (40%)

5. Due to difficult economic conditions, a clothing store is considering some cost cuttings. Theircurrent annual sales are at $1m., operating costs at $700,000, and inventory at $100,000. Theowners' proposal for the next 3 years is to cut inventory in half and reduce operating costs by$25,000. Due to cutbacks, they expect to lose 30% of their sales. The owners are at a 30%average tax rate.(a) You were hired as a consultant for the project. Given the above scenario provided to

you, would you recommend the proposal?(b) Can you come up with a better proposal?

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ANSWERS TO QUESTIONS

I. Agree/Disagree-Explain

1. Disagree. When you calculate NPV you better use the appropriate cost of capital. In this case,it looks like you used the wrong number and ended up with project NPV > 0.

2. Agree. An increase in inventories is a short-term investment. Thus, a cash-outflow.

3. Disagree. We should look at incremental cash flow, that is the difference between AR at end of1991 and beginning of 1991.

4. Disagree. Whoever is doing the analysis is forgetting to include the owner's salary--opportunitycost. If you include opportunity cost, then NPV might turn out to be negative.

5. Disagree. The reason for the distinction is in calculating tax CF. NWC does not influence thetax bill, while operating costs do.

6. Disagree. Although depreciation is not a CF, it enters into the calculation of OCF through thetax bill the firm has to pay. Thus, depreciation _Ytax bill ` Y CF_ Y NPV_.

7. Disagree. Although NPV is still very useful, the difficulty lies in estimating CFs and the discountrate. With no financial markets, it is very difficult to determine the required rates of return thatwe take for granted in the U.S.

8. Disagree. It does make sense. The number of years you use in the analysis is the best estimateyou have. As we shall see in the next chapter, you can analyze different scenarios.

9. Disagree. Although it does not affect the CFs, it does impact the NPV calculation through tocost of capital (k). Thus, it is relevant.

10. Agree. An increase in NWC is a short-term investment. Thus, it is a cash outflow.

11. Disagree. Inventory tracking costs are part of operating costs. Thus, NWC would not beaffected.

12. Agree. When sales increase, the firm has to incur additional AR and inventory. Although APmight increase too, such an increase need not be enough to offset the increase in CA. Thus,NWC tends to increase.

13. Disagree. When Revenue increases, it is usually accompanied by an increase in AR. Thus, The

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statement would only be Agree if the corresponding ) AR = 0.

14. Disagree. Floatation costs are paid to an investment banker for assisting in the issuing and saleof a new securities. These are part of the financing cost, not OCF. Thus, they are not included.

Alex Tajirian



II. Problems.

1. Machine Purchase

Step 1: Calculate Initial outlays (t = 0)

Outlays Cash Flow

price ($100,000)

Freight & installation 0

) NWC (10,000)

Sale of old machine 0

Tax on sale of old machine 0

Net initial outlays -110,000

Step 2: Calculate OCFs Step 2A: Depreciation of new machine

year Factor Depreciation Book Value

1 0.33 33,000 67,000

2 0.45 45,000 22,000

3 0.15 15,000 7,000

4 0.07 7,000 0

100,000

Depreciation = (amount depreciated)(factor) = ($100,000) (factor)Book Value = un-depreciated amount

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Step 2B: Calculate OCF (t = 3)

t= 1 t=2 t=3 t=4

Revenue 10,000 10,000 10,000 0

Cost 2,000 2,000 2,000 0

T 0.4 0.4 0.4 0.4

(R-C)(1-T) 4,800 4,800 4,800 0

(Tax) x (Depreciation) 13,200 18,000 6,000 0

OCF 18,000 22,800 10,800 0

Step 3: Calculate Terminal outlays

Terminal outlays Cash Flow

Salvage Value (SV) 8,000

Tax on Salvage† (400)

NWC Recovery 10,000

Total 17,600

† Tax on Salvage value = ( SV - Book Value )(T) = (8,000 - 7,000)(.4) = $400

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NPV ' &110,000 %18,000(1% .2)

%22,800

(1% .2)2%

28,400

(1% .2)3

Step 4: Calculate Net Cash Flows

t = 0 t = 1 t= 2 t= 3

Initialoutlays

(110,000)

OCF 18,000 22,800 10,800

Terminaloutlays

17,600

Net CF (110,000.00) 18,000.00 22,800.00 28,400.00


Using a calculator or spreadsheet ....IRR =

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Problem 2. Machine Replacement

Step 1: Calculate Initial outlays (t = 0)

price ($100,000)

Freight & installation 0

) NWC (10,000)

Sale of old machine 10,000

Tax on sale of old machine (4,000)

Net initial outlays (104,000)

Note: Since the machine has already been depreciated, there is nochange in future tax CFs due to differences in tax shield.

Step 2: Calculate OCFsIdentical to problem 1

Step 3: Calculate Terminal outlaysIdentical to problem 1

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NPV ' &104,000 %18,000(1% .2)

%22,800

(1% .2)2%

28,400

(1% .2)3

Step 4: Calculate Net Cash Flows

t = 0 t = 1 t= 2 t= 3

Initialoutlays

(104,000)

OCF 18,000 22,800 10,800

Terminaloutlays

17,600

Net CF (104,000) 18,000 22,800 28,400


Using a calculator or spreadsheet, IRR =

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3) All numbers are in (000)

Depreciationold machine = $20, Depreciationnew machine = $40 = (110 + 10)/3

Cost Saving = $60 - $25 = $35

t = 0 t = 1 t = 2 t = 3

cost of newmachine

-110

cost ofmodification

-10

Sale of oldmachine

30

Tax impact of sale -(30-20)(.4)

(R-C)(1-T) (35)(.6)† (35)(.6) (35)(.6)

Tax xDepreciation

(40-20)(.4)‡ (40)(.4) (40)(.4)

terminal outlays 0

Net CF -94 29 37 37

† (R-C)(1-T) = (0-(-35))(1-.4) = 21

‡ Since the old machine is not fully depreciated, the incrementalDepreciation = (new machine depreciation - old machinedepreciation) = (40 - 20) = 20

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4)Step 1: Calculate Incremental CFs

1989 1990 1991 1992

Cost of machine 14

Machine ModificationCosts

1 1

Revenue 10 20 40

Operating Cost 5 10 15

Inventory 1 1 0

Depreciation 8 5 2

Step 2: Calculate Net CFs

1989 1990 1991 1992

Investment Outlays 15 1

(R - C)(1-T) (10-5)(.6) (20-10)(.6) (40-15)(.6)

Tax x Depreciation (.4)(8) (.4)(5) (.4)(2)

NWC 1 1 0

NWC recovery 2

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5a. (in 000)

(R - C)(1 - T) = [-300 - (-25)](1-.3)= (-275)(.7) = -192.5

)NWC = -50

Net CF = OCF - )NWC = -192.5 - (-50) = - $142.5

No, since all Net CFs < 0.

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ELIMINATIONS4. An important factor in whether the government should support a non-defense industry, is the

existence of positive spillover to other industries or sectors.

4. Agree. Without spillover, the country would be undertaking negative NPV projects. Withthe spillover, you would be creating other positive NPV projects that would outweigh anynegative ones. However, the difficulty is in determining industries with potential spilloverand measuring the amount of such spillover.

554.

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ch10 measuring cash flow

Economy & Finance