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# Cash Flow NPV Lecture

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```									    Goal of the Lecture:

Understand how to properly
compute cash flows under
different conditions.
Cash Flows and Net Present Value
Calculating Cash Flow After Tax
“Cash flow before tax times (1 - the marginal tax rate), plus
depreciation for tax purposes times the marginal tax rate.”

I. Cash Flow Calculation
a. CFBT = Cash Flows Before Tax
b. CF      = Cash Flow After Tax = CFBT - Taxes
c. Depreciation = Non-Cash Expense is a Tax Shield
d. CF      = CFBT(1 - T) + Depr(T) where T = tax rate
II. Depreciation
a. Write-off of Original Cost of Asset over Normal
Recovery Period for Tax Purposes
b. Straight Line or MACRS
c. Depreciable Life vs. Economic Life

III.Example: Inventory = 70,000      Plant   = 180,000
Accruals = 15,000    Current Assets =     120,000
Cash Sales = 400,000      Interest Expense = 15,000
Depr = 6 Years, Straight Line     Tax Rate = 40%
Total Costs Before Depr, Int, and Tax = 290,000

CF = (\$400,000 - \$290,000 - \$15,000)(1 - .4) + \$30,000(.4)
= \$57,000 + \$12,000 = \$69,000
Initial, Operating, and Terminal Cash Flows
for an Expansion Project
“Initial = Outflow Associated with Initial Investment,
Operating = Occur Over Economic Life of a Project, and
Terminal = Net Inflow or Outflow When Project Ends”

0         1         2          3         4         5
I.           |----------|----------|---------|----------|---------|
Init. Invest.    Operating Cash Flows Terminal Cash Flow

II. INITIAL COSTS - AT t=0

•      Plant, equipment, land purchased
•      Opportunity costs of land, etc. (owned but could be sold).
•      Transportation, installation costs of new plant/equipment
•      Additional working capital=DCur. Assets - DCur. Liabilities.

III.      OPERATING CASH FLOWS

(Cash in - Cash out)(1 - T) + Depr(T)

We consider the asset's FULL economic life which is
generally longer than its depreciable life => tax shield
only in first few years.

If the acceptance of the project reduces cash flows
from other projects this opportunity cost must be
factored in, e. g., rent lost on floor space.

QUESTION: Suppose the building was not being rented?
IV.    TERMINAL CASH FLOWS

•Salvage value from asset sale = After-Tax Salvage
= Sale Price - (Sale Price - Book Value)(Tax Rate).

Where Book Value is the asset’s remaining depreciation.

•Tax shield from loss due to asset sale - firm must be
profitable.

•Recapture of Net Working Capital

•Cost of disposal of asset - strip-mine, nuclear plant (has
been underestimated).

•Tax liability due to sale of asset at a gain.

Example:
Suppose we have purchased a machine at \$1.0M, with a
depreciable life of 3 years, we use straight line depreciation,
the tax rate is 40%, it produces revenues of \$400,000 per
year and variable expenses of \$300,000 per year, and we
can sell it for \$100,000 at the end of 5 years. Show initial
investment, operating and terminal cash flows.
Initial   = \$1,000,000 at Time 0

Operating CF - Years 1 - 3
= (\$400,000 - \$300,000)(.6) + \$333,333(.4)
= \$60,000 + 133,333 = \$193,333

Operating CF - Years 4 - 5
= (\$400,000 - \$300,000)(.6) = \$60,000

Terminal CF - Year 5
Salvage = \$100,000(.6) = \$60,000

Summary
Year 0 = - \$1,000,000
Year 1 = \$ 193,333
Year 2 = \$ 193,333
Year 3 = \$ 193,333
Year 4 = \$ 60,000
Year 5 = \$ 120,000

Question: Is this a good corporate investment?
Initial, Operating, and Terminal Cash Flows
for a Replacement Project
“Unlike an Expansion Project - a Replacement Project Must
Consider the Cash Flows Forgone By Replacing the Old
Equipment, i.e., Incremental (new - old) Cash Flows.”
Flows

ESTIMATING INCREMENTAL CASH FLOWS.

A. Incremental Initial investment DCF0

Same

•          Equipment cost, transport costs, D in working
capital compared to old project, opportunity
cost.

New
•          Inflow of funds from old asset sale including
disposal costs (+)
•          Tax benefit (liability) on sale of old asset (+/-)

B. Operating Cash Flow

Incremental operating CF = D CF

= (CFBTnew - CFBTold)(1 - T) + (Deprnew - Deprold)(T)

Just the difference between new and old cash
flows and depreciation.
C. Terminal Cash Flow

Same
•           CF on new asset sale (+)
•           Tax benefit (liability) if asset sold at loss/gain (+/-)
•           Recapture all net working capital (+)
•           Disposal costs of new asset (-)

New
•          Funds that would inflow if old asset were sold (-)
•          Disposal costs that would have been paid on old
asset (+)
•          Tax benefit (liab.) on replaced asset if it would have
been sold for a loss (gain) (-,+)

ESSENTIAL DIFFERENCES

1. Old asset is sold early - immediate inflow, disposal & tax
consequences (*Big Benefit-> May get tax benefit since
market value may be less than book value; eg. computers.)

2. Old asset is not sold later - opportunity costs, disposal
and tax consequences. Examples include asbestos and
asphalt shingles - cost more to dispose later.

3. Any effect on present and continuing investments.

4. Forgone operating cash flows from replaced investment
Example: E Services is considering replacement of a
machine that was purchased 3 years ago for \$60,000 and is
generating CFBT of \$15,000 per year. The machine’s
depreciation is 5-year straight-line. If sold today it would
bring \$18,000; sold in 5 more years it would bring \$10,000.
The new machine would cost \$75,000, be depreciated over
5 years with straight-line, require \$8,000 in installation costs
which will be expensed immediately, and generate \$30,000
in CFBT. Its resale value in 5 years is \$20,000. If E services’
tax rate is 40 percent and its cost of capital is 14 percent,
should the machine be replaced?

Calculate Incremental After-Tax CF’s
Initial Investment
Cost of new machine            \$75,000
Installation (\$8,000)(1 - .40)   4,800
Old machine sale               (18,000)
Tax Saving from old’s sale      (2,400)
[\$60,000 - (60,000/5)(3) - \$18,000](.40)
\$59,400
Incremental Operating CF’s
CF1-2 = (30,000 - 15,000)(1-.40) + (15,000 - 12,000)(.40) =
10,200
CF3-5 = (30,000 - 15,000)(1 - .40) + (15,000)(.40) = 15,000
Terminal CF
After-tax CF on sale of new machine
(20,000 - 0)(.60)   12,000
minus the foregone
After-tax CF on sale of old machine
(10,000 - 0)(.60)   (6,000)
6,000

NPV = -59,400 + [=PV(0.14, 2,-10200,0)]

+ [=PV(0.14, 3,-15000,0)][1/1.14]2
+ [=PV(0.14, 5, 0, -6000)]

= -59,400 + 16,796 + 34,824(0.7695) + 3116
Or use Excel
= -59,400 + NPV(.14,10200,10200,15000,15000,21000)
= -12,690

Do Not Replace
Complications in Capital Budgeting

•         Incremental cash flows when replacing an asset
or considering an asset that may impact
profitability of other assets.
•         Shorter life cycles and more frequent replacement
decisions.
• Replacement Project <--------|--------> New Related Project
(pure substitute)     (independent)         (pure compliment)
•         Risk adjustment to the discount rate for different
risk projects.
•         Different discount rate for different parts of a
single project.
Complimentary and Substitute Projects
“A Complementary Project Increases Other Projects Cash
Flows While a Substitute Project Reduces Other Projects.

Whenever a new project is accepted, in order to judge its
merits properly, we must consider the positive or negative
impact it has on the projects we already have or plan to
accept.

Example: T Products has two projects it may undertake.
Project 1 produces Hawiian shirts and requires an initial
investment of \$150,000 and provides CFs of \$60,000,
\$80,000 and \$100,000 in years 1, 2, and 3 respectively.
Project 2 produces Jamaican shirts and requires an initial
investment of \$60,000 and provides CFs of \$30,000,
\$30,000 and \$30,000 in years 1, 2, and 3 respectively. If
both 1 and 2 are undertaken then project 1’s CF’s will be
reduced by \$10,000 per year. If the cost of capital is 14
percent, what should T Products do?

NPVonly 1 = -150,000 + [=NPV(0.14, 60000,80000,100000)]
= 31,700

NPVonly 2 = -60,000 + [=PV(0.14, 3,-30000,0)] = 9,649

NPV1 and 2 = 31,640 + 9,660 - [=PV(0.14, 3,-10000,0)]
= 18,084
Just do project 1 alone.
Risk and Capital Budgeting
“Various Methods to Handle Projects with Different Risk:
CAPM and RADR”

1. CAPM Method - assign project a beta and use
k = kf + B(km - kf)
2. Risk-Adjusted Discount Rate (RADR) Method
(Also Called Expected NPV Approach)

Risk Adj. NPV = -E(CF0) +

Here, E() means Expectation. We need to attach
probabilities to possible CFs and find expected CFs.
One Way to get RADR
a. Calculate the Coefficient of Variation for CFs
where CV = Standard Deviation of CFs / E(CFs)
b. Start with MCC (Marginal Cost of Capital)
Then Adjust MCC as follows
RADR = MCC + Risk Adjustment (positive, zero negative)

By Project Type
Cost Reduction = Low Risk (small CV) -> adjust down
Replacement Projects = Average Risk (average CV) -> no
New Projects = High Risk (large CV) -> adjust up
Risk and Capital Budgeting
“Various Methods to Handle Projects with Different Risk:
Sequential Analysis”

Sequential Analysis to Adjust for Different Risks at Different
Project Stages
=> Success => Large CF’s

Research and      => Sell in Test Market
Build Prototype
=>Failure => zero/Small CFs

Use a large k for early risky stages and a smaller k for later,
less risky stages. Similar to options analysis covered later.
Steps:
a. Get NPVs for Branches Using Small k
b. Apply Probabilities to Each Branch NPV and
Sum to Get Expected NPV
c. Discount the Expected NPV Back to Time 0
Using Large k
d. Discount Other Cash Flows From Earlier
Periods in First Stage at Large k
Risk and Capital Budgeting
“Sequential Analysis Continued”

II. Example: Suppose you have a project that requires an
initial investment of \$400,000 and \$400,000 at the end of
this year and next year for research. The required return for
this research phase of the project is 30%. The projects
second marketing phase will be a success with 75%
probability or a failure with 25% probability. If a success,
you will invest another \$500,000 at the end of year 3 and
receive \$1,000,000 at the end of each of the next 4 years. If
a failure, you will invest \$200,000 at the end of year 3 and
receive \$200,000 at the end of each of the next 4 years. If
the required rate of return for the second phase is 10%,
should you make the investment?
NPVsuccess = [=PV(0.10, 4,-1000000,0)] - \$500,000
= \$3,170,000 - \$500,000
= \$2,670,000
NPVfailure   = [=PV(0.10, 4,-200000,0)] - \$200,000
= \$634,000 - \$200,000
= \$ 434,000
Exp. NPV = .75(\$2,670,000) + .25(\$434,000)
= \$2,111,000
NPVoverall = -\$400,000 - [=PV(0.30, 2,-400000,0)] +
[=PV(0.30, 3, 0, -2111000]
= \$16,476     Decision: Accept.
Risk and Capital Budgeting
“Various Methods to Handle Projects with Different Risk:
Sensitivity Analysis and Break-Even Analysis”

SENSITIVITY ANALYSIS

Vary some assumptions about the economy or industry (say
oil prices) and find the effects on CFs and NPVs

This is a way to force one to consider possible problems but
is not an accurate method.

Simulation - more complex sensitivity analysis - more
variables change at once, random number
generator chooses, results given as probability
distribution,
--> difference is that interdependency between
changing variables can be handled easier.

BREAK EVEN ANALYSIS IN A FINANCE (NPV=0) SENSE,
NOT AN ACCOUNTING (DOLLAR) SENSE -> (EAT= 0)

STEPS

1. Find CF annuity required to get NPV = 0

PVout = PVin

[=PMT(k, n, Initial Investment, 0)]

PMT = CF (break even cash flow)
Risk and Capital Budgeting
“Various Methods to Handle Projects with Different Risk:
Break-Even Analysis”

2. Now find sales needed to get CF

Sales - (variable costs + fixed costs) - taxes = CF

X - VX - F - (X - VX - F - Depr)(t) = CF

where     X = break even sales
V = Variable cost as % of sales
F = fixed cost
t = Tax rate
Depr = depreciation (actually a fixed cost)

Compare to Accounting Break Even

X - VX - F - Depr - (X - VX - F - Depr)(t) = 0
or
X - VX - F - (X - VX - F - Depr)(t) = Depr

Finance breakeven gets back present value of
investment while accounting breakeven gets
back dollars invested.
Risk and Capital Budgeting
“Various Methods to Handle Projects with Different Risk:
Break-Even Analysis”

Example: E Products plans a \$4 million investment that will
be depreciated over 10 years with straight-line. Variable
costs are 50 percent of sales, fixed costs are \$300,000 per
year, the tax rate is 30 percent and the cost of capital is 18
percent. Find the accounting and financial break-even sales
points and explain why they differ.
Depreciation = 4,000,000/10 = 400,000
Accounting break-even
X - .5X - 300,000 - 400,000 -
(X - .5X -300,000 - 400,000)(.30) = 0

.35X -490,000 = 0     => X = 1,400,000
Financial break-even

[=PMT(0.18, 10, -4000000, 0)]

=> PMT = CF = 890,059
X - .5X -300,000 - (X - .5X -300,000 - 400,000)(.30) =
890,059
.35X - 90,000 = 890,059     => X = 2,800,169
Financial breakeven is larger because it requires future cash
flows to recover the present value of the investment.

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