Ch10 measuring cash flow

Chapter 10

MEASURING
CASH FLOW

Alex Tajirian

Capital Budgeting CFs 10-2

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.

© morevalue.com, 1997
Alex Tajirian


2 WHAT ARE A PROJECT’S CFs?
2.1 Basics

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

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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 storage
cost for the project = 0?

No, you have to include storage cost, as if you had to go and
rent 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 as
sales _.

! Investment in C/A is recoverable at end of project as A/R is
collected 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, unsold
defective 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 would
be worth $2,200. The junkyard would only pay you $200.
Repair or scrap?

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

# 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 firm
Q 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 Firm
You own a jazzercise enterprise for women. If you include
men, you will obtain new source of revenue. Should you
undertake the project?

New proposal can _ or ` in women patronage.

2.2.6 CONSIDER POTENTIAL OF CREATING NEW
PRODUCTS IN THE FUTURE

Note: This is easier said than done. Easy methods to
incorporate these effects are not available yet. They
involve game theory and option pricing. However, this
does 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 the
CFs -- 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 the
financing decisions.

! In practice, firms calculate NPV as if there will be no debt
financing, 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 end
of 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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# 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

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

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Putting all the above components together, we have,

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

Notes.
! ) NWC > 0 means cash outflow.
! _ in investment outlays is cash outflow.

! Cost of financing a project is not included as a CF. It is
reflected 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 = 470
cash 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 considerations
are very important. (FI 320)

# Depends on Economic Life of asset in consideration. The
government sets depreciation schedule. Obviously, if salvage value
after being fully depreciated is zero, then economic life = years of
depreciation.

# For this class:
! economic life / useful life / # of years of CFs generated by
project

! 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 for
the entire duration. After some search, you have narrowed down your
choices to a Ferrari and a Moscovich. The latter is expected to last only
two years. The CFs from the two cars are below. Which car would you
buy?

Net Cash Flow
Year Moscovich Ferrari
0 ($100,000) ($100,000)
1 60,000 33,500
2 60,000 33,500
3 0 33,500
4 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 longer
time 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 to
re-purchase another car after two years.

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

0 1 2 3 4
CFs from first
-100,000 60,000 60,000
purchase
CFs from
-100,000 60,000 60,000
re-purchase
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
ˆ choose Moscovich, since higher NPV

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5.2.2 Solution 2: Equivalent Annual Annuity (EAA)

Method is based on continuous replacement (re-purchase). This
technique is used to simplify the problem of having to make lives
equal.

Original NPV
EAA '
PVIFAk,original life

$4,132 $4,132
EAAMoscovich ' ' ' $2,381
PVIFA10%,2 1.7355

6,190 6,190
EAAFerrari ' ' ' $1,953
PVIFA10%,4 3.1699

ˆ choose one with
highest EAA.

Y

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 as
accounting numbers can be manipulated. An example would be
changing from LIFO to FIFO.

Illustration
Revenue 510
Cost 310
Net Income 200

Beginning End Change
AR 880 1,390 510
AP 0 0 0

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

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

Alex Tajirian


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
Initial initial
Outlay outlays

OCF
OCF - -
)NWC )NWC

Terminal Outlays Terminal
Outlays

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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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 = Book Value =
(factor)(Net cost) Net cost - Total Depreciation
2
1 33% 39,600 120,000 - 39,600
2 45 54,000 120,000 - (39,600 + 54,000)
3 15 18,000 ...
4 7 8,400 0
$120,000

1
Depreciation factors depend on the appropriate depreciation schedule. They are given
Appendix. Depreciation includes all costs incurred to bring the purchased asset to an operational
condition.
2
(33%) x ($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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Step 5: Calculate NPV

45,840 51,600 61,360
NPV ' & 130,000 % % % ... %
(1% .1) (1% .1)2 (1% .1)4
' & 130,000 % 45,850×[PVIF10%,1] % ... % 61,360×[PVIF10%,4]

= $24,176; IRR = 18.1%

Note:
(R-C)(1-T) = (0 - (- $50,000))(1-.4) = $30,000
Tax x Depreciation = .4(39,600) = $15,840 in year 1
Salvage 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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8 Endnotes

1.Varies with the quantity of output produced.

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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 > operating
expenses, 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, there
is 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 a
firm 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 long
you 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 undertaking
the 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 a
corresponding 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 included
as part of the project CFs.

Alex Tajirian


II. Numerical
The 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 Purchase
You are interested in the purchase of a machine that costs $100,000. The machine has an
economic life of 4 years, with 3-year MACRS depreciation. However, you expect to sell it after
3 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 to
operate. If the corporate tax rate is 40%, and k = 20%, should the machine be purchased?

2. Machine Replacement
You are considering the replacement of an existing machine that has been fully depreciated. It
can be sold for $10,000. The cost of the new machine is $100,000.The machine has an
economic life of 4 years, with 3-year MACRS depreciation. However, you expect to sell it after
3 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 be
replaced?

3.H Machine Replacement
You 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 replacement
with 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 an
economic life of 3 years and would be straight line depreciated. On a time line write down the
relevant 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 relevant
annual 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. Their
current annual sales are at $1m., operating costs at $700,000, and inventory at $100,000. The
owners' 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?

Alex Tajirian


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 of
1991 and beginning of 1991.

4. Disagree. Whoever is doing the analysis is forgetting to include the owner's salary--opportunity
cost. 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 the
tax bill, while operating costs do.

6. Disagree. Although depreciation is not a CF, it enters into the calculation of OCF through the
tax 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 discount
rate. With no financial markets, it is very difficult to determine the required rates of return that
we 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 estimate
you 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 to
cost 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 be
affected.

12. Agree. When sales increase, the firm has to incur additional AR and inventory. Although AP
might 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 sale
of 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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Step 4: Calculate Net Cash Flows

t=0 t=1 t= 2 t= 3
Initial (110,000)
outlays
OCF 18,000 22,800 10,800
Terminal 17,600
outlays
Net CF (110,000.00) 18,000.00 22,800.00 28,400.00


18,000 22,800 28,400
NPV ' & 110,000 % % %
(1% .2) (1% .2)2 (1% .2)3

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 no
change in future tax CFs due to differences in tax shield.

Step 2: Calculate OCFs
Identical to problem 1

Step 3: Calculate Terminal outlays
Identical to problem 1

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Step 4: Calculate Net Cash Flows

t=0 t=1 t= 2 t= 3
Initial (104,000)
outlays
OCF 18,000 22,800 10,800
Terminal 17,600
outlays
Net CF (104,000) 18,000 22,800 28,400


18,000 22,800 28,400
NPV ' & 104,000 % % %
(1% .2) (1% .2)2 (1% .2)3

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 new
-110
machine
cost of
-10
modification
Sale of old
30
machine
Tax impact of sale -(30-20)(.4)
(R-C)(1-T) (35)(.6)† (35)(.6) (35)(.6)
Tax x
(40-20)(.4)‡ (40)(.4) (40)(.4)
Depreciation
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 incremental
Depreciation = (new machine depreciation - old machine
depreciation) = (40 - 20) = 20

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4)
Step 1: Calculate Incremental CFs

1989 1990 1991 1992
Cost of machine 14
Machine Modification 1 1
Costs
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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ELIMINATIONS
4. 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. With
the spillover, you would be creating other positive NPV projects that would outweigh any
negative ones. However, the difficulty is in determining industries with potential spillover
and measuring the amount of such spillover.

554.

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