Download Capital investment decisions and time value of money

Capital Investment Decisions and
the Time Value of Money
Chapter 9
1
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Objective 1
Describe the importance of capital
investments and the capital
budgeting process
2
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Capital Budgeting
• Budgeting for the acquisition of “capital
assets”
• Capital budgeting models
(a) Payback period
(b) Accounting Rate of Return
(c) Net Present Value
(d) Internal Rate of Return
3
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Capital Budgeting
• Focus on cash flows
• Cash inflows
– Future cash revenue generated
– Future savings in ongoing cash operating
costs
– Future residual value
• Cash outflows
– Initial investment
– Operating costs, maintenance, repairs
4
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Capital Budgeting Process
•
•
•
•
•
Identify potential investments
Project net cash inflows
Analyze using one or more of methods
Capital rationing
Post-audits
5
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Objective 2
Use the payback and accounting
rate of return methods to make
capital investment decisions
6
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Payback Period
• Time period required to recover in net
cash receipts the dollars of the investment
Amount invested
Expected annual net cash inflows
7
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Payback with Unequal Net Cash
Inflows
• Accumulate net cash inflows until amount
invested is recovered
8
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Payback Period
DECISION RULE:
Payback Period
Investments with shorter
payback periods are more
desirable, all else being equal
9
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E9-16
Amount invested
Expected annual net cash inflow
$1,236,100
$309,025
=
4 years
10
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E9-17
Investment
Year 1
Unrecovered cost
Year 2
Unrecovered cost
Year 3 on
$1,454,000
(310,000)
$1,144,000
(280,000)
$864,000
÷ $240,000
3.6 years
Payback period = 2 + 3.6 = 5.6 years
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
12
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Accounting Rate of Return
• Compare accounting rate of return to
company’s required minimum rate of
return for investments of similar risk
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
14
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E9-18
Atlas
$160,000
($1,000,000 + 0)/2
Veras
240,500
(1,200,000+100,000)/2
32%
37%
15
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E9-19
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
16
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E9-19
Average annual operating income from asset
Average amount invested in asset
$105,600
($1,454,000+0) ÷ 2
14.53%
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
18
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Time Value of Money
• Invested money earns income over time
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
20
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Present Value & Future Value
Time Periods
1
2
3
4
5
6
Future Value
Present Value
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
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
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
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
$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
25
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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
$1,000
Future value = Payment x table factor
= $1,000 x 3.310
= $3,310
26
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E9-20
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
27
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E9-20
Req 4.
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
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
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
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
31
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Present Value of an Annuity
Present
Value
Future
Value
10%
1 yr
2 yrs
$1,100
?????
Present Value of $1,100
in one year:
$1,100 x 0.909 = $1,000
$1,100
Present Value of $1,100
in two years:
$1,100 x 0.826 = $909
$1,000 + $909 = $1,909
32
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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
33
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E9-22
Req 1
Present value of annuity = Payment x table factor
= $30,000 x 3.993
= $119,760
Req 2
Present value of annuity = Payment x table factor
= $30,000 x 4.212
= $126,360
34
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E9-23
Option 1:
Present value of $1 = $12,000,000 x .681
= $8,172,000
Option 2:
Present value annuity = $2,250,000 x 3.993
= $8,984,000
35
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E9-23
Option 3:
Present value of $1 = $10,000,000 x .794
= $7,940,000
36
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Objective 4
Use discounted cash flow models
to make capital investment
decisions
37
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Discounted Cash Flows
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
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
39
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Net Present Value
DECISION RULE:
Invest in capital assets?
Is NPV positive?
Is NPV negative?
Invest
Do not invest
40
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E9-24
Cash
Flow
When?
Type of PV factor
cash flow
14%
Project A
(272,000) Now
PV
(272,000)
60,000 Yrs 1-8 Annuity
NPV
4.639
278,340
$6,340
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)
42
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Net Present Value
When annual cash inflows are unequal
you must use the present value of one
table applied to each annual cash
inflow.
43
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E9-25
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
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228,020
192,250
151,875
124,320
103,800
79,800
$(19,935)
44
E9-25 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
45
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Profitability Index
• Number of dollars returned for every dollar
invested
Present value of net cash inflows
Investment
46
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E9-28
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
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
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
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.
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
51
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E9-26
Project A:
PVAo = Payment x Table Factor
272,000 = 60,000 x Factor
4.533 = Factor
Between 14% and 16%
52
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E9-26
Project B:
PVAo = Payment X Table Factor
380,000 = 70,000 x Factor
5.429 = Factor
Between 10% and 12%
53
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IRR with Unequal Periodic Cash
Flows
• Trial and error procedure
54
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E9-27
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 Yrthan
3 10%.
LumpTry
sum
$60,200
55
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E9-27
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
Since the Yr
NPV
the IRR
must be318,800
higher
400,000
2 is positive,
.797
Lump sum
14% .712
next.
213,600
300,000 Yrthan
3 12%.
LumpTry
sum
$28,900
56
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E9-27
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)
57
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Objective 5
Compare and contrast the four
capital budgeting methods
58
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Comparison of Capital
Budgeting Models
Payback Period
• Simple
• Focus – 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
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
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
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
62
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End of Chapter 9
63
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