Net Present Value and Other Investment RulesChapter 5Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

5-*

Key Concepts and SkillsBe able to compute payback and discounted payback and understand their shortcomingsBe able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approachesBe able to compute net present value and understand why it is the best decision criterion

5-*

Chapter Outline5.1 Why Use Net Present Value?5.2 The Payback Period Method5.3 The Discounted Payback Period Method5.4 The Internal Rate of Return5.5 Problems with the IRR Approach5.6 The Profitability Index5.7 The Practice of Capital Budgeting

5-*

5.1 Why Use Net Present Value?Accepting positive NPV projects benefits shareholders.NPV uses cash flowsNPV uses all the cash flows of the projectNPV discounts the cash flows properly

5-*

The Net Present Value (NPV) RuleNet Present Value (NPV) = Total PV of future CFs + Initial InvestmentEstimating NPV:1. Estimate future cash flows: how much? and when?2. Estimate discount rate3. Estimate initial costsMinimum Acceptance Criteria: Accept if NPV > 0Ranking Criteria: Choose the highest NPV

5-*

Calculating NPV with SpreadsheetsSpreadsheets 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.

Sheet1

Year0123

Cash Flows-165000631207080091080

Required Return0.12

NPV - Incorrect$11,274.48

NPV - Correct$12,627.41

Sheet2

Sheet3

Sheet1

Year0123

Cash Flows-165000631207080091080

Required Return0.12

NPV - Incorrect$11,274.48

NPV - Correct$12,627.41

Sheet2

Sheet3

5-*

5.2 The Payback Period MethodHow long does it take the project to pay back its initial investment?Payback Period = number of years to recover initial costsMinimum Acceptance Criteria: Set by managementRanking Criteria: Set by management

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The Payback Period MethodDisadvantages:Ignores the time value of moneyIgnores cash flows after the payback periodBiased against long-term projectsRequires an arbitrary acceptance criteriaA project accepted based on the payback criteria may not have a positive NPVAdvantages:Easy to understandBiased toward liquidity

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5.3 The Discounted Payback PeriodHow 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.

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5.4 The Internal Rate of ReturnIRR: the discount rate that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the required returnRanking Criteria: Select alternative with the highest IRRReinvestment assumption: All future cash flows are assumed to be reinvested at the IRR

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Internal Rate of Return (IRR)Disadvantages:Does not distinguish between investing and borrowingIRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments

Advantages:Easy to understand and communicate

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IRR: ExampleConsider the following project:The internal rate of return for this project is 19.44%

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

Sheet1

0123

-20050100150

19.44%

Discount RateNPV

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 RateNPV

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

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

NPV

Discount rate

NPV

Sheet1

0123

-20050100150

19.44%

Discount RateNPV

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 RateNPV

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

Sheet2

Sheet3

5-*

Calculating IRR with SpreadsheetsYou 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.

Sheet1

Year0123

Cash Flows-165000631207080091080

Required Return0.12

NPV - Incorrect$11,274.48

NPV - Correct$12,627.41

IRR16%16.13%

Default Format

Sheet2

Sheet3

5-*

5.5 Problems with IRR

Multiple IRRsAre We Borrowing or LendingThe Scale ProblemThe Timing Problem

5-*

Mutually Exclusive vs. IndependentMutually 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 IRRsThere are two IRRs for this project: Which one should we use?

Chart4

-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

NPV

Discount rate

NPV

Sheet1

0123

-200200800-800

-0.00%

Discount RateNPV

-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 RateNPV

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

-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

NPV

Discount rate

NPV

Sheet2

Sheet3

5-*

Modified IRRCalculate 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

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

5-*

The Timing Problem

Chart7

20004000

1851.87629634453617.4768344396

1707.41268441253249.4289526653

1566.47543256462895.1696077794

1428.93718707332554.0509786072

1294.6766007992225.4616132167

1163.57798719751908.824062817

1035.53099768741603.5926902158

910.43032058121309.2516384697

788.17539993311025.3129466599

668.6701728024751.3148009016

551.822823554486.8199097564

437.5455539359231.4139941691

325.7543677754-15.2956170815

216.3688692337-253.6812946494

109.3120736418-484.096326128

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

Project A

Project B

Discount rate

NPV

Sheet1

0123

$(10,000.00)$10,000.00$1,000.00$1,000.00A

$(10,000.00)$1,000.00$1,000.00$12,000.00B

16.04%IRR A

12.94%IRR B

Discount RateProject AProject 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 RateNPV

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

20004000

1833.54088746983581.6602321185

1673.9340043263185.7146594758

1520.84993452872810.8442793975

1373.97806449352455.8182486608

1233.02533409432119.4872506826

1097.71508226181800.7774177518

967.78597914711498.684757211

842.99103757521212.2700356201

723.0966971864940.6540795045

607.8819752749683.0134553651

497.1376788775438.576495276

390.665673157206.619637651

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

Project A

Project B

Discount rate

NPV

Sheet2

Sheet3

5-*

Calculating the Crossover RateCompute the IRR for either project A-B or B-A

Sheet1

YearProject AProject BProject A-BProject 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 rtaeA-BB-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

Sheet2

Sheet3

Chart2

-20002000

-1765.60053809521765.6005380952

-1542.01626825281542.0162682528

-1328.69417521481328.6941752148

-1125.11379153391125.1137915339

-930.7850124177930.7850124177

-745.2460756195745.2460756195

-568.0616925283568.0616925283

-398.8213178885398.8213178885

-237.1375467268237.1375467268

-82.644628099282.6446280992

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

1035.4512541546-1035.4512541546

1134.2592592593-1134.2592592593

A-B

B-A

Discount rate

NPV

Sheet1

YearProject AProject BProject A-BProject 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 rtaeA-BB-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 IRRNPV and IRR will generally give the same decision.Exceptions:Non-conventional cash flows cash flow signs change more than onceMutually exclusive projectsInitial investments are substantially differentTiming of cash flows is substantially different

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5.6 The Profitability Index (PI)Minimum Acceptance Criteria: Accept if PI > 1

Ranking Criteria: Select alternative with highest PI

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The Profitability IndexDisadvantages:Problems with mutually exclusive investmentsAdvantages:May be useful when available investment funds are limitedEasy to understand and communicateCorrect decision when evaluating independent projects

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5.7 The Practice of Capital BudgetingVaries by industry:Some firms use payback, others use accounting rate of return.The most frequently used technique for large corporations is either IRR or NPV.

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Example of Investment RulesCompute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%. Year Project A Project B0-$200-$1501$200$502$800$1003-$800$150

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Example of Investment RulesProject AProject BCF0-$200.00-$150.00PV0 of CF1-3$241.92$240.80

NPV =$41.92$90.80IRR = 0%, 100% 36.19%PI =1.20961.6053

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Example of Investment RulesPayback Period:Project AProject B Time CF Cum. CFCF Cum. CF0-200-200-150-1501200050-100280080010003-8000150150

Payback period for project B = 2 years.Payback period for project A = 1 or 3 years?

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NPV and IRR RelationshipDiscount rate NPV for A NPV for B-10%-87.52234.770%0.00150.0020%59.2647.9240%59.48-8.6060%42.19-43.0780%20.85-65.64100%0.00-81.25120%-18.93-92.52

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($200)($100)$0$100$200$300$400-15%0%15%30%45%70%100%130%160%190%Discount ratesNPVNPV ProfilesIRR 2(A)

Cross-over Rate

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Summary Discounted Cash FlowNet present valueDifference between market value and costAccept the project if the NPV is positiveHas no serious problemsPreferred decision criterionInternal rate of returnDiscount rate that makes NPV = 0Take the project if the IRR is greater than the required returnSame decision as NPV with conventional cash flowsIRR is unreliable with non-conventional cash flows or mutually exclusive projectsProfitability IndexBenefit-cost ratioTake investment if PI > 1Cannot be used to rank mutually exclusive projectsMay be used to rank projects in the presence of capital rationing

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Summary Payback CriteriaPayback periodLength of time until initial investment is recoveredTake the project if it pays back in some specified periodDoes not account for time value of money, and there is an arbitrary cutoff periodDiscounted payback periodLength of time until initial investment is recovered on a discounted basisTake the project if it pays back in some specified periodThere is an arbitrary cutoff period

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Quick QuizConsider 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?

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Review1.A project will produce cash inflows of $1,750 a year for four years. The project initially costs $10,600 to get started. In year five, the project will be closed and as a result should produce a cash inflow of $8,500. What is the net present value of this project if the required rate of return is 13.75%? A.-$5,474.76 B.-$1,011.40 C.-$935.56 D.$1,011.40 E.$5,474.76

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65.You are considering two mutually exclusive projects with the following cash flows. Will your choice between the two projects differ if the required rate of return is 8% rather than 11%? If so, what should you do? A.yes; Select A at 8% and B at 11%. B.yes; Select B at 8% and A at 11%. C.yes; Select A at 8% and select neither at 11%. D.no; Regardless of the required rate, project A always has the higher NPV. E.no; Regardless of the required rate, project B always has the higher NPV.

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67.An investment has the following cash flows. Should the project be accepted if it has been assigned a required return of 9.5%? Why or why not? A.yes; because the IRR exceeds the required return by about 0.39%. B.yes; because the IRR is less than the required return by about 3.9%. C.yes; because the IRR is positive. D.no; because the IRR exceeds the required return by about 3.9%. E.no; because the IRR is 9.89%.

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71.Based on the profitability index (PI) rule, should a project with the following cash flows be accepted if the discount rate is 8%? Why or why not? A.yes; because the PI is 1.008. B.yes; because the PI is .992. C.yes; because the PI is .999. D.no; because the PI is 1.008. E.no; because the PI is .992.

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77.Jack is considering adding toys to his general store. He estimates that the cost of inventory will be $4,200. The remodeling and shelving costs are estimated at $1,500. Toy sales are expected to produce net cash inflows of $1,200, $1,500, $1,600, and $1,750 over the next four years, respectively. Should Jack add toys to his store if he assigns a three-year payback period to this project? A.yes; because the payback period is 2.94 years. B.yes; because the payback period is 2.02 years. C.yes; because the payback period is 3.80 years. D.no; because the payback period is 2.02 years. E.no; because the payback period is 3.80 years.

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79.Yancy is considering a project which will produce cash inflows of $900 a year for 4 years. The project has a 9% required rate of return and an initial cost of $2,800. What is the discounted payback period? A.3.11 years B.3.18 years C.3.82 years D.4.18 years E.never

****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.*Note that although we add the initial investment, this value is a negative number.*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.**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.*Similar advantages and disadvantages as standard payback method, with the exception that cash flows prior to the cutoff are not discounted at zero.*****Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on a spreadsheet.***It is good to mention that the number of IRRs is equivalent to the number of sign changes in the cash flows.*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. **The preferred project in this case depends on the discount rate, not the IRR.

*The cross-over rate is the IRR of project A-B*************Payback period = 4 yearsThe project does not pay back on a discounted basis.NPV = -2758.72IRR = 7.93%B.-$1,011.40**A.yes; because the IRR exceeds the required return by about 0.39%.*E.no; because the PI is .992.*Jack should reject the toy project because the payback period exceeds 3 years.E.no; because the payback period is 3.80 years.*C.3.82 years*