Download TABLE 7-3 Calculating Container Pier`s Estimated NPV, IRR, and

CHAPTER 7
Discounted Cash
Flow Techniques
7-1
McGraw-Hill/Irwin
Copyright © 2007 The McGraw-Hill Companies, Inc. All rights reserved.
TABLE 7-1 Cash Flows for Container-Loading Pier
($ millions)
Year
0
1
2
3
4
5
6
7
8
9
10
Cash flow ($40) 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 17
7-2
FIGURE 7-1 Cash Flow Diagram for Container-Loading
Pier
7.5
17
1
40
7-3
2
3
4
5
6
7
8
9
10
Calculator Conventions
PMT
FV
…
0
PV
7-4
1
2
3
4
…
n
Using a Calculator to Find the Present Value of a
$2 million, 4-year Annuity, Discounted at 15%
Input:
Output:
7-5
4
15
?
n
i
PV
-5.71
2
PMT
-FV
$5,710,000 Today is Equivalent to $2 million a Year for
4 Years When the Interest Rate is 15 %
BeginningEnd-of
of-Period Interest at
-Period
Year Principal
15%
Principal
1
$5,710,000 $856,500 $6,566,500
2
4,566,500
684,975
5,251,475
3
3,251,475
487,721
3,739,196
4
1,739,196
260,879
2,000,075
Withdrawal
$2,000,000
2,000,000
2,000,000
2,000,000
Note: The $75 remaining in the account after the last withdrawal is due to
round-off error in the present value tables.
7-6
TABLE 7-2 NPV of Container Pier at Different Discount
Rates
Discount Rate
NPV ($ millions)
10%
12%
$9.75
5.44
IRR = 15%
18%
7-7
-4.48
FIGURE 7-2 NPV of Container Pier at Different Discount
Rates
NPV ($ millions)
50
40
30
20
IRR
10
0
-10
-20
0
4
8
12
16
Discount rate (%)
7-8
20
24
TABLE 7-3 Calculating Container Pier’s Estimated NPV,
IRR, and BCR with a Computer Spreadsheet
A
B
C
D
E
F
G
H
1 ESTIMATED ANNUAL CASH FLOWS ($ millions)
2 Year
0
1
2
3
4
5
6
3 Cash flow
($40)
7.5
7.5
7.5
7.5
7.5
7.5
4
5 Discount rate:
10%
6
Equation
7 Net present value (NPV):
=NPV(C5,C3:L3) + B3
8 Benefit Cost Ratio (BCR):
=NPV(C5,C3:L3)/-B3
9 Internal Rate of Return (IRR):
=IRR(B3:L3,0.12)
7-9
I
7
7.5
J
8
7.5
Answer
$9.75
1.24
15%
K
9
7.5
L
10
17
TABLE 7-4 Division Financial Analysis of New Line of
Cellular Telephones ($ millions)
Plant & equipment
Increased working caital
Preliminary engineering
Excess capacity
Total Investment
Total salvage value
Sales
Cost of sales
Gross profit
Interest expense
Allocated expenses
Selling & administrative expenses
Total operating expenses
7-10
1
0
Year
$
$
2
3
$
15
$
15
157 $
68
89
120
52
68
(30)
(14)
(2)
0
(46)
$
60 $
26
34
82 $
35
47
5
0
10
14
4
0
13
17
140 $
60
80
4
0
22
26
5
4
3
0
25
28
3
0
19
22
TABLE 7-4 (Continued)
Operating income
Depreciation
20
3
29
3
54
3
61
3
46
3
Income before tax
Tax at 40 percent
Income after tax
$
17
7
10 $
26
11
16 $
51
20
30 $
58
23
35 $
43
17
26
(46) $
10 $
16 $
30 $
35 $
41
Free cash flow
$
Net present value @ 15%
Benefit cost ratio
$
Internal rate of return
Totals may not add due to rounding.
7-11
35
1.76
37%
The Two-Step Treatment of Depreciation when Calculating
Aftertax Cash Flow (ATCF)
Operating income
7-12
$20
Less Depreciation
Profit before tax
3
17
Less Tax at 40%
Income aftertax
7
10
Plus Depreciation
Aftertax cash flow
3
$13
Calculating the Investment in Working Capital
Year
New phone sales
Working capital @ 20%
of sales
0
1
2
3
4
5
$0
$60
$82
$140
$157
$120
0
12
16
28
1
24
0
12
4
12
3
-7
Change in working capital
Recovery of working
capital
Total working capital
investment
7-13
24
$0
$(12)
$(4)
$(12)
$(3)
$31
TABLE 7-5 Revised Financial Analysis of New Line of
Cellular Telephones ($ millions)
Year
Assumptions
Increased working capital
Preliminary engineering
Excess capacity
Interest expense
Allocated expenses
Plant & equipment
Increased working capital
Preliminary engineering
Excess capacity
Total costs
Total salvage value
Sales
Cost of sales
Gross profit
7-14
0
1
2
3
4
5
20 percent of sales, full recovery at end of year 5
Already spent, sunk cost
$20 million cost of new capacity year 2, $2 million annual depreciation
Subsumed in discount rate
Variable allocated costs equal to 14% of sales
$
$
(30)
0
0
(12)
(30) $
$
(12) $
60 $
26
34
(4)
(20)
(24) $
82 $
35
47
(12)
15
31
(3)
14
(12) $
140 $
60
80
(3)
$
60
157 $
68
89
120
52
68
TABLE 7-5 (Continued)
Year
0
1
2
3
4
5
Interest expense
Allocated expenses
Selling & administrative expenses
Total operating expenses
0
8
10
18
0
11
13
25
0
20
22
42
0
22
25
47
0
17
19
36
Operating income
Depreciation
16
3
22
3
38
5
42
5
32
5
Income before tax
Tax at 40 percent
Income after tax
Add back depreciation
13
5
8 $
3
19
8
11 $
3
33
13
20 $
5
37
15
22 $
5
27
11
16
5
$
11 $
14 $
25 $
27 $
21
(30) $
(1) $
(10) $
13 $
24 $
82
$
After tax cash flow
Free cash flow
$
Net present value @ 15%
$
Benefit cost ratio
1.76
Internal rate of return
30%
Totals may not add due to rounding.
7-15
25
FIGURE 7A-1 Cash Flow Diagrams for Alternative
Service Station Designs
$100,000
1
2
3
4
5
6
7
$522,000
Inexpensive option
7-16
8
9
10
FIGURE 7A-1 (Continued)
$195,000
1
2
3
4
5
6
$1.1 million
Expensive option
7-17
7
8
9
10
TABLE 7A-1 Figures of Merit for Service Station Designs
Inexpensive option
Expensive option
7-18
NPV at
10%
BCR at
10%
IRR
$92,500
1.18
14%
98,200
1.09
12
TABLE 7A-2 Four Independent Investment Opportunities
under Capital Rationing (Capital budget =$200,000)
Investment
A
7-19
Initial
Cost
NPV at BCR at
12%
12%
$200,000 $10,000
IRR
1.05
14.4%
B
120,000
8,000
1.07
15.1
C
50,000
6,000
1.12
17.6
D
80,000
6,000
1.08
15.5
FIGURE 7A-2 Capital Budgeting Decision Tree
Use NPV, IRR, or BCR
Rank by NPV
Mutually exclusive
Rank by NPV over
common investment
horizon
No fractional
projects
Accept bundle
of investments
with highest NPV
Accept bundle of
investments with
highest NPV over
common horizon
Accept bundle
of investments
with highest NPV
Rank by BCR
7-20