Chapter 13-A
Capital Budgeting
M11-Chp-13-1A-Capital-Budget-2011-0525
Edited May 25, 2011.
Copyright © 2011, Dr. Howard Godfrey
This file contains illustrative problems that will be used
in the lecture to illustrate important concepts and
procedures.
See separate PowerPoint file with review material on
interest.
1
Chapter Learning Objectives
LO1: Net present value
LO2: Internal rate of return
LO3: Uncertain cash flows
LO4: Preference ranking
LO5: Payback
LO6: Simple rate of return
LO7: Present value concepts
LO8: Income tax
Introductory
Exercise
Joe’s Package Delivery Service.
Joe had started a package delivery
service in Charlotte.
He bought a truck at a cost of $20,000.
The truck will have a 5-year life, and will
have no salvage value after 5 years.
Joe receives a salary of $30,000
and has other expenses of $10,000
for insurance, oil, gas, etc.
Please fill in the blanks on next slide.
Joe's Package Delivery Service
Cost of Truck (5 year life)
Revenue per year
Salary - Joe
30,000
Insurance, Gas, etc. 10,000
Cash Expenses
Net Cash Inflow
Depreciation
Net Income
What is Payback Period?
(Ignore Income Taxes)
$20,000
$50,000
40,000
10,000
Joe's Package Delivery Service
Cost of Truck (5 year life)
$20,000
Revenue per year
$50,000
Salary - Joe
30,000
Insurance, Gas, etc. 10,000
Cash Expenses
40,000
Net Cash Inflow
10,000
Depreciation
(4,000)
Net Income
$6,000
What is Payback Period?
2 years
(Ignore Income Taxes)
Remember, depreciation is not a cash expense.
Review the problem on the
preceding slides.
Suppose revenue is only $44,000
per year.
What is payback period?
Would you recommend the
project?
Joe's Package Delivery Service
Cost of Truck (5 year life)
Revenue per year
Salary - Joe
30,000
Insurance, Gas, etc. 10,000
Cash Expenses
Net Cash Inflow
Depreciation
Net Income
What is Payback Period?
(Ignore Income Taxes)
$20,000
$44,000
Joe's Package Delivery Service
Cost of Truck (5 year life)
$20,000
Revenue per year
$44,000
Salary - Joe
30,000
Insurance, Gas, etc. 10,000
Cash Expenses
40,000
Net Cash Inflow
4,000
Depreciation
(4,000)
Net Income
$0
What is Payback Period?
5 years
(Ignore Income Taxes)
1: Net
present
value
Present Value Problem - Bonkins
On Jan 1, Bonkins Inc., bought for $520,000 a
new machine with a useful life of 8 years & no
salvage value. Machine will be depreciated using
the straight-line method. It will produce annual
cash flow from operations, net of income taxes,
of $132,500. PV of an ordinary annuity of $1 for
eight periods at 14% is 4.639. PV of $1 for eight
periods at 14% is 0.351. Assume a time adjusted
rate of return of 14%, what is the NPV?
a. $ 36,680
b. $ 94,668
c. $154,440
d. $255,145
Present Value Problem - Bonkins
Compute NPV for a new machine
Cost of Machine
$ 520,000
Annual after-tax cash flow
132,500
Annuity factor for PV at 14%
Present value
Cost of Machine
(520,000)
Net present Value
Present Value Problem - Bonkins
Compute NPV for a new machine
Cost of Machine
$520,000
Annual after-tax cash flow
132,500
Annuity factor for PV at 14%
4.6390
Present value
614,668
Cost of Machine
(520,000)
Net present Value
$ 94,668
Hillsdale
Hillsdale Company purchased a machine for $480,000.
The machine has a useful life of six years and no salvage value.
Straight-line depreciation is to be used.
Machine will generate cash flow each year, net of taxes,
of $140,000 for 6 years. Hillsdale's desired rate of return is 14%.
Period P. V. of $1 At 14%
P. V. of Annuity of $1 At 14%
1
2
3
4
5
6
0.877
0.769
0.675
0.592
0.519
0.456
What would be the net present value?
a. $63,840 b. $64,460
c. $218,880
0.877
1.647
2.322
2.914
3.433
3.889
d. $233,340
PV Problem-Willsdale
Willsdale purchased a machine for $480,000. The machine has a
useful life of six years and no salvage value. Straight-line
depreciation is used. The machine will generate cash flow from
operations, net of income taxes, of $180,000 in each of the six
years. Willsdale's desired rate of return is 14%. Information on
present value factors is as follows:
Period
P. V. of $1 AT 14%
1
.877
2
.769
3
.675
4
.592
5
.519
6
.456
What would be the net present value?
a. $63,840 b. $64,460 c. $219,840
d. $233,340
Garwood
Garwood bought a machine which will be depreciated
on the straight-line basis over an estimated useful life of
7 years and no salvage value. Machine will generate
cash flow from operations, net of income taxes, of
$80,000 in each of the 7 years Garwood's expected rate
of return is 12%. Information on present value is:
P.V. of $1 at 12% for 7 periods
0.452
P.V. of annuity of $1 at 12% for 7 periods
4.564
Assuming a positive net present value of $12,720, what
was the machine's cost?
a. $240,400
b. $253,120
c. $352,400
d. $377,840
2: Internal
rate of
return
Internal Rate of Return
Scott will invest $110,000 in ten year project.
Annual cash in flow, net of income taxes: $20,000.
Scott's desired rate of return is 10%.
Present value factors:
At 10% At 12%
P V of $1 for ten periods
0.368 0.322
P V of annuity of $1 for ten periods
6.145 5.65
Expected rate of return on this investment:
a. Less than 10%, but more than 0%
b. 10%.
c. Less than 12%, but more than 10%.
d. 12%.
e. More than 12%
Rott
Rott is considering investing $130,000 in 10-year project.
Rott estimates that the annual cash in flow, net of income taxes,
from this project will be $20,000.
Rott's desired rate of return on investment of this type is 10%.
Information on present value factors is as follows:
At 10%
At 12%
P V of $1 for ten periods
0.368
0.322
P V of annuity of $1 for ten periods
6.145
5.650
Rott's excepted rate of return on this investment is:
a. Less than 10%, but more than 0%
b. 10%.
c. Less than 12%, but more than 10%. d. 12%.
Rott, Inc.
Compute internal rate of return
Amount to be invested
130,000
Life of project
10
Annual cash flow (after taxes) $20,000
P.V. annuity factor for 10%
6.1450
P.V. of cash flows
$122,900
Cost of investment
130,000
Net P.V. - negative
$ (7,100)
Rate of return must be less than 10% .
How would you estimate rate of return?
3: Uncertain
cash flows
4: Preference
ranking
5: Payback
Payback Model
Payback time, or payback period, is the time it
will take to recoup, in the form of cash inflows
from operations, the initial dollars invested in a
project.
P= I ÷ O
[P= I ÷ Cash flow]
Payback Model Example
Assume that $12,000 is spent for a machine
with an estimated useful life of 8 years.
Annual savings of $4,000 in cash outflows
are expected from operations.
What is the payback period?
P = I ÷ O = $12,000 ÷ $4,000 = 3 years
Payback Problem
Which of these is necessary to
calculate the pay-back period for a
project?
a. Useful life.
b. Minimum desired
rate of return.
c. Net present value.
d. Annual cash flow
Note. In the following question, you are
given the net amount of cash from the
project, after subtracting expenses and
income taxes.
In later problems, you must compute
taxable income, so you will know how much
cash is spent for income taxes.
Of course, tax payments are cash outflows.
Payback Problem-Womark
Womark Co. bought a new machine on January 1,
for $90,000 with an estimated useful life of five
years and a salvage value of $0. The machine will
be depreciated using the straight-line method.
The machine is expected to produce cash flow from
operations, net of income taxes, of $22,500 a year
in each of the next five years.
The payback period will be:
a. 2.2 years. b. 2.5 years.
c. 4.0 years. d. 4.5 years.
Payback Problem-Womark
Payback. After tax cash flows given
Cost of investment
After tax cash flow per year
Payback period
$90,000
Payback Problem-Womark
Payback. After tax cash flows given
Cost of investment
$90,000
After tax cash flow per year $22,500
Payback period
4
In the next few problems, you must
compute taxable income, so you will know
how much cash is spent for income taxes.
Of course, tax payments are cash
outflows.
Payback-Monroe
Monroe is planning to purchase a new machine for
$500,000.
The new machine is expected to produce cash flow
from operations, before income taxes, of $155,000 a
year in each of the next five years.
Depreciation of $100,000 year will be charged to
income for each of the next five years.
The income tax rate is 40%.
The payback period is approximately
a. 2.2 years b. 3.4 years
c. 3.7 years d. 4.1 years
Payback-Monroe
Cash Flow from Operations
Depreciation Expense
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Cost of Project
Annual Cash flow-after taxes
Payback Period
155,000
Payback-Monroe
Cash Flow from Operations
Depreciation Expense
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Cost of Project
Annual Cash flow-after taxes
Payback Period
155,000
100,000
55,000
40%
22,000
33,000
100,000
133,000
500,000
133,000
3.759398
Payback Problem-Gravina
Gravina plans to spend $6,000 for machine
which it will depreciate on a straight-line
basis over a ten-year period. The machine
will generate additional cash revenues of
$2,400 a year. Gravina will incur no
additional costs except for depreciation and
income tax. The income tax rate is 50%.
What is the pay-back period?
a. 3.3 years b. 4.0 years
c. 5.0 years d. 6.7 years
Payback Problem-Gravina
Cash Flow from Operations
2,400
Depreciation Expense - 10 Yrs 600
Taxable Income
1,800
Tax Rate
50%
Income Tax
900
Net Income After Taxes
900
Add: Depreciation Expense
600
Equals net after-tax cash flow
Cost of Project
Annual Cash flow-after taxes
Payback Period
Payback Problem-Gravina
Cash Flow from Operations
Depreciation Expense - 10 Yrs
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Cost of Project
Annual Cash flow-after taxes
Payback Period
2,400
600
1,800
50%
900
900
600
1,500
6,000
1,500
4
6: Simple
rate of
return
Accounting Rate-of-Return Model
The accounting rate-of-return (ARR) model
expresses a project’s return as the increase in
expected average annual operating income divided
by the required initial investment.
Increase in
ARR
=
average annual
income
Initial
÷
required
investment
Accounting Rate-of-Return Model
Assume the following:
Investment is $6,075.
Useful life is four years.
Estimated disposal value is zero.
Expected annual cash inflow
from operations is $2,000.
What is the annual depreciation?
Ignore Depreciation here.
Accounting Rate-of-Return
$6,075 ÷ 4 = $1,518.75, (rounded
to $1,519) (Deprec.)
What is the ARR?
ARR =
($2,000 – $1,519) ÷ $6,075 = 7.9%
Acct Rate of Return - Saratoga
Saratoga will purchase a new machine for
$600,000. The new machine will be
depreciated on the straight line basis over a 6
years, with no salvage, and a full year's
depreciation is taken in the year of
acquisition. The new machine will produce
cash flow from operations, net of income
taxes, of $200,000 a year in each of the next
six years. The accounting (book value) rate of
return on the initial investment will be
a. 8.3% b. 12.0% c. 16.7%
d. 25.0%
Acct Rate of Return - Saratoga
Saratoga - accounting rate of return
Cost of new machine
$600,000
Life of machine
6 years
Deprec. per year - S-L
$100,000
Cash flow after taxes
$200,000 per yr
Deprec. (not a cash flow )
($100,000)
Book income
$100,000
Acct rate of return
(income/cost)
Acct Rate of Return - Saratoga
Saratoga - accounting rate of return
Cost of new machine
$600,000
Life of machine
6 years
Deprec. per year - S-L
$100,000
Cash flow after taxes
$200,000 per yr
Deprec. (not a cash flow )
($100,000)
Book income
$100,000
Acct rate of return
(income/cost)
16.67%
Apex
Apex Company is evaluating a capital budgeting
proposal. Relevant data follow:
Year.............. 1
2
3
4
5
6
P. V. of Annuity
of $1 at 15%.... $.870 1.626 2.284 2.856 3.353 3.785
The initial investment would be $30,000. It would be
depreciated on a straight- line basis over six years with
no salvage value. The before tax annual cash flow due
to this investment is $10,000, and the income tax rate is
40% paid in the same year as incurred. The desired rate
of return is 15%.
All cash flows occur at the end of the year.
What is the net present value of this proposal?
a. $(7,290) b. $280 c. $7,850 d. $11,860
Apex
Refer to the preceding slide.
What is the after tax accounting
rate of return?
a. 10%
b. 16-2/3%
c. 26-2/3%
d. 33-1/3%
8: Income
tax
NPV after Tax- Studley
On Jan. 1, Studley bought a new machine for $100,000
with an estimated useful life of five years and no
salvage. For book and tax purposes, the machine will be
depreciated using the straight line method and it is
expected to produce annual cash flow from operations,
before income taxes, of $40,000.
Studley uses a time adjusted rate of 12% and its income
tax rate will be 40% for all years.
The present value of $1 at 12% for five periods is 0.57,
and the present value of an ordinary annuity of $1 at
12% for five periods is 3.61.
The NPV of the machine should be
a. $15,520 positive b. $15,520 negative
c. $14,000 positive d. $13,680 negative
NPV after Tax- Studley
Cost of Project
Cash Flow from Operations
Depreciation Expense
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Annuity factor
Gross Present Value
Net Present Value
$ 100,000
NPV after Tax- Studley
Cost of Project
Cash Flow from Operations
Depreciation Expense
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Annuity factor
Gross Present Value
Net Present Value
$ 100,000
40,000
20,000
20,000
40%
8,000
12,000
20,000
32,000
NPV after Tax- Studley
Cost of Project
Cash Flow from Operations
Depreciation Expense
Taxable Income
Tax Rate
Income Tax
Net Income After Taxes
Add: Depreciation Expense
Equals net after-tax cash flow
Annuity factor
Gross Present Value
Net Present Value
$ 100,000
40,000
20,000
20,000
40%
8,000
12,000
20,000
32,000
3.61
115,520
$ 15,520
Form for Capital Budgeting-1
This format (following slides) can be used
for revenue and expenses for a proposed
project. If the same depreciation method
is used on both the books and the return,
you only need to complete the first
column.
(Many capital budgeting problems allow
you to assume that the same depreciation
methods is used for both purposes.)
Form for Capital Budgeting-2
Books Tax Return
1. Revenue
2. Cost of Sales
3. Gross Margin
4. Operating Expenses Requiring Cash
5. Cash Flow from Operations
6. Depreciation Expense (Books)
7. Depreciation Expense (Tax Return)
8. Book Income
9. Taxable Income
10. Income Tax Expense
11. Tax Paid
12. Net Income After Taxes
Form for Capital Budgeting-3
Now Compute Net Cash Flow After Income Taxes:
Cash Flow from Operation of asset (5)
Less: Taxes on income from asset (11)
Net after-tax cash flow from the asset
If Depreciation is Same on Tax Return & Books:
Net Income after taxes (12)
Add: Depreciation (6)
Equals Net after-tax cash flow
Gains or Losses on Disposal -1
Suppose a piece equipment purchased
for $125,000 is sold at the end of year
3 after taking three years of straightline depreciation.
What is the book value?
$125,000 – (3 × $25,000) = $50,000
Gains or Losses on Disposal - 2
Assume that it is sold for $70,000
and the tax rate is 40%.
What is the cash inflow?
($70,000 – $50,000) × 40% = $8,000
$70,000 – $8,000 = $62,000
Gains or Losses on Disposal
• If it is sold for book value, there is no
gain or loss and so there is no tax
effect.
• If it is sold for more than $50,000,
there is a gain and an additional tax
payment.
• If it is sold for less than $50,000, there
is a loss and a tax savings.
Combination of Problems-1
Items 1 through 4 are based on the following:
Ram Co. is negotiating for the purchase of
equipment that would cost $100,000. Ram
expects that $25,000 per year could be saved in
after-tax cash costs if the equipment were
acquired. The equipment's estimated useful life is
10 years, with no residual value, and would be
depreciated by the straight-line method. Ram's
minimum desired rate of return is 12%.
PV of an annuity of 1 at 12% for 10 periods:
PV of 1 due in 10 periods at 12%:
5.65
.322
Combination of Problems-2
Continue from preceding slide.
1. The net present value is
a. $ 41,250
b. $ 6,440
c. $12,200 d. $13,000
2. The payback period is
a. 4.0 years. b. 4.4 years.
c. 4.5 years. d. 5.0 years.
Combination of Problems-3
Continue from preceding slide.
3. The accrual accounting rate of return based on
initial investment is
a. 20%
b. 15%
c. 12%
d. 10%
4. In estimating the internal rate of return, the
factors in the table of present values of an
annuity should be taken from the columns closest
to the following multiple.
a. 0.65
b. 4.00
c. 5.00 d. 5.65
Combination of Problems
Information for Questions 1-4
Cost of Machine
$ 100,000
Annual after-tax cash flow
25,000
Useful Life in years
10
Desired rate of return
12%
P.V. of annuity of 1 at 12%-10 periods
5.65
P.V of 1 due in 10 periods at 12%
0.322
Combination of Problems
1 A Compute Present value
Annuity factor - P.V - 12%
Annual Cash Flow
Present value
Cost of Machine
Net present Value
5.65
25,000
141,250
(100,000)
$ 41,250
Combination of Problems
2 A Payback period
Cost of investment
After tax cash flow per yr
Payback period
$ 100,000
25,000
4
Combination of Problems
3 B Accounting Rate of Return
Cost of new machine
Life of machine
Deprec. per year - S-L method
Cash flow after taxes
Deprec. (not a cash flow item)
Book income
Accounting rate of return
$ 100,000
10
$10,000
25,000
($10,000)
$15,000
15.00%
Combination of Problems
4 B Approx. Internal Rate of Return
Cost of equipment
$ 100,000
Annual after tax cash flow $ 25,000
Multiple
4
Hilltop
Hilltop Company invested $100,000 in a two-year
project. Hilltop's expected rate of return was 12%. The
cash flow, net of income taxes, was $40,000 for the first
year. Present value and future value factors are as
follows:
Period
Present value
Future value
of $1 at 12%
of $1 at 12%
1
.8929
1.1200
2
.7972
1.2544
Assuming that the rate of return was exactly 12%, what
was the cash flow, net of income taxes, for the second
year of the project?
a. $51,247 b. $60,000 c. $64,284 d. $80,638
Hilltop
Present value problem-different unknown amount
Amount to be invested
$ 100,000
Desired return
12%
P.V. of cash flows must equal
$ 100,000
P.V. of first year cash flow
$ 40,000
P.V. factor-Year 1
0.8929
$
35,716
P.V. of second year cash flow
$
64,284
(Note this is the discounted P.V.)
Present value factor-Year 2
0.7972
2nd year cash flow-Undiscounted
$ 80,637.23
The End
68