Finance reserch report based on provided data

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McGraw-Hill/Irwin

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

Net Present Value and Other Investment Rules

Chapter 5

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5-*

Example:

  • Project A: renting
  • Project B: buying (with or withouth financing)
  • What are the cash flows in 20 years?
  • How to compare these projects?

5-*

Key Concepts and Skills

  • Be able to compute payback and discounted payback and understand their shortcomings
  • Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches
  • Be able to compute net present value and understand why it is the best decision criterion

*

5-*

Chapter Outline

5.1 Why Use Net Present Value?

5.2 The Payback Period Method

5.3 The Discounted Payback Period Method

5.4 The Internal Rate of Return

5.5 Problems with the IRR Approach

5.6 The Profitability Index

5.7 The Practice of Capital Budgeting

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5-*

5.1 Why Use Net Present Value?

  • Accepting positive NPV projects benefits shareholders.

NPV uses cash flows

NPV uses all the cash flows of the project

NPV discounts the cash flows properly

*

Note that the NPV recognizes the magnitude, risk, and timing of cash flows, which was an important description of why stock price maximization should be the primary corporate goal.

5-*

The Net Present Value (NPV) Rule

  • Net Present Value (NPV) =

Total PV of future CF’s + Initial Investment

  • Estimating NPV:

1. Estimate future cash flows: how much? and when?

2. Estimate discount rate

3. Estimate initial costs

  • Minimum Acceptance Criteria: Accept if NPV > 0
  • Ranking Criteria: Choose the highest NPV

*

Note that although we add the initial investment, this value is a negative number.

5-*

Calculating NPV with Spreadsheets

  • Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well.
  • Using the NPV function:
  • The first component is the required return entered as a decimal.
  • The second component is the range of cash flows beginning with year 1.
  • Add the initial investment after computing the NPV.

*

Click on the Excel icon to go to an embedded Excel worksheet that has example cash flows, along with the correct and incorrect ways to compute NPV. Click on the cell with the solution to show the students the difference in the formulas.

Again, note that when we add the initial investment, this is a negative number.

Sheet1

Year 0 1 2 3
Cash Flows -165000 63120 70800 91080
Required Return 0.12
NPV - Incorrect $11,274.48
NPV - Correct $12,627.41

Sheet2

Sheet3

Sheet1

Year 0 1 2 3
Cash Flows -165000 63120 70800 91080
Required Return 0.12
NPV - Incorrect $11,274.48
NPV - Correct $12,627.41

Sheet2

Sheet3

5-*

5.2 The Payback Period Method

  • How long does it take the project to “pay back” its initial investment?
  • Payback Period = number of years to recover initial costs
  • Minimum Acceptance Criteria:
  • Set by management
  • Ranking Criteria:
  • Set by management

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5-*

The Payback Period Method

  • Disadvantages:
  • Ignores the time value of money
  • Ignores cash flows after the payback period
  • Biased against long-term projects
  • Requires an arbitrary acceptance criteria
  • A project accepted based on the payback criteria may not have a positive NPV
  • Advantages:
  • Easy to understand
  • Biased toward liquidity

*

Cash flows prior to the cutoff are implicitly discounted at a rate of zero, and cash flows after the cutoff are discounted using an infinite discount rate.

5-*

5.3 The Discounted Payback Period

  • How long does it take the project to “pay back” its initial investment, taking the time value of money into account?
  • Decision rule: Accept the project if it pays back on a discounted basis within the specified time.
  • By the time you have discounted the cash flows, you might as well calculate the NPV.

*

Similar advantages and disadvantages as standard payback method, with the exception that cash flows prior to the cutoff are not discounted at zero.

5-*

5.4 The Internal Rate of Return

  • IRR: the discount rate that sets NPV to zero
  • Minimum Acceptance Criteria:
  • Accept if the IRR exceeds the required return
  • Ranking Criteria:
  • Select alternative with the highest IRR
  • Reinvestment assumption:
  • All future cash flows are assumed to be reinvested at the IRR

*

5-*

Internal Rate of Return (IRR)

  • Disadvantages:
  • Does not distinguish between investing and borrowing
  • IRR may not exist, or there may be multiple IRRs
  • Problems with mutually exclusive investments

  • Advantages:
  • Easy to understand and communicate

*

5-*

IRR: Example

Consider the following project:

The internal rate of return for this project is 19.44%

0

1

2

3

$50

$100

$150

-$200

*

5-*

NPV Payoff Profile

If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept.

IRR = 19.44%

*

Sheet1

0 1 2 3
-200 50 100 150
19.44%
Discount Rate NPV
0% $100.00
1% $92.20
2% $84.79
3% $77.74
4% $71.04
5% $64.66
6% $58.60
7% $52.82
8% $47.32
9% $42.08
10% $37.09
11% $32.33
12% $27.79
13% $23.47
14% $19.34
15% $15.41
16% $11.65
17% $8.07
18% $4.65
19% $1.38
20% ($1.74)
21% ($4.72)
22% ($7.56)
23% ($10.28)
24% ($12.88)
25% ($15.36)
26% ($17.73)
27% ($20.00)
28% ($22.17)
29% ($24.24)
30% ($26.22)
31% ($28.12)
32% ($29.93)
33% ($31.67)
34% ($33.32)
35% ($34.91)
36% ($36.43)
37% ($37.88)
38% ($39.26)
39% ($40.59)
40% ($41.86)
Discount Rate NPV
0% $100.00
4% $73.88
8% $51.11
12% $31.13
16% $13.52
20% ($2.08)
24% ($15.97)
28% ($28.38)
32% ($39.51)
36% ($49.54)
40% ($58.60)
44% ($66.82)
48% ($50.20)
52% ($53.36)
56% ($55.99)
60% ($58.17)
64% ($59.95)
17% $8.07
18% $4.65
19% $1.38
20% ($1.74)
21% ($4.72)
22% ($7.56)
23% ($10.28)
24% ($12.88)
25% ($15.36)
26% ($17.73)
27% ($20.00)
28% ($22.17)
29% ($24.24)
30% ($26.22)
31% ($28.12)
32% ($29.93)
33% ($31.67)
34% ($33.32)
35% ($34.91)
36% ($36.43)
37% ($37.88)
38% ($39.26)
39% ($40.59)
40% ($41.86)

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
NPV
Discount rate
NPV

Sheet2

Sheet3

Chart5

0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
NPV
Discount rate
NPV
100
93.1230776249
86.484836149
80.0745291367
73.8819981793
67.8976352446
62.112347777
56.5175263236
51.1050144795
45.8670809688
40.796393689
35.8859955646
31.12928207
26.5199802897
22.0521294001
17.720062464
13.5183894379
9.4419813026
5.485955234
1.6456607359
-2.0833333333
-5.7052509058
-9.2241200805
-12.6437837847
-15.9679097714
-19.2
-22.3433994409
-25.4013043459
-28.3767700195
-31.2727181254
-34.0919435594
-36.8371209173
-39.5108105852
-42.1154644767
-44.6534314394
-47.1269623533
-49.53821494
-51.889258301
-54.1820772034
-56.4185761271
-58.6005830904

Sheet1

0 1 2 3
-200 50 100 150
19.44%
Discount Rate NPV
0% $100.00
1% $93.12
2% $86.48
3% $80.07
4% $73.88
5% $67.90
6% $62.11
7% $56.52
8% $51.11
9% $45.87
10% $40.80
11% $35.89
12% $31.13
13% $26.52
14% $22.05
15% $17.72
16% $13.52
17% $9.44
18% $5.49
19% $1.65
20% ($2.08)
21% ($5.71)
22% ($9.22)
23% ($12.64)
24% ($15.97)
25% ($19.20)
26% ($22.34)
27% ($25.40)
28% ($28.38)
29% ($31.27)
30% ($34.09)
31% ($36.84)
32% ($39.51)
33% ($42.12)
34% ($44.65)
35% ($47.13)
36% ($49.54)
37% ($51.89)
38% ($54.18)
39% ($56.42)
40% ($58.60)
Discount Rate NPV
0% $100.00
4% $73.88
8% $51.11
12% $31.13
16% $13.52
20% ($2.08)
24% ($15.97)
28% ($28.38)
32% ($39.51)
36% ($49.54)
40% ($58.60)
44% ($66.82)
48% ($74.29)
52% ($81.11)
56% ($87.35)
60% ($93.07)
64% ($98.33)
17% $9.44
18% $5.49
19% $1.65
20% ($2.08)
21% ($5.71)
22% ($9.22)
23% ($12.64)
24% ($15.97)
25% ($19.20)
26% ($22.34)
27% ($25.40)
28% ($28.38)
29% ($31.27)
30% ($34.09)
31% ($36.84)
32% ($39.51)
33% ($42.12)
34% ($44.65)
35% ($47.13)
36% ($49.54)
37% ($51.89)
38% ($54.18)
39% ($56.42)
40% ($58.60)

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
NPV
Discount rate
NPV
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Sheet2

Sheet3

5-*

Calculating IRR with Spreadsheets

  • You start with the same cash flows as you did for the NPV.
  • You use the IRR function:
  • You first enter your range of cash flows, beginning with the initial cash flow.
  • You can enter a guess, but it is not necessary.
  • The default format is a whole percent – you will normally want to increase the decimal places to at least two.

*

Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on a spreadsheet.

Sheet1

Year 0 1 2 3
Cash Flows -165000 63120 70800 91080
Required Return 0.12
NPV - Incorrect $11,274.48
NPV - Correct $12,627.41
IRR 16% 16.13%
Default Format

Sheet2

Sheet3

5-*

5.5 Problems with IRR

  • Multiple IRRs
  • Are We Borrowing or Lending
  • The Scale Problem
  • The Timing Problem

*

5-*

Mutually Exclusive vs. Independent

  • Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system.
  • RANK all alternatives, and select the best one.

  • Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
  • Must exceed a MINIMUM acceptance criteria

*

5-*

Multiple IRRs

There are two IRRs for this project:

Which one should we use?

0 1 2 3

$200 $800

-$200

- $800

100% = IRR2

0% = IRR1

*

It is good to mention that the number of IRRs is equivalent to the number of sign changes in the cash flows.

Chart4

-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
NPV
Discount rate
NPV
-87.5171467764
-36.1277154104
0
25.0296944174
41.9233658903
52.8149913701
59.2592592593
62.4
63.0860263996
61.9519382208
59.4752186589
56.0170568699
51.8518518519
47.1887482797
42.1875
36.9702534992
31.6303684103
26.2390670554
20.8504801097
15.5054981936
10.2347280945
5.0607731081
0
-4.9360862437
-9.7397689234
-14.4062786924
-18.9331329827
-23.3196159122
-27.5663680447
-31.6750623658
-35.6481481481
-39.4886484373
-43.2
-46.7859269813
-50.2503413746
-53.5972648562
-56.8307676675
-59.9549211119
-62.9737609329
-65.8912593889
-68.7113042765

Sheet1

0 1 2 3
-200 200 800 -800
-0.00%
Discount Rate NPV
-10% ($87.52)
-5% ($36.13)
0% $0.00
5% $25.03
10% $41.92
15% $52.81
20% $59.26
25% $62.40
30% $63.09
35% $61.95
40% $59.48
45% $56.02
50% $51.85
55% $47.19
60% $42.19
65% $36.97
70% $31.63
75% $26.24
80% $20.85
85% $15.51
90% $10.23
95% $5.06
100% $0.00
105% ($4.94)
110% ($9.74)
115% ($14.41)
120% ($18.93)
125% ($23.32)
130% ($27.57)
135% ($31.68)
140% ($35.65)
145% ($39.49)
150% ($43.20)
155% ($46.79)
160% ($50.25)
165% ($53.60)
170% ($56.83)
175% ($59.95)
180% ($62.97)
185% ($65.89)
190% ($68.71)
Discount Rate NPV
0% $0.00
4% $20.76
8% $35.99
12% $46.90
16% $54.42
20% $59.26
24% $61.99
28% $63.06
32% $62.82
36% $61.55
40% $59.48
44% $56.77
48% $53.59
52% $50.04
56% $46.21
60% $42.19
64% $38.03
17% $55.85
18% $57.13
19% $58.27
20% $59.26
21% $60.12
22% $60.86
23% $61.48
24% $61.99
25% $62.40
26% $62.71
27% $62.93
28% $63.06
29% $63.11
30% $63.09
31% $62.99
32% $62.82
33% $62.59
34% $62.30
35% $61.95
36% $61.55
37% $61.10
38% $60.60
39% $60.06
40% $59.48

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
NPV
Discount rate
NPV
-87.5171467764
-38.0291741162
0
23.8378042071
38.1121508094
45.9260794523
49.3827160494
49.92
48.5277126151
45.890324608
42.4822990421
38.6324530137
34.5679012346
30.4443537288
26.3671875
22.4062142419
18.6060990649
14.9937526031
11.583600061
8.3813503749
5.3866989971
2.5952682606
0
-2.4078469481
-4.6379852016
-6.7005947407
-8.6059695376
-10.3642737388
-11.9853774107
-13.4787499429
-14.8533950617
-16.1178156887
-17.28
-18.3474223456
-19.3270543748
-20.2253829646
-21.0484324695
-21.8017894953
-22.4906289046
-23.1197401364
-23.6935531988

Sheet2

Sheet3

5-*

Modified IRR

  • Calculate the net present value of all cash outflows using the borrowing rate.
  • Calculate the net future value of all cash inflows using the investing rate.
  • Find the rate of return that equates these values.
  • Benefits: single answer and specific rates for borrowing and reinvestment

*

The alternative approach discussed in the text is to discount cash flows over a single period (or subset of time), then combine them as necessary to eliminate any sign differences. The approach presented in the slide is more generalized.

5-*

The Scale Problem

Would you rather make 100% or 50% on your investments?

What if the 100% return is on a $1 investment, while the 50% return is on a $1,000 investment?

*

5-*

The Timing Problem

0 1 2 3

$10,000 $1,000 $1,000

-$10,000

Project A

0 1 2 3

$1,000 $1,000 $12,000

-$10,000

Project B

*

The preferred project in this case depends on the discount rate, not the IRR.

5-*

The Timing Problem

10.55% = crossover rate

16.04% = IRRA

12.94% = IRRB

*

The cross-over rate is the IRR of project A-B

Chart7

0 0
0.01 0.01
0.02 0.02
0.03 0.03
0.04 0.04
0.05 0.05
0.06 0.06
0.07 0.07
0.08 0.08
0.09 0.09
0.1 0.1
0.11 0.11
0.12 0.12
0.13 0.13
0.14 0.14
0.15 0.15
0.16 0.16
0.17 0.17
0.18 0.18
0.19 0.19
0.2 0.2
0.21 0.21
0.22 0.22
0.23 0.23
0.24 0.24
0.25 0.25
0.26 0.26
0.27 0.27
0.28 0.28
0.29 0.29
0.3 0.3
0.31 0.31
0.32 0.32
0.33 0.33
0.34 0.34
0.35 0.35
0.36 0.36
0.37 0.37
0.38 0.38
0.39 0.39
0.4 0.4
Project A
Project B
Discount rate
NPV
2000
4000
1851.8762963445
3617.4768344396
1707.4126844125
3249.4289526653
1566.4754325646
2895.1696077794
1428.9371870733
2554.0509786072
1294.676600799
2225.4616132167
1163.5779871975
1908.824062817
1035.5309976874
1603.5926902158
910.4303205812
1309.2516384697
788.1753999331
1025.3129466599
668.6701728024
751.3148009016
551.822823554
486.8199097564
437.5455539359
231.4139941691
325.7543677754
-15.2956170815
216.3688692337
-253.6812946494
109.3120736418
-484.0963261281
4.5102300217
-706.8760506786
-98.1073455323
-922.3389170792
-198.6084263727
-1130.7874709683
-297.0580224181
-1332.5092765727
-393.5185185185
-1527.7777777778
-488.0498046638
-1716.8531029979
-580.709398584
-1899.9828179451
-671.5525612524
-2077.4026300644
-760.6324057601
-2249.3370481018
-848
-2416
-933.7044635609
-2577.5954120625
-1017.7930592082
-2734.3177521001
-1100.3112792969
-2886.3525390625
-1181.3029274385
-3033.8768214678
-1260.8101957214
-3177.0596267638
-1338.8737377624
-3316.0623835957
-1415.5327378468
-3451.0393188079
-1490.8249763988
-3582.1378308681
-1564.7868920047
-3709.4988412804
-1637.4536401971
-3833.2571254382
-1708.859149196
-3953.5416242622
-1779.0361727853
-4070.4757378703
-1848.016340496
-4184.1776024401
-1915.8302052525
-4294.760351338
-1982.5072886297
-4402.332361516

Sheet1

0 1 2 3
$ (10,000.00) $ 10,000.00 $ 1,000.00 $ 1,000.00 A
$ (10,000.00) $ 1,000.00 $ 1,000.00 $ 12,000.00 B
16.04% IRR A
12.94% IRR B
Discount Rate Project A Project B
0% $2,000.00 $4,000.00
1% $1,851.88 $3,617.48
2% $1,707.41 $3,249.43
3% $1,566.48 $2,895.17
4% $1,428.94 $2,554.05
5% $1,294.68 $2,225.46
6% $1,163.58 $1,908.82
7% $1,035.53 $1,603.59
8% $910.43 $1,309.25
9% $788.18 $1,025.31
10% $668.67 $751.31
11% $551.82 $486.82
12% $437.55 $231.41
13% $325.75 ($15.30)
14% $216.37 ($253.68)
15% $109.31 ($484.10)
16% $4.51 ($706.88)
17% ($98.11) ($922.34)
18% ($198.61) ($1,130.79)
19% ($297.06) ($1,332.51)
20% ($393.52) ($1,527.78)
21% ($488.05) ($1,716.85)
22% ($580.71) ($1,899.98)
23% ($671.55) ($2,077.40)
24% ($760.63) ($2,249.34)
25% ($848.00) ($2,416.00)
26% ($933.70) ($2,577.60)
27% ($1,017.79) ($2,734.32)
28% ($1,100.31) ($2,886.35)
29% ($1,181.30) ($3,033.88)
30% ($1,260.81) ($3,177.06)
31% ($1,338.87) ($3,316.06)
32% ($1,415.53) ($3,451.04)
33% ($1,490.82) ($3,582.14)
34% ($1,564.79) ($3,709.50)
35% ($1,637.45) ($3,833.26)
36% ($1,708.86) ($3,953.54)
37% ($1,779.04) ($4,070.48)
38% ($1,848.02) ($4,184.18)
39% ($1,915.83) ($4,294.76)
40% ($1,982.51) ($4,402.33)
Discount Rate NPV
0% $2,000.00
4% $1,428.94
8% $910.43
12% $437.55
16% $4.51
20% ($393.52)
24% ($760.63)
28% ($1,100.31)
32% ($1,415.53)
36% ($1,708.86)
40% ($1,982.51)
44% ($2,238.40)
48% ($2,478.23)
52% ($2,703.47)
56% ($2,915.42)
60% ($3,115.23)
64% ($3,303.93)
17% ($98.11)
18% ($198.61)
19% ($297.06)
20% ($393.52)
21% ($488.05)
22% ($580.71)
23% ($671.55)
24% ($760.63)
25% ($848.00)
26% ($933.70)
27% ($1,017.79)
28% ($1,100.31)
29% ($1,181.30)
30% ($1,260.81)
31% ($1,338.87)
32% ($1,415.53)
33% ($1,490.82)
34% ($1,564.79)
35% ($1,637.45)
36% ($1,708.86)
37% ($1,779.04)
38% ($1,848.02)
39% ($1,915.83)
40% ($1,982.51)

Sheet1

0 0
0.01 0.01
0.02 0.02
0.03 0.03
0.04 0.04
0.05 0.05
0.06 0.06
0.07 0.07
0.08 0.08
0.09 0.09
0.1 0.1
0.11 0.11
0.12 0.12
0.13 0.13
0.14 0.14
0.15 0.15
0.16 0.16
0.17 0.17
0.18 0.18
0.19 0.19
0.2 0.2
0.21 0.21
0.22 0.22
0.23 0.23
0.24 0.24
0.25 0.25
0.26 0.26
0.27 0.27
0.28 0.28
0.29 0.29
0.3 0.3
0.31 0.31
0.32 0.32
0.33 0.33
0.34 0.34
0.35 0.35
0.36 0.36
0.37 0.37
0.38 0.38
0.39 0.39
0.4 0.4
Project A
Project B
Discount rate
NPV
2000
4000
1833.5408874698
3581.6602321185
1673.934004326
3185.7146594758
1520.8499345287
2810.8442793975
1373.9780644935
2455.8182486608
1233.0253340943
2119.4872506826
1097.7150822618
1800.7774177518
967.7859791471
1498.684757211
842.9910375752
1212.2700356201
723.0966971864
940.6540795045
607.8819752749
683.0134553651
497.1376788775
438.576495276
390.665673157
206.619637651
288.2782015711
-13.5359443199
189.7972537138
-222.5274514468
95.0539770798
-420.9533270679
3.8881293291
-609.3759057574
-83.8524320789
-788.3238607515
-168.3122257396
-958.2944669223
-249.6285902673
-1119.7556945989
-327.9320987654
-1273.1481481482
-403.3469460031
-1418.8868619817
-475.9913103148
-1557.3629655288
-545.9776920751
-1688.9452276946
-613.4132304517
-1813.9814904047
-678.4
-1932.8
-741.0352885404
-2045.7106444941
-801.4118576442
-2153.0061040158
-859.6181869507
-2254.9629211426
-915.7387034407
-2351.8424972619
-969.8539967088
-2443.8920205875
-1022.0410211927
-2531.3453309891
-1072.3732862476
-2614.4237263696
-1120.9210348863
-2693.3367149384
-1167.7514119438
-2768.2827173734
-1212.9286223682
-2839.4497225468
-1256.5140802912
-2907.0159001928
-1298.5665494783
-2971.150173628
-1339.1422757217
-3032.0127553914
-1378.2951116924
-3089.7556484446
-1416.0766347355
-3144.5231153686

Sheet2

Sheet3

5-*

Calculating the Crossover Rate

Compute the IRR for either project “A-B” or “B-A”

10.55% = IRR

*

Sheet1

Year Project A Project B Project A-B Project B-A
0 ($10,000) ($10,000) $0 $0
1 $10,000 $1,000 $9,000 ($9,000)
2 $1,000 $1,000 $0 $0
3 $1,000 $12,000 ($11,000) $11,000
10.55%
Discount rtae A-B B-A
0% ($2,000.00)
1% ($1,748.12)
2% ($1,511.78)
3% ($1,289.99)
4% ($1,081.84)
5% ($886.46)
6% ($703.06)
7% ($530.90)
8% ($369.28)
9% ($217.56)
10% ($75.13)
11% $58.56
12% $184.05
13% $301.81
14% $412.32
15% $516.01
16% $613.26
17% $704.47
18% $789.98
19% $870.13
20% $945.22

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
A-B
Discount rate
NPV
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Sheet2

Sheet3

Chart2

0 0
0.01 0.01
0.02 0.02
0.03 0.03
0.04 0.04
0.05 0.05
0.06 0.06
0.07 0.07
0.08 0.08
0.09 0.09
0.1 0.1
0.11 0.11
0.12 0.12
0.13 0.13
0.14 0.14
0.15 0.15
0.16 0.16
0.17 0.17
0.18 0.18
0.19 0.19
0.2 0.2
A-B
B-A
Discount rate
NPV
-2000
2000
-1765.6005380952
1765.6005380952
-1542.0162682528
1542.0162682528
-1328.6941752149
1328.6941752149
-1125.1137915339
1125.1137915339
-930.7850124177
930.7850124177
-745.2460756195
745.2460756195
-568.0616925283
568.0616925283
-398.8213178885
398.8213178885
-237.1375467268
237.1375467268
-82.6446280992
82.6446280992
65.0029137977
-65.0029137977
206.1315597668
-206.1315597668
341.0499848569
-341.0499848569
470.0501638831
-470.0501638831
593.4083997699
-593.4083997699
711.3862807003
-711.3862807003
824.2315715469
-824.2315715469
932.1790445956
-932.1790445956
1035.4512541547
-1035.4512541547
1134.2592592593
-1134.2592592593

Sheet1

Year Project A Project B Project A-B Project B-A
0 ($10,000) ($10,000) $0 $0
1 $10,000 $1,000 $9,000 ($9,000)
2 $1,000 $1,000 $0 $0
3 $1,000 $12,000 ($11,000) $11,000
10.55%
Discount rtae A-B B-A
0% ($2,000.00) $2,000.00
1% ($1,765.60) $1,765.60
2% ($1,542.02) $1,542.02
3% ($1,328.69) $1,328.69
4% ($1,125.11) $1,125.11
5% ($930.79) $930.79
6% ($745.25) $745.25
7% ($568.06) $568.06
8% ($398.82) $398.82
9% ($237.14) $237.14
10% ($82.64) $82.64
11% $65.00 ($65.00)
12% $206.13 ($206.13)
13% $341.05 ($341.05)
14% $470.05 ($470.05)
15% $593.41 ($593.41)
16% $711.39 ($711.39)
17% $824.23 ($824.23)
18% $932.18 ($932.18)
19% $1,035.45 ($1,035.45)
20% $1,134.26 ($1,134.26)

Sheet1
A-B
B-A
Discount rate
NPV

Sheet2

Sheet3

5-*

NPV versus IRR

  • NPV and IRR will generally give the same decision.
  • Exceptions:
  • Non-conventional cash flows – cash flow signs change more than once
  • Mutually exclusive projects
  • Initial investments are substantially different
  • Timing of cash flows is substantially different

*

5-*

5.6 The Profitability Index (PI)

  • Minimum Acceptance Criteria:
  • Accept if PI > 1

  • Ranking Criteria:
  • Select alternative with highest PI

*

5-*

The Profitability Index

  • Disadvantages:
  • Problems with mutually exclusive investments
  • Advantages:
  • May be useful when available investment funds are limited
  • Easy to understand and communicate
  • Correct decision when evaluating independent projects

*

5-*

5.7 The Practice of Capital Budgeting

  • Varies by industry:
  • Some firms may use payback, while others choose an alternative approach.
  • The most frequently used technique for large corporations is either IRR or NPV.

*

5-*

Example of Investment Rules

Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%.

Year Project A Project B

0 -$200 -$150

1 $200 $50

2 $800 $100

3 -$800 $150

*

5-*

Example of Investment Rules

Project A Project B

CF0 -$200.00 -$150.00

PV0 of CF1-3 $241.92 $240.80

NPV = $41.92 $90.80

IRR = 0%, 100% 36.19%

PI = 1.2096 1.6053

*

5-*

Example of Investment Rules

Payback Period:

Project A Project B

Time CF Cum. CF CF Cum. CF

0 -200 -200 -150 -150

1 200 0 50 -100

2 800 800 100 0

3 -800 0 150 150

Payback period for project B = 2 years.

Payback period for project A = 1 or 3 years?

*

5-*

NPV and IRR Relationship

Discount rate NPV for A NPV for B

-10% -87.52 234.77

0% 0.00 150.00

20% 59.26 47.92

40% 59.48 -8.60

60% 42.19 -43.07

80% 20.85 -65.64

100% 0.00 -81.25

120% -18.93 -92.52

*

5-*

($200)

($100)

$0

$100

$200

$300

$400

-15%

0%

15%

30%

45%

70%

100%

130%

160%

190%

Discount rates

NPV

NPV Profiles

IRR 2(A)

Cross-over Rate

Project A

Project B

IRR 1(A)

IRR (B)

*

5-*

Summary – Discounted Cash Flow

  • Net present value
  • Difference between market value and cost ?
  • Accept the project if the NPV is positive
  • Has no serious problems
  • Preferred decision criterion
  • Internal rate of return
  • Discount rate that makes NPV = 0
  • Take the project if the IRR is greater than the required return
  • Same decision as NPV with conventional cash flows
  • IRR is unreliable with non-conventional cash flows or mutually exclusive projects ?
  • Profitability Index
  • Benefit-cost ratio
  • Take investment if PI > 1
  • Cannot be used to rank mutually exclusive projects ?
  • May be used to rank projects in the presence of capital rationing

*

5-*

Summary – Payback Criteria

  • Payback period
  • Length of time until initial investment is recovered
  • Take the project if it pays back in some specified period
  • Does not account for time value of money, and there is an arbitrary cutoff period ?
  • Discounted payback period
  • Length of time until initial investment is recovered on a discounted basis
  • Take the project if it pays back in some specified period
  • There is an arbitrary cutoff period

*

5-*

Quick Quiz

  • Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9%, and payback cutoff is 4 years.
  • What is the payback period?
  • What is the discounted payback period?
  • What is the NPV?
  • What is the IRR?
  • Should we accept the project?
  • What method should be the primary decision rule?
  • When is the IRR rule unreliable?

*

Payback period = 4 years

The project does not pay back on a discounted basis.

NPV = -2758.72

IRR = 7.93%

32

)1(

150$

)1(

100$

)1(

50$

2000

IRRIRRIRR

NPV



0%$100.00

4%$73.88

8%$51.11

12%$31.13

16%$13.52

20%($2.08)

24%($15.97)

28%($28.38)

32%($39.51)

36%($49.54)

40%($58.60)

44%($66.82)

($100.00)

($50.00)

$0.00

$50.00

$100.00

$150.00

-1%9%19%29%39%

Discount rate

NPV

($100.00)

($50.00)

$0.00

$50.00

$100.00

-50%0%50%100%150%200%

Discount rate

NPV

($5,000.00)

($4,000.00)

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

0%10%20%30%40%

Discount rate

NPV

Project A

Project B

YearProject AProject BProject A-B Project B-A

0($10,000)($10,000)$0$0

1$10,000$1,000$9,000($9,000)

2$1,000$1,000$0$0

3$1,000$12,000($11,000)$11,000

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

0%5%10%15%20%

Discount rate

NPV

A-B

B-A

Investent Initial

FlowsCash Future of PV Total

PI