Capital Investment Decisions and
the Time Value of Money
Chapter 9
9-1
Copyright © 2008 Prentice Hall All rights reserved
Objective 1
Describe the importance of capital
investments and the capital
budgeting process
9-2
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Capital Budgeting: The Process of
Making Capital Investment Decisions
• Companies make capital investments when they
acquire capital assets – assets used for a long
period of time
• Capital investments include buying new
equipment, building new plants, automating
production and developing major commercial
websites
• Capital investments affect operations for many
years and usually require large sums of money
9-3
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Four Popular Methods of Capital
Budgeting Analysis
•
•
•
•
Payback period
Accounting Rate of Return (ARR)
Net Present Value (NPV)
Internal Rate of Return (IRR)
9-4
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Capital Budgeting Process
• Identify potential investments
• Project the investment’s net cash
inflows
• Analyze the investments using one or
more of the four methods listed
previously
9-5
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Typical Capital Budgeting Process
1. Identify potential capital investments
2. Estimate future net cash inflows
3. Analyze potential investments:
a. Screen out undesirable investments using
payback and/or ARR
b. Further analyze investments using NPV
and/or IRR
4. Engage in capital rationing if necessary to
choose among alternative investments
5. Perform post-audits
9-6
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Objective 2
Use the payback and accounting
rate of return methods to make
capital investment decisions
9-7
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Payback Period
Payback – the length of time it takes to
recover, in net cash inflows, the cost of the
capital outlay
Amount invested
Expected annual net cash inflows
When the net cash inflows are equal each year, the computation of the
payback period is performed by dividing the amount invested by the
expected annual net cash inflows. The result is the payback period in
years.
9-8
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Payback with Unequal Net Cash
Inflows
Accumulate net cash inflows until amount
invested is recovered
9-9
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Payback Period
DECISION RULE:
Payback Period
Investments with shorter payback
periods are more desirable, all else
being equal
9-10
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E9-16: Compute Payback Period
with Equal Cash Flows
Amount invested
Expected annual net cash inflow
$1,236,100
$309,025
= 4 years
9-11
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Accounting Rate of Return
Average annual operating income from asset
Average amount invested in asset
Average amount invested in asset =
Original Investment + Residual Value
2
9-12
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Accounting Rate of Return
• Managers compare the accounting rate of
return to company’s required minimum
rate of return for investments of similar risk
• If the ARR is less than the required
minimum, the investment is rejected
9-13
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Accounting Rate of Return
DECISION RULE:
Invest in capital
assets?
Is expected accounting rate
of return > the required
rate of return?
Is expected accounting rate
of return < the required
rate of return?
Invest
Do not invest
9-14
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E9-19: Compute and Compare ARR
Atlas
$160,000
($1,000,000 + 0)/2
Veras
240,500
(1,200,000+100,000)/2
= 32%
= 37%
9-15
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E9-18: ARR with Unequal Cash
Flows
Average annual operating income:
Year 1
Year 2
Years 3-10 ($240,000 x 8)
Total net cash flows
Less: Total depreciation
Total operating income over life
Divided by years of life
Average annual operating income
$310,000
280,000
1,920,000
$2,510,000
(1,454,000)
$1,056,000
10
$105,600
9-16
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E9-18: ARR with Unequal Cash
Flows
Average annual operating income from asset
Average amount invested in asset
$105,600
($1,454,000+0) ÷ 2
= 14.53%
9-17
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Objective 3
Use the time value of money to
compute the present and future values
of single lump sums and annuities
9-18
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Time Value of Money
• The fact that invested money earns
income over time is called the time value
of money
• This is why we prefer to receive cash
sooner, rather than later
9-19
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Factors That Affect
Time Value of Money
• Principal – amount of the investment
 Lump sum
 Annuity
• Number of periods – number of times
interest is computed
• Interest rate – annual percentage
 Simple interest
 Compound interest
9-20
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Present Value & Future Value
Time Periods
1
2
3
4
5
6
Future Value
Present Value
9-21
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Future Value
Present
Value
Future
Value
10%
1 yr
2 yrs
$1,000
3 yrs
?
Interest = $1,000 x .10
Principal =
Future value after 1 year
$100
1,000
$1,100
9-22
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Future Value
Present
Value
Future
Value
10%
1 yr
2 yrs
$1,000
3 yrs
?
Future value after 1 year
Plus 10% interest
Future value after 2 years
Plus 10% interest
Future value after 3 years
$1,100
110
$1,210
121
$1,331
9-23
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Future Value
Present
Value
Future
Value
10%
1 yr
2 yrs
3 yrs
$1,000
?
Or use the Future Value of $1 table
Future value = Present value x table factor
= $1,000 x 1.331
= $1,331
9-24
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Future Value of an Annuity
Present
Value
10%
2 yrs
1 yr
0
Future
Value
$1,000
3 yrs
$1,000
Year 3
$1,000
Year 2 Future value of $1,000 in 1 year
($1,000 + ($1,000 x 10%)
1,100
Year 1 Future value of $1,000 in 2 years
($1,100 + ($1,100 x 10%)
1,210
$3,310
Copyright © 2008 Prentice Hall All rights reserved
$1,000
9-25
Future Value of an Annuity
Present
Value
10%
2 yrs
1 yr
0
Future
Value
$1,000
3 yrs
$1,000
$1,000
Future value = Payment x table factor
= $1,000 x 3.310
= $3,310
9-26
Copyright © 2008 Prentice Hall All rights reserved
E9-20: Compare Retirement Savings
Plans Using Future Value Concepts
Plan 1
Future value = Payment x table factor
= $3,000 x 164.494
= $493,482
Plan 2
Future value = Payment x table factor
= $7,500 x 21.384
= $160,380
9-27
Copyright © 2008 Prentice Hall All rights reserved
E9-20: Compare Retirement Savings
Plans Using Future Value Concepts
Plan 1
Future value of $1 = present value x table factor
= $493,482 x 2.594
= $1,280,092
Plan 2
Future value of $1 = present value x table factor
= $160,380 x 2.594
= $416,026
9-28
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Present Value
Present
Value
10%
Future
Value
1 yr
?
$1,100
Present value x 1.10 = $1,100
Present value = $1,100/1.10
Present value = $1,000
9-29
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Present Value
Present
Value
Future
Value
10%
1 yr
2 yrs
$1,100
?
Present value x 1.10 = $1,000 Present value x 1.10 = $1,100
Present value = $1,000/1.10 Present value = $1,100/1.10
Present value = $909
Present value = $1,000
9-30
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Present Value of $1 Table
Present
Value
Future
Value
10%
1 yr
2 yrs
$1,100
?
Present Value = Future Value x Table Factor
= $1,100 x 0.826
= $909
9-31
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Present Value of an Annuity
Present
Value
Future
Value
10%
1 yr
?
Present Value of $1,100
in one year:
$1,100 x 0.909 = $1,000
2 yrs
$1,100
$1,100
Present Value of $1,100
in two years:
$1,100 x 0.826 = $909
$1,000 + $909 = $1,909
9-32
Copyright © 2008 Prentice Hall All rights reserved
Present Value of an Annuity Table
Present
Value
10%
1 yr
?
Future
Value
2 yrs
$1,100
$1,100
Present Value of Annuity = Payments x Table Factor
= $1,100 x 1.736
= $1,909.60
9-33
Copyright © 2008 Prentice Hall All rights reserved
E9-22: Fund Future Cash Flows
Req. 1
Present value of annuity = Payment x table factor
= $30,000 x ?
=?
Req. 2
Present value of annuity = Payment x table factor
= $30,000 x ?
=?
9-34
Copyright © 2008 Prentice Hall All rights reserved
E9-23: Choosing a Lottery Payout
Option Using Present Value
Option 1:
Present value of $1 = $12,000,000 x ?
=?
Option 2:
Present value annuity = $2,250,000 x ?
=?
9-35
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E9-23: Choosing a Lottery Payout
Option
Option 3:
Present value of $1 = $10,000,000 x ?
=?
9-36
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Objective 4
Use discounted cash flow models
to make capital investment
decisions
9-37
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Discounted Cash Flow
Models
• Recognize time value of money
• Two methods
 Net present value
 Internal rate of return
• Compare amount of investment with its
expected net cash inflows
9-38
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Net Present Value Method
• Discount cash inflows to their present value and
then compare with capital outlay required by the
investment
• Discount rate (hurdle rate or required rate of
return) – required minimum rate of return given
riskiness of investment
• Proposal is acceptable when NPV is ≥ zero
• The higher the NPV, the more attractive the
investment
9-39
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Net Present Value
DECISION RULE:
Invest in capital
assets?
Is NPV positive?
Is NPV negative?
Invest
Do not invest
9-40
Copyright © 2008 Prentice Hall All rights reserved
E9-25: Calculate NPV – Equal Annual
Cash Flows
Cash
Flow
When?
Type of PV factor
cash flow
14%
Project A
(272,000) Now
60,000 Yrs 1-8 Annuity
NPV
PV
(272,000)
4.639
278,340
$6,340
9-41
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E9-24
Cash
Flow
When?
Type of PV factor
cash flow
12%
PV
Project B
(380,000) Now
70,000
NPV
Yrs 1-9 Annuity
5.328
(380,000)
372,960
$(7,040)
9-42
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Net Present Value for Unequal Cash
Inflows
When annual cash inflows are unequal,
you must use the present value of one
table applied to each annual cash inflow
9-43
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E9-27: Calculate NPV – Unequal
Cash Flows
Cash
Flow
When?
Type of PV factor
cash flow
14%
(900,000) Now
260,000
250,000
225,000
210,000
200,000
PV
(900,000)
Yr 1
Yr 2
Yr 3
Yr 4
Yr 5
Lump sum
Lump sum
Lump sum
Lump sum
Lump sum
.877
.769
.675
.592
.519
175,000 Yr 6
NPV
Lump sum
.456
Copyright © 2008 Prentice Hall All rights reserved
228,020
192,250
151,875
124,320
103,800
79,800
$(19,935)
9-44
E9-27 2.
Cash
Flow
When?
Type of PV factor
cash flow
14%
PV
(100,000) Yr 6
Lump sum
.456
(45,600)
75,000 Yr 7
50,000 Yr 7
NPV
Lump sum
Lump sum
.400
.400
30,000
20,000
$4,400
9-45
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Profitability Index
Number of dollars returned for every dollar
invested
Present value of net cash inflows
Investment
9-46
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E9-29: Capital Rationing Decision
Present value of net cash inflows
Investment
A: $1,695,000 ÷ $1,500,000 = 1.13
B: $1,960,000 ÷ $1,750,000 = 1.12
C: $2,200,000 ÷ $2,000,000 = 1.10
9-47
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Internal Rate of Return
• Rate of return a company can expect to
earn by investing in the project
• The interest rate that will cause the
present value to equal zero
9-48
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Internal Rate of Return
Step 1: Identify the expected net cash
receipts
Step 2: Find the discount rate that makes
total present value of net cash receipts =
present value of cash outflows
Annuity PV factor = Investment ÷ Annual Net Cash Receipts
9-49
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Internal Rate of Return
Step 3: On the present value of an annuity
of $1 table, scan the row corresponding to
the expected life
Choose column closest to annuity factor
you calculated in Step 2
9-50
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Internal Rate of Return
DECISION RULE:
Invest in capital
assets?
Does the IRR exceed
required rate of return?
Is the IRR less than
required rate of return?
Invest
Do not invest
9-51
Copyright © 2008 Prentice Hall All rights reserved
E9-26: Calculate IRR of
Equal Cash Flows
Project A:
PVA = Payment x Table Factor
272,000 = 60,000 x Factor
4.533 = Factor
Between 14% and 16%
9-52
Copyright © 2008 Prentice Hall All rights reserved
E9-26: Calculate IRR of
Equal Cash Flows
Project B:
PVA = Payment X Table Factor
380,000 = 70,000 x Factor
5.429 = Factor
Between 10% and 12%
9-53
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IRR with Unequal Periodic
Cash Flows
Trial and error procedure is needed to
determine the discount rate making the
project’s NPV equal to zero
9-54
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E9-28: Compute IRR for Unequal
Cash Flows
Compute net present value at 10%:
Cash
Flow
When?
Type of PV factor
cash flow
10%
(950,000) Now
PV
(950,000)
Lump sum .909
500,000 Yr 1
454,500
400,000
2 is positive,
.826
Lump sum
Since the Yr
NPV
the IRR
must be330,400
higher
225,300
12% .751
next.
300,000 Yr than
3 10%.
LumpTry
sum
$60,200
9-55
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E9-28: Compute IRR – Unequal
Cash Flows
Compute net present value at 12%:
Cash
Flow
When?
Type of PV factor
cash flow
12%
(950,000) Now
PV
(950,000)
Lump sum .893
500,000 Yr 1
446,500
400,000
2 is positive,
.797
Lump sum
Since the Yr
NPV
the IRR
must be318,800
higher
213,600
14% .712
next.
300,000 Yrthan
3 12%.
LumpTry
sum
$28,900
9-56
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E9-28: Compute IRR – Unequal
Cash Flows
Compute net present value at 14%:
Cash
Flow
When?
Type of PV factor
cash flow
14%
(950,000) Now
500,000
400,000
300,000
Yr 1
Yr 2
Yr 3
PV
(950,000)
Lump sum
Lump sum
Lump sum
.877
.769
.675
438,500
307,600
202,500
$(1,400)
9-57
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Objective 5
Compare and contrast the four
capital budgeting methods
9-58
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Comparison of Capital
Budgeting Models
Payback Period
• Simple
• Focus is the time it takes to recover cash
• Ignores cash flows after payback period
• Highlights risks of investments with longer
cash recovery periods
• Ignores time value of money
9-59
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Comparison of Capital
Budgeting Models
Accounting Rate of Return
• Only method that uses accrual accounting
• Shows how investment will affect
operating income
• Measures profitability of asset over its
entire life
• Ignores time value of money
9-60
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Comparison of Capital
Budgeting Models
Net Present Value
• Incorporates time value of money and net
cash flows
• Indicates if asset will earn minimum
required rate of return
• Shows excess (deficiency) of present
value of cash inflows over cost
• Profitability index can be computed for
capital rationing decisions
9-61
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Comparison of Capital
Budgeting Models
Internal Rate of Return
• Incorporates time value of money and net
cash flows
• Computes unique rate of return
• No additional steps needed for capital
rationing decisions
9-62
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End of Chapter 9
9-63
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