Team project 2

Chapter 8: Investment
decision rules
Team-2 ITM-2005
Chapter 9: Umbeteeva Amina 8.3 & 9.7
Fundamentals of Capital Sadykova Aiym 8.1 & 9.2
Sekenova Kamila 8.2 & 9.5
Budgeting Kaskin Daniyal 8.6 & 9.4
 Chapter 8
Investment decision rules
 Introduction to the
chapter 8:

Net present value (NPV) - the Growth rate - the percentage change
difference between the present value of of a specific variable within a specific
cash inflows and the present value of time period.
Cost of capital - the cost of the
cash outflows over a period
company's funds
Mutually Exclusive - a statistical term
Payback Rule
describing two or more events that NPV Rule
cannot happen simultaneously.
 Problem 8.1

The NPV Is Equivalent to

Cash Today
NPV

Net present value (NPV) is the difference between the present value
of cash inflows and the present value of cash outflows over a period
of time. NPV is used in capital budgeting and investment planning to
analyze the profitability of a projected investment or project.
 After saving $1500 by waiting tables, you are about to buy a 50-
inch LCD TV. You notice that the store is offering a “one year same
as cash” deal. You can take the TV home today and pay nothing
until one year from now, when you will owe the store the $1500
purchase price.

If your savings account earns 5% per year, what is the NPV of this
offer? Show that its NPV represents cash in your pocket.
 01 You are getting something worth
$1500 today (the TV) and in
exchange will need to pay $1500
in one year.

Solution plan
02
You need to compare the
present value of the cost ($1500
in one year) to the benefit today
(a $1500 TV).
 Execution

NPV= +1500-(1500/1.05) = 1500-1428,57 =

$71.43
Evaluation

By taking the delayed payment offer, we have extra net cash flows of $71.43
today. If we put $1428.57 in the bank, it will be just enough to offset our $1500
obligation in the future. Therefore, this offer is equivalent to receiving $71.43
today, without any future net obligations
Problem 8.2
Using the payback rule
Payback
The simplest investment rule is the payback
investment rule, which states that you
should only accept a project if its cash flows

Rule pay back its initial investment within a

prespecified
period.

To apply the payback rule:

1. Calculate the amount of time it takes to pay back
the initial investment, called the
payback period.
2. Accept the project if the payback period is less
than a prespecified length of time—
usually a few years.
3. Reject the project if the payback period is
greater than that prespecified length of
time.
 Problem
Assume Fredrick’s requires all projects to have a payback
period of two years or less.Would the firm undertake
the fertilizer project under this rule?
 Solution
The project has inflows of $28 million per year and an initial investment of $81.6
million.
01 02 03

The sum of the cash In fact, it will not be until Because the payback
flows for years 1 and 2 year 3 that the cash period for this project
inflows exceed the initial exceeds two years,
$28 × 2 = $56 million, investment Fredrick’s will reject the
which will not cover the project.
$28 × 3 = $84 million.
initial investment of $81.6
million.
 Evaluation
While simple to compute, the payback rule requires us to use an arbitrary cutoff period in
summing the cash flows.
Further, also note that the payback rule does not discount future cash flows. Instead, it
simply sums the cash flows and compares them to a cash outflow in the present. In this
case, Fredrick’s would have rejected a project that would have increased the value of the
firm.
 Problem 8.3

NPV and Mutually Exclusive

Projects
 NPV and Mutually Exclusive Projects

01 02 03

NPV Mutually exclusive projects. NPV Rule

When choosing any one Pick the project with the

Net present value (NPV) is the
project excludes us from highest NPV.
difference between the
taking the other projects, we
present value of cash inflows
are facing mutually exclusive
and the present value of cash
projects.
outflows over a period of time.
 Cost of capital & Growth Rate

Cost of capital Growth rate

the cost of capital is the cost of a company's Growth rates refer to the percentage
funds (both debt and equity), or, from an change of a specific variable within a
investor's point of view "the required rate of specific time period. For investors, growth
return on a portfolio company's existing rates typically represent the compounded
securities". It is used to evaluate new projects of annualized rate of growth of a company's
a company. revenues, earnings, and dividends.
 Problem

You own small commercial Alternatives for yourself

land near the university

You assume that you would operate
your choice indefinitely, eventually
what to do with it?
leaving the business to your children.
sell it for 220 000$
Bar
Coffee shop
Apparel store
 Information about the uses
Initial Cash Flow in the Growth Cost of
Investment First Year (CF1 ) Rate (g) Capital (r)

Bar $400.000 $50.000 3.5% 12%

Coffee shop $200.000 $40.000 3% 10%

Apparel store $500.000 $75.000 3% 13%

 You can only do one project

In order to decide which project is

most valuable, you need to rank
them by NPV.

Solution
Plan Cash flows can be valued as
growing perpetuity, the
present value of the inflows is
The NPV of each investment
will be:

(CF1 / r - g)- Initial

investment
 Bar:
01 (60.000 / (0.12 - 0.035)) -
400.000 = $305.882
Execute
NPVs Coffee shop:
02 (40.000 / (0.10 - 0.03)) -
we use formula: 200.000 = $371.429
(CF1 / r - g) - initial
investment Apparel store:
03 (75.000 / (0.13 - 0.003)) -
500,000 = $250.000
 Ranking is

25

20

15
Coffee shop
10
$371.429 Bar
Apparel store
5
$305.882 Selling land
$250.000
0
$220.000
Ranking
Evaluate
All the alternatives have positive NPVs, but you can take
only one of them, so you should choose the one that
creates the most value. Even though the coffee shop has
the lowest cash flows, its lower start-up cost coupled with
its lower cost of capital (it is less risky) make it the best
choice

Answer: Coffee shop

 Problem 8.6
Profitability Index with a
Human Resource Constraint

 Problem
Your division at NetIt, a large networking company, has
put together a project proposal to develop a new home
networking router. The expected NPV of the project is $17.7
million, and the project will require 50 software engineers.
NetIt has a total of 190 engineers available, and is unable
to hire additional qualified engineers in the short run.

Problem 8.6 | Profitability Index with a Human Resource Constraint

 Problem

How should NetIt

prioritize these projects?

Problem 8.6 | Profitability Index with a Human Resource Constraint

 Therefore, the router project must

compete with the following other projects
for these engineers:

Project NPV ($ millions) Engineering Headcount

Router 17.7 50
Project A 22.7 47
Project B 8.1 44
Project C 14.0 40
Project D 11.5 61
Project E 20.6 58
Project F 12.9 32
Total 107.5 332

Problem 8.6 | Profitability Index with a Human Resource Constraint

 The goal is to maximize the total
NPV that we can create with 190

Solution
engineers.
In this case, since engineers are our
limited resource, we will use

Plan Engineering Headcount in the

denominator.
Once we have the profitability index
for each project, we can sort them
based on the index.

Problem 8.6 | Profitability Index with a Human Resource Constraint

 Profitability Index = NPV / Resource

consumed

Project Profitability index

Router
Project A 0.483
Project B 0.403
0.355
Project C
0.354
Project D 0.350
Project E 0.189
Project F 0.184
Total

Problem 8.6 | Profitability Index with a Human Resource Constraint

 Execute
We now assign the resource to the projects in
descending order according to the profitability index. •
The final column shows the cumulative use of the
resource as each project is taken on until the resource is
used up. To maximize NPV within the constraint of 190
employees, NetIt should choose the first four projects on
the list.
 Chapter 9
Fundamentals of Capital Budgeting
 Cash Flow After Taxes - a measure of a company's cash
flow after all taxes are paid.
Introduction
to the Capital gain is an increase in a capital asset's value and is
considered to be realized when the asset is sold
chapter 9:
Book value is a company’s equity value as reported in its
financial statements.
 Introduction to the
chapter 9:
incremental earnings - The amount by marginal corporate tax rate - The tax
which a firm’s earnings are expected to rate a firm will pay on an incremental
change as a result of an investment dollar of pre-tax income.
decision.

straight-line depreciation - A method unlevered net income - Net income

of depreciation in which an asset’s cost that does not include interest
is divided equally over its life. expenses associated with debt.
Problem 9.2

Taxing Losses for Projects

in Profitable Companies
 Tax

A tax is a compulsory financial charge or some other type of

levy imposed on a taxpayer (an individual or legal entity) by
a governmental organization in order to fund government
spending and various public expenditures.
 Problem
Kellogg Company plans to launch a new line of high-fiber, zero-trans-fat breakfast pastries.
The heavy advertising expenses associated with the new product launch will generate
operating losses of $15 million next year for the product. Kellogg expects to earn pre-tax
income of $460 million from operations other than the new pastries next year.

If Kellogg pays a 40% tax rate on its pre-tax income, what will it owe in taxes next year without the
new pastry product? What will it owe with the new product?
Solution

With the new product, Kellogg’s pre-tax income next year

will be only
$460 million - $15 million =$445 million,
and it will owe in tax.
 Evaluation

Thus, launching the new product reduces Kellogg’s taxes next year by
$184 million - $178 million= $6 million.
Because the losses on the new product reduce Kellogg’s taxable income dollar for dollar, it is
the same as if the new product had a tax bill of negative $6 million.
 Problem 9.4
Incorporating Changes in Net
Working Capital
 Problem
HomeNet will have no incremental cash or inventory
requirements. However, receivables related to HomeNet
are expected to account for 15% of annual sales, and
payables are expected to be 15% of the annual cost of
goods sold.

Problem 9.4 | Incorporating Changes in Net Working Capital

 Fifteen percent of $13 million in sales is $1.95 million and 15% of $5.5
million in COGS is $825.000. HomeNet’s net working capital
requirements are shown in the following table:

Year 0 1. 2. 3 4. 5
Net Working Capital Forecast ($000s)
Cash Requirements 0 0 0 0 0 0
Inventory 0 0 0 0 0 0
Receivables (15% of Sales) 0 1,950 1,950 1,950 1,950 0
Payables (15% of COGS) 0 -825 -825 -825 -825 0
Net Working Capital 0 1.125 1.125 1.125 1.125 0

Problem 9.4 | Incorporating Changes in Net Working Capital

 How does this
requirement affect the
project’s free cash flow?

Problem 9.4 | Incorporating Changes in Net Working Capital

 Net Working Capital = Current Assets - Current Liabilities
= Cash + Inventory + Receivables - Payables

More generally, we define the

change in net working capital in year
t as:
Change in NWC in Year t = NWCt -
NWCt-1

Problem 9.4 | Incorporating Changes in Net Working Capital

 We can use our forecast of HomeNet’s net

Solution
working capital requirements to complete
our estimate of HomeNet’s free cash flow.
In year 1, net working capital increases by

Plan
$1.125 mil- lion. This increase represents a
cost to the firm.
This reduction of free cash flow corresponds
to the fact that in year 1, $1.950 million of the
firm’s sales and $0.825 million of its costs
have not yet been paid.

Problem 9.4 | Incorporating Changes in Net Working Capital

Problem 9.5
Calculating the Projects NPV
Calculating
NPV To compute a project’s NPV, we must
discount its free cash flow at the appropriate
cost of capital.
The cost of capital for a project is the
expected return that investors could earn on
their best alternative investment with similar
risk and maturity.

NPV = FCF/(1+r)ⁿ
FCF - Free cash flow
r - cost of capital
n - year
 Problem
Assume that Linksys’s managers believe that the HomeNet
project has risks similar to its existing projects,
for which it has a cost of capital of 12%. Compute the NPV
of the HomeNet project.
 Solution

The incremental free cash flows for the HomeNet project are (in $000s):

To compute the NPV, we sum the present values of all of the cash
flows, noting that the year 0 cash outflow is already a present value.
 Solution

NPV = FCF/(1+r)ⁿ = -7500 + 2295/(1.12) + 3420/(1.12)² +

3420/(1.12)³ + 3420/(1.12)⁴ + 1725/(1.12)⁵ = 2862
 Evaluation
Based on our estimates, HomeNet’s NPV is $2.862 million. While HomeNet’s upfront cost is
$7.5 million, the present value of the additional free cash flow that Linksys will receive from
the project is $10.362 million. Thus, taking the HomeNet project is equivalent to Linksys
having an extra $2.862 million in the bank today.
Problem 9.7

Computing After-Tax Cash

Flows from an Asset Sale
 After-Tax Cash Flow

Cash flow after taxes (CFAT) is a measure

of financial performance that shows a
company's ability to generate cash flow The Modified Accelerated Cost Recovery
through its operations. System (MACRS) is the current tax
depreciation system in the United States.
After-Tax Cash Flow from Asset Sale =
Sale Price - (Tax Rate * Capital Gain)
 Capital Gain Book value
Capital gain is an increase in a Book value is a company’s
capital asset's value and is equity value as reported in its
considered to be realized when the financial statements.
asset is sold

Book Value = Purchase Price -
Capital Gain = Sale Price - Book Value Accumulated Depreciation
 the shutdown of a production line for
a discontinued product
Problem equipment can be sold for a total
price of $50.000
originally purchased 4 years ago for
$500.000
according to the five-year MACRS
schedule
what is the after-tax cash flow you can the marginal tax rate is 35%
expect from selling the equipment?
 Use the MACRS schedule to determine
01 the accumulated depreciation.

Determine the book value as purchase

02 price minus accumulated depreciation

Solution Plan 03
Determine the capital gain as the sale
price less the book value.

Compute the tax owed on the capital

04 gain and subtract it from the sale price,
and then subtract the tax owed from
the sale price.
 Execute

Book Value = Purchase Price - Accumulated

Depreciation

AD = 100.000+160.000+96.000+57.600+57.600 = 471.200

BV = $500.000 - $471.200 = $28.800

 Capital Gain = Sale Price - Book Value

Execute CG = $50.000 - $28.800 = $21.200

Tax owed:

0.35 * $21.800 = $7.420

After-Tax CashFlow = Sale Price - (Tax Rate * Capital

Gain)

$50.000 - $7.420 = $42.580

 Evaluate
only taxed on the capital gain
portion of the sale price...
determine the
a portion of the sale price that represents
a gain and computes the tax from there.
In NPV

Conclusion Calculating the NPV and Payback rule

NPV Rule
while working with mutually exclusive projects

After-Tax Cash Flow

Calculating Capital gain, Book value, using
MACRS table
 References
Berk J., DeMarzo P., Fundamentals of Corporate Finance, 2012|
ISBN 10: 0-132-14823-4 ISBN 13: 978-0-13-214823-8| Global 2nd
Edition, Pearson Education Inc
Thank you!
for your attention

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