10
10-1
Chapter CHAPTER Overview
Capital investment decisions
Comparing capital investment alternatives
Ignoring time value of money
Payback Method
Unadjusted Rate of Return
Time value of money concept
PV of future CF
PV of annuity
Comparing capital investment alternatives
Adjusting for time value of money
NPV
Capital Investment Decisions
How managers plan significant outlays on projects that have
long-term implications such as the purchase of new equipment
and introduction of new products?
Purchases of long-term operational assets are capital
investments. Once a company purchases operational assets, it
is committed to these investments for an extended period of
time. Understanding the time value of money concept will help
you make rational capital investment decisions.
Typical Capital Budgeting Decisions
Plant expansion
Equipment selection
Cost reduction
Equipment replacement
Lease or buy
Typical Capital Budgeting Decisions
Capital
budgeting
tends to fall
into two broad
categories . . .
Screening decisions.
Does a proposed
project meet some
present standard of
acceptance?
Preference
decisions. Selecting
from among several
competing courses of
action.
Purchases of long-term operational assets
are capital investments.
Evaluating an investment opportunity
requires identifying cash flows
Measuring
Investment
Cash Inflows
Incremental
Revenues
Release
of
Working
Capital
Measuring
Investment
Cash Outflows
Initial
Investment
Cost
Savings
Increases
in
Operating
Cash Outflows Expenses
Cash Inflows
Salvage
Value
Increase in
Working
Capital
Requirements
Approaches to
Capital Budgeting Decisions
Simple
Methods
Methods
of making
capital
budgeting
decisions
include
Time Value
Methods
Payback
Method
Net Present
Value
Unadjusted
(Simple) Rate
of Return
Internal Rate
of Return
Payback Method
This is a simple and easy approach to
looking at the recovery of an investment.
The payback period is the length of
time that it takes for a project to
recover its initial cost out of the cash
receipts that it generates.
When the net annual cash inflow is the same
each year, the following formula can be
used to compute the payback period:
Payback
=
period
Net cost of investment
Annual net cash inflows
Payback Method
Winston Cleaners can purchase a piece of
equipment for $100,000 that will reduce labor costs
by $40,000 per year over a four-year useful life.
Lets calculate the payback period.
Payback
=
period
Net cost of investment
Annual net cash inflows
$
Payback
=
$
period
=
years
Generally, the shorter the payback period,
the better
Payback Method
The payback method requires adjustment when cash
flows are unequal
Lets assume a company purchases a machine for $6,000,
with the cash inflows shown below:
2009
$ 3,000
2010
$ 1,000
Year
2009
2010
2011
2012
2011
$ 1,000
Annual
Amount
2012
$ 1,000
2013
$ 1,500
Cumulative
Amount
Payback Period = ? Years
Payback Method
Another approach is to calculate the average annual
cash inflows to compute the payback period.
Year
2009
2010
2011
2012
2013
Annual
Amount
$ 3,000
1,000
1,000
1,000
1,500
Payback
=
period
Net cost of investment
Average Annual cash
inflows
$
Payback
=
period
$
=?
years
Check Yourself
Management at The Daily Grind wants to
install an espresso bar in its restaurant.
The espresso bar:
Costs $140,000 and has a 10-year life.
Will generate net annual cash inflows of
$35,000.
Management requires a payback period of
5 years or less on all investments.
What is the payback period for the
espresso bar?
Check Yourself
Payback period =
Investment required
Net annual cash inflow
Payback period =
According to the companys criterion,
management would invest or not invest in
the espresso bar?
Evaluation of the Payback
Method
Short-comings
of the Payback
Period.
Ignores the
time value
of money.
Ignores cash
flows after
the payback
period.
Unadjusted Rate of Return
Does not focus on cash flows -- rather it
focuses on accounting income.
Does not adjust to reflect the time value
of money.
The return is computed as follows:
Unadjusted
rate of return =
Average incremental increase
in annual net income
Net cost of original
investment
Unadjusted Rate of Return
Dining Table, Inc. is considering opening a new
restaurant that will require an investment of $2,000,000.
Over a 10-year period the restaurant is expected to
provide average after-tax return of $280,000 per year.
Unadjusted
rate of return =
Unadjusted
=
rate of return
Average incremental increase
in annual net income
Net cost of original
investment
$
$
=
%
Unadjusted Rate of Return
The accuracy of this method suffers from the failure to
recognize the recovery of invested capital.
A company can purchase a depreciable asset with a twoyear life and no salvage value for $1,000. The asset
produces incremental revenue of $600 per year. The
income statement for the first year would look like this:
Income Statement
Revenue
Depreciation Expense
Net Income
Unadjusted
rate of return =
=
%
Unadjusted
rate of return =
Average
=
%
Unadjusted Rate of Return
Given the pattern of cash flows over the life of the
investment, the amount of invested capital will range
from a beginning balance of $1,000 to an ending balance
of zero. On average, the company will have $500
invested in the asset.
To avoid distortions caused by the failure to
recognize the recovery of invested capital,
the unadjusted rate of return is based
on the average investment when working with
investments in depreciable assets.
This method is not recommended for
a variety of reasons, the most
important of being that it ignores the
time value of money.
Time Value of Money
Business investments
extend over long periods
of time, so we must
recognize the time value
of money.
Investments that promise
returns earlier in time are
preferable to those that
promise returns later in
time.
Time Value of Money
This concept recognizes that the present value of
a dollar received in the future is < than todays
dollar. The further into the future the receipt is
expected to occur, the smaller its present value.
When a company invests
in capital assets, it
sacrifices present dollars in
exchange for the
opportunity to receive
future dollars.
Time Value of Money
A bond will pay $100 in two years. What is
the present value of the $100 if an investor
can earn a return of 12% on the
investment?
We can determine the present value
factor using the formula or using present
value tables.
Present Value of $1 Table 1 in the Appendix
Time Value of Money
Periods
1
2
3
4
5
10%
0.909
0.826
0.751
0.683
0.621
Rate
12%
0.893
0.797
0.712
0.636
0.567
14%
0.877
0.769
0.675
0.592
0.519
Present value factor of $1 for 2 periods at 12%
from Table 1.
n=
PV = $100
,r=
=$
Check Yourself
EZ Rental wants to add LCD projectors to its product line.
How much does EZ have to invest now to have $200,000 at
the end of the first year? EZ requires a rate of return of 12%.
Table 1 in the Appendix
Period
1
2
3
4
5
Present Value Factor
10%
12%
0.909091
0.892857
0.826446
0.797194
0.751315
0.711780
0.683013
0.635518
0.620921
0.567427
PV $200,000 =
for $1
14%
0.877193
0.769468
0.674972
0.592080
0.519369
=$
(rounded)
If EZ Rental invests $
now , the company should
expect $200,000 cash inflow at the end of the first year.
Time Value of Money - Annuity
An investment that involves a series of
identical cash flows at the end of each year
is called an annuity.
$100
$100
1
$100
2
$100
3
$100
4
$100
5
An ordinary annuity is a series of
equal payments made at the end of
each period.
6
Ordinary Annuity Assumption
An annuity must meet three criteria: (1) equal
payment amounts, (2) equal time intervals between
payments, and (3) a constant rate of return.
Capital investment decisions often involve
uncertainties about future cash inflows and outflows.
The assumptions inherent in ordinary annuities
simplify the calculation process
Rent on your apartment or home, or
insurance on your automobile is probably paid
in the form of an equal periodic payment
How do we determine the present value when
face with a series of payments?
Present Value Table for Annuities
Lets assume that EZ Rentals is going to receive
$200,000 at the end of each of the next 4 years. The
company uses an interest rate for present value
calculations of 12%.
Present Value of $1 Table 2 in the Appendix
PV Annuity = $200,000
Period
1
2
3
4
5
=$
(rounded)
Present Value Factor for an Annuity of $1
8%
10%
12%
14%
0.925926
0.909091
0.892857
0.877193
1.783265
1.735537
1.690051
1.646661
2.577097
2.486852
2.401831
2.321632
3.312127
3.169865
3.037349
2.913712
3.992710
3.790787
3.604776
3.433081
Present Value Table for Annuities
Table 1 in the Appendix
Period
1
2
3
4
5
Present Value Factor
10%
12%
0.909091
0.892857
0.826446
0.797194
0.751315
0.711780
0.683013
0.635518
0.620921
0.567427
for $1
14%
0.877193
0.769468
0.674972
0.592080
0.519369
PV of $200,000 Cash Inflows Received for 4 Years
Period
FV
Factor
Amount
1
$ 200,000
0.892857 = $ 178,571
2
200,000
0.797194 =
159,439
3
200,000
0.711780 =
142,356
4
200,000
0.635518 =
127,104
$ 607,470
Investing $607,470 today at a 12% return is equivalent
to receiving $200,000 each year for the next four years.
Choosing a Discount Rate
The firms cost of capital is usually regarded as the most
appropriate choice for the discount rate.
Creditors expect interest payments; in most companies, owners expect
dividends and increased stock value. The blend of creditor and owner
costs is considered the cost of capital for an organization.
The cost of capital is the average rate of return the company must
pay to its long-term creditors and stockholders for the use of their
funds.
Minimum Rate of Return
Net Present Value
Difference between the cost of the investment
and the present value of future cash inflows
You have an opportunity to invest in one of the two
projects shown below. Both require an investment of
$6,000, and return total cash inflows of $8,000.
2006
2007
2008
2009
Total
Project 1
$ 3,500
3,000
1,000
500
$ 8,000
Project 2
$ 2,000
2,000
2,000
2,000
$ 8,000
If you have a desired rate of return of 10%, in
which project would you invest?
Net Present Value
Period
1
2
3
4
PV of cash inflows
PV of cash outflows
NPV of Project 1
PV of cash inflows
PV of cash outflows
Project 1
Cash Inflow
$
3,500
$
3,000
$
1,000
$
500
PV Factor
PV
=
=
=
=
Project 2
$
2,000
=
If you have a desired rate of return of 10%, in
which project would you invest?
Project 1?
or
Project 2?
Net Present Value
Calculation
To determine net
present value we . . .
Calculate the present
value of cash inflows,
Calculate the present
value of cash
outflows,
Subtract the present
value of the outflows
from the present
value of the inflows.
General decision rule . . .
If the Net
Present Value is
Then the Project is . . .
Positive . . .
Acceptable, since it promises a
return greater than the required
rate of return.
Zero . . .
Acceptable, since it promises a
return equal to the required rate
of return.
Negative . . .
Not acceptable, since it
promises a return less than the
required rate of return.
Net Present Value
Lets assume that EZ Rentals can purchase the LCD
projectors for $582,742. The company has a desired
rate of return of 12%. The investment will provide a
$200,000 cash inflow for the next four years. Should
EZ buy the projectors?
Present value of future cash inflows
Cost of the investment
Net present value
EZ should invest or not in the LCD projectors?
Check Yourself
To increase productivity, Wald Corporation is considering
the purchase of a new machine that costs $50,000. The
machine is expected to provide annual net cash inflows
of $12,500 for each of the next five years. Wald desires a
minimum annual rate of return of 10%. Would you
recommend that Wald invest in the new machine?
PV of cash inflows = $
=$
Present value of future cash inflows
Cost of the investment
Net present value
Should Wald purchase the new machine?
Internal Rate of Return
(NOT COVERED)
The internal rate of return is the rate at
which the present value of cash inflows
equals cash outflows.
An investment cost $582,742, and will return $200,000 at
the end of each of the next 4 years. What is the IRR?
$582,742
Period
1
2
3
4
5
$200,000 = 2.91371
Present Value Factor for an Annuity of $1
8%
10%
12%
14%
0.92593
0.90909
0.89286
0.87719
1.78326
1.73554
1.69005
1.64666
2.57710
2.48685
2.40183
2.32163
3.31213
3.16987
3.03735
2.91371
3.99271
3.79079
3.60478
3.43308
Internal Rate of Return
(NOT COVERED)
When management uses the internal rate of return
(IRR), the higher the return, the more profitable the
investment.
Calculating IRR can be tedious. Companies use Excel
to make the process efficient.
To use Excels special functions, we must know the
values involved and make a reasonable guess as to
the IRR. The guess is necessary to help Excel
determine the correct IRR.
Tax Considerations
Taxes affect the amount of cash flows generated by investments.
In the following example, Wu Company purchases an asset for $240,000. The
asset has a four-year useful life, no salvage value, and straight-line
depreciation is used. The asset is expected to generate incremental revenues
of $90,000 per year. Wus income tax rate is 40%, and the company has a
desired after tax return of 10%.
Cash revenue
Depreciation expense (noncash)
Income before taxes
Income tax at 40%
Income after tax
Depreciation add back
Annual cash inflows
Period 1
$ 90,000
(60,000)
30,000
(12,000)
18,000
60,000
$ 78,000
Period 2
$ 90,000
(60,000)
30,000
(12,000)
18,000
60,000
$ 78,000
Annual cash annuity
PV of annuity of $1, 4 periods, 10%
PV of annual cash annuity
PV of cash outflow
Net present value
Period 3
$ 90,000
(60,000)
30,000
(12,000)
18,000
60,000
$ 78,000
Net PV
$ 78,000
3.169865
247,249
(240,000)
$
7,249
Period 4
$ 90,000
(60,000)
30,000
(12,000)
18,000
60,000
$ 78,000
Postaudits
A postaudit is conducted at the completion
of a capital investment project, using the
same analytical technique that was used to
justify the original investment. The focus
should be on continuous improvement in the
capital expenditure process.