Investment_appraisal

8/8/2019 Investment_appraisal

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Investment appraisal Lecture 11

Lesson 1

Investment appraisal and Evaluation techniques for capital budgeting

BABS SEM 1 Page 1


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Investment involves the sacrifice of current consumption opportunities in order to obtain the benefit of

re con sumption possibilities. The commitment of funds to capital projects gives rise to a management decision

lem, the solution of which, if incorrectly arrived at, may seriously impair company profitability and growth.

The proper use of evaluation techniques and criteria should enable management to make more effective

decisions which result in future success. The purpose of investment appraisal is to evaluate whether or not thecurrent sacrifice is worthwhile.

Capital investment decisions have certain characteristics which are not always present in other management

decisions, and as a result, special techniques are required to ensure that only the best information is availableto the decision maker.

These characteristics are:

a significant outlay of cash;

long term involvement with greater risks and uncertainty because forecasts of the future are less

reliable; irreversibility of some projects due to the specialised nature of, for example, plant which having been

bought with a specific project in mind may have little or no scrap value;

a significant time lag between commitment of resources and the receipt of benefits; managements ability is often stretched with some projects demanding an awareness of all relevant

diverse factors;

limited resources require priorities on capital expenditure; project completion time requires adequate continuous control information as costs can be exceeded by

a significant amount.

Factors to consider with capital projects

When considering any capital investment project there are six factors to be examined:

the initial cost of the project; the phasing of the expenditure;

the estimated life of the investment;

the amount and timing of the resulting cash flow; the effect, if any, on the rest of the undertaking;

the working capital required.

There are different/multiple objectives for a company, for example, survival. These can change in

priority at different stages of a companys life cycle, but the one overriding objective is maximisation

of owners wealth. Stated differently, it is the present value of future cash flows. Therefore, allinvestment opportunities should eventually be viewed in financial terms.

Evaluation techniques

There are a number of methods for evaluating capital expenditure projects but no matter what method is usedit is important to realise that the information used for the evaluation has to be properly screened as it can

materially affect the evaluation.

Some of the methods available are:BABS SEM 1 Page 2


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BABS SEM 1 Page 3


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Practice Questions- Investment appraisal and Capital Budgeting

1. A firm is considering investing in a project with the following cashflows. The firmhas a cost of capital of 10%.

0 1 2 3 4 5-1000 600 300 200 150 150

Calculate the NPV. Should the project be taken?

2. A firm is considering investing in a new 5 year project. The new project will require initial investment of300,000, depreciated on a straight line basis. There is no corporation tax. The project will result in the

following incremental cashflows per annum.

Units Price/Unit

Revenue 100,000 2

Direct Labour 5 units produced per manhour 4 per manhour

Direct Materials 100,000 0.10

In addition, the project will attract 4 per unit ofexisting overheads. The firm has just undertaken a

feasibility study for this project, costing 5000. The firm has a cost of capital of 12%.

What is the NPV of the project? Should the project be taken?

Using the interpolation method, calculate the IRR.

A firm is considering the following mutually exclusive projects.

YEAR A B C

0 -1000 -1000 -1000

1 400 200 2502 600 300 250

3 200 500 250

4 -300 300 250

5 -400 300 250

a) Calculate the NPV of each project, given that the cost of capital is 10%.

b) Plot NPV against different discount rates for project A.c) Calculate the IRRs of each project by trial and error.

d) Calculate the paybacks of each project.

e) Compare the IRRs, NPVs, and paybacks and comment.

f) Which project should be taken? Justify your choice of decision rule.

BABS SEM 1 Page 4


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Appendix

Table A3 Present Value Interest Factors for One discounted at Percent for n Periods:

= 1 .

(1 + x)0

Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1

2

3

4

5

.990

.980

.971

.961

.951

.980

.961

.942

.924

.906

.971

.943

.915

.888

.863

.962

.925

.889

.855

.822

.952

.907

.864

.823

.784

.943

.890

.840

.792

.747

.935

.873

.816

.763

.713

.926

.857

.794

.735

.681

.917

.842

.772

.708

.650

.909

.826

.751

.683

.621

6

7

89

10

.942

.933

.923

.914

.905

.888

.871

.853

.837

.820

.837

.813

.789

.766

.744

.790

.760

.731

.703

.676

.746

.711

.677

.645

.614

.705

.665

.627

.592

.558

.665

.623

.582

.544

.508

.630

.583

.540

.500

.463

.596

.547

.502

.450

.422

564.

.513

.467

.424

.386

1112

13

14

15

.896

.887

.879

.870

.861

.804

.789

.773

.758

.743

.722

.701

.681

.661

.642

.650

.625

.601

.577

.555

.585

.557

.530

.505

.481

.527

.497

.469

.442

.417

475..444

.415

.388

.362

.429

.397

.368

.340

.315

.388

.356

.326

.299

.275

.350

.319

.290

.263

.239

16

17

18

19

20

.853

.844

.836

.828

.820

.728

.714

.700

.686

.673

.623

.605

.587

.570

.554

.534

.513

.494

.475

.456

.458

.436

.416

.396

.377

.394

.371

.350

.331

.312

.339

.317

.296

.277

.258

.292

.270

.250

.232

.215

.252

.231

.212

.194

.178

.218

.198

.180

.164

.149

21

22

2324

25

.811

.803

.795

.788

.780

.660

.647

.634

.622

.610

.538

.522

.507

.492

.478

.439

.422

.406

.390

.375

.359

.342

.326

.310

.295

.294

.278

.262

.247

.233

.242

.226

.211

.197

.184

.199

.184

.170

.158

.146

.164

.150

.138

.126

.116

.135

.123

.112

.102

.092

30 .742 .552 .412 .308 .231 .174 .131 .099 .075 .057

35 .706 .500 .355 .253 .181 .130 .094 .068 .049 .036

40 .672 .453 .307 .208 .142 .097 .067 .045 .032 .022

45 .639 .410 .264 .171 .111 .073 .048 .031 .021 .014

50 .608 .372 .228 .141 .087 .054 .034 .021 .013 .009

BABS SEM 1 Page 5


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Table A3 Present Value Interest Factors for One discounted at Percent for n Periods:

(continued)

= 1

(1 + x) 0

Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

1

2

34

5

.901

.812

.731

.659

.593

.893

.797

.712

.636

.567

.885

.783

.693

.613

.543

.877

.769

.675

.592

.519

.870

.756

.658

.572

.497

.862

.743

.641

.552

.476

.855

.731

.624

.534

.456

.847

.718

.609

.516

.437

.840

.706

.593

.499

.419

.833

.694

.579

.482

.402

6

7

8

9

10

.535

.482

.434

.391

.352

.507

.452

.404

.361

.322

.480

.425

.376

.333

.295

.455

.400

.351

.308

.270

.432

.376

.327

.284

.247

.410

.354

.305

.263

.227

.390

.333

.285

.243

.208

.370

.314

.266

.225

.191

.352

.296

.249

.209

.176

.335

.279

.233

.194

.162

11

12

1314

15

.317

.286

.258

.232

.209

.287

.257

.229

.205

.183

.261

.231

.204

.181

.160

.237

.208

.182

.160

.140

.215

.187

.163

.141

.123

.195

.

.469

.442

.417

.475

.444

.415

.388

.362

.429

.397

.368

.340

.315

.388

.356

.326

.299

.275

.350

.319

.290

.263

.239

16

17

18

19

20

.853

.844

.836

.828

.820

.728

.714

.700

.686

.673

.623

.605

.587

.570

.554

.534

.513

.494

.475

.456

.458

.436

.416

.396

.377

.394

.371

.350

.331

.312

.339

.317

.296

.277

.258

.292

.270

.250

.232

.215

.252

.231

.212

.194

.178

.218

.198

.180

.164

.149

21

22

2324

25

.811

.803

.795

.788

.780

.660

.647

.634

.622

.610

.538

.522

.507

.492

.478

.439

.422

.406

.390

.375

.359

.342

.326

.310

.295

.294

.278

.262

.247

.233

.242

.226

.211

.197

.184

.199

.184

.170

.158

.146

.164

.150

.138

.126

.116

.135

.123

.112

.102

.092

30 .742 .552 .412 .308 .231 .174 .131 .099 .075 .057

35 .706 .500 .355 .253 .181 .130 .094 .068 .049 .036

40 .672 .453 .307 .208 .142 .097 .067 .045 .032 .022

45 .639 .410 .264 .171 .111 .073 .048 .031 .021 .014

50 .608 .372 .228 .141 .087 .054 .034 .021 .013 .009

BABS SEM 1 Page 6


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Compound Table

Future Value Interest Factors for One discounted at Percent for n Periods:

FVIF = (1 + x)0

Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

123

45

1.0101.0201.030

1.0411.051

1.0201.0401.061

1.0821.104

1.0301.0611.093

1.1261.159

1.0401.0821.125

1.1701.217

1.0501.1021.158

1.2161.276

1.0601.1241.191

1.2621.338

1.0701.1451.225

1.3111.403

1.0801.1681.260

1.3601.459

1.0901.1881.295

1.4121.539

1.1001.2101.331

1.4641.611

67

8910

1.0621.072

1.0831.0941.105

1.1261.149

1.1721.1951.219

1.1941.230

1.2671.3051.344

1.2651.316

1.3691.4231.480

1.3401.407

1.4771.5511.629

1.4191.504

1.5941.6891.791

1.5011.606

1.7181.8381.967

1.5871.714

1.8511.9992.159

1.6771.828

1.9932.1722.367

1.7721.949

2.1442.3582.594

11

12131415

1.116

1.1271.1381.1491.161

1.243

1.2681.2941.3191.346

1.384

1.4261.4691.5131.558

1.539

1.6011.6651.7321.801

1.710

1.7961.8861.9802.079

1.898

2.0122.1332.2612.397

2.105

2.2522.4102.5792.759

2.332

2.5182.7202.9373.172

2.580

2.8133.0663.3423.642

1.853

3.1383.4523.7974.177

16171819

20

1.1731.1841.1961.208

1.220

1.3731.4001.4281.457

1.486

1.6051.6531.7021.753

1.806

1.8731.9482.0262.107

2.191

2.1832.2922.4072.527

2.653

2.5402.6932.8543.026

3.207

2.9523.1593.3803.616

3.870

3.4263.7003.9964.316

4.661

3.9704.3284.7175.142

5.604

4.5955.0545.5606.116

6.727

212223

2425

1.2321.2451.257

1.2701.282

1.5161.5461.577

1.6081.641

1.8601.9161.974

2.0332.094

1.1792.3702.465

2.5632.666

2.7862.9253.071

3.2253.386

3.3993.6033.820

4.0494.292

4.1404.4304.740

5.0725.427

5.0345.4365.871

6.3416.848

6.1096.6587.258

7.9118.623

8.954

9.85010.834

30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.062 1 3.267 1 7.44935 1.417 2.000 2.814 3.946 5.516 7.686 10.676 14.785 20.413 28.102

40 1.489 2.208 3.262 4.801 7.040 10.285 14.974 21.724 31.408 45.258

45 1.565 2.438 3.781 5.841 8.965 13.764 21.002 31.920 48.325 72.888

50 1.645 2.691 4.384 7.106 11.467 18.419 29.456 46.900 74.354 117.386

BABS SEM 1 Page 7


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Future Value Interest Factors for One discounted at Percent for n Periods:

FVIF = (1 + x) 0 (Contd)

Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

1

23

4

5

1.110

1.2321.368

1.518

1.685

1.120

1.2541.405

1.574

1.762

1.130

1.2771.443

1.630

1.842

1.140

1.3001.482

1.689

1.925

1.150

1.3221.521

1.749

2.011

1.160

1.3461.561

1.811

2.100

1.170

1.3691.602

1.874

2.192

1.180

1.3921.643

1.939

2.288

1.190

1.4161.685

2.005

2.386

1.200

1.4401.728

2.074

6

7

8

9

10

1.870

2.076

2.305

2.558

2.839

1.974

2.211

2.476

2.773

3.106

2.082

2.353

2.658

3.004

3.395

2.195

2.502

2.853

3.252

3.707

2.313

2.660

3.059

3.518

4.046

2.436

2.826

3.278

3.803

4.411

2.565

3.001

3.511

4.108

4.807

2.700

3.185

3.759

4.435

5.234

2.840

3.379

4.021

4.785

5.695

3.583

4.300

5.160

6.192

11

12

13

14

15

3.152

3.498

3.883

4.310

4.785

3.479

3.896

4.363

4.887

5.474

3.836

4.334

4.898

5.535

6.254

4.226

4.8118

5.492

6.261

7.138

4.652

5.350

6.153

7.076

8.137

5.117

5.936

6.886

7.987

9.265

5.624

6.580

7.699

9.007

10.539

6.176

7.288

8.599

10.147

11.974

6.777

8.064

9.596

11.420

13.589

7.430

8.916

10.699

12.839

15.407

16

17

18

1920

5.311

5.895

6.543

7.2638.062

6.130

6.866

7.690

8.6139.646

7.067

7.986

9.024

10.19711.523

8.137

9.276

10.575

12.05513.743

9.358

10.761

12.375

14.23216.366

10.748

12.468

14.462

16.77619.461

12.330

14.426

16.879

19.74823.105

14.129

16.672

19.673

23.21427.393

16.171

19.244

22.900

27.25132.429

18.488

22.186

26.623

31.94838.337

21

22

23

24

25

8.949

9.933

11.026

12.239

13.585

10.804

12.110

13.552

15.178

17.000

13.021

14.713

16.626

18.788

21.230

15.667

17.861

20.361

23.212

26.461

18.821

21.644

24.891

28.625

32.918

22.574

26.186

30.376

35.236

40.874

27.033

31.629

37.005

43.296

50.656

32.323

38.141

45.007

53.108

62.667

38.591

45.923

54.648

65.031

77.387

46.005

55.205

66.247

79.496

95.395

30 22.895 29.960 39.115 50.949 66.210 85.849 111.061 143.367 184.672 237.373

35 38.574 52.799 72.066 98.097 133.172 180.311 243.495 327.988 440.691 590.657

40 64.999 93.049 132.776 188.876 267.856 378.715 533.846 750.353 1051.642 1469.740

45 109.527 163.985 244.629 363.662 538.752 795.429 1170.425 1716.619 2509.583 3657.176

50 184.559 184.559 450.711 700.197 1083.619 1670.080 2566.080 3927.189 5988.730 9100.191

BABS SEM 1 Page 8


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Present Value Interest Factors for One Annuity Discounted at k Percent for n Periods:

PVIFA = 1 .

(1 + k0)

Annuity Table

Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

12

34

5

.9901.970

2.9413.902

4.853

.9801.942

2.8843.808

4.713

.9711.913

2.8293.717

4.580

.9621.886

2.7753.630

4.452

.9521.859

2.7233.546

4.329

.9431.833

2.6733.485

4.212

.9351.808

2.6243.387

4.100

.9261.783

2.5773.312

3.993

.9171.759

2.5313.240

3.890

.9091.736

2.4873.170

3.791

678

910

5.7956.7287.652

8.5669.471

5.6016.4727.326

8.1628.983

5.4176.2307.020

7.7858.530

5.2426.0026.733

7.4358.111

5.0765.7866.463

7.1087.722

4.9175.5826.210

6.8027.360

4.7675.3895.971

6.5157.024

4.6235.2065.747

6.2476.710

4.4865.0335.535

5.9956.418

4.3554.8685.335

5.7596.145

1112

1314

15

10.36811.255

12.13413.004

13.865

9.78710.575

11.34812.106

12.849

9.2539.954

10.63511.296

11.938

8.7509.385

9.98610.563

11.118

8.3068.863

9.3949.899

10.380

7.8878.384

8.8539.295

9.712

7.4997.943

8.3588.745

9.108

7.1397.536

7.9048.244

8.560

6.8057.161

7.4877.786

8.061

6.4956.814

7.07.367

7.606

16

1718

1920

14.718

15.56216.398

17.22618.046

13.578

14.29214.992

15.67916.352

12.561

13.16613.754

14.32414.878

11.652

12.16612.659

13.13413.590

10.838

11.27411.690

12.08512.462

10.106

10.47710.828

11.15811.470

9.447

9.76310.059

10.33610.594

8.851

9.1229.372

9.6049.818

8.313

8.5448.756

8.9509.129

7.824

8.0228.201

8.3658.514

2122

2324

25

18.85719.661

20.45621.224

22.023

17.01117.658

18.29218.914

19.524

15.41515.937

16.44416.936

17.413

14.02914.451

14.85715.247

15.622

12.82113.163

13.48913.799

14.094

11.76412.042

12.30312.550

12.783

10.83611.061

11.27211.469

11.654

10.01710.201

10.37110.529

10.675

9.2929.442

9.5809.707

9.823

8.6498.772

8.8839.985

9.077

30 25.808 22.396 19.601 17.292 15.373 13.765 12.409 11.258 10.274 9.42735 29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567 9.644

40 32.835 27.356 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779

45 36.095 29.490 24.519 20.720 17.774 15.456 13.606 12.108 10.881 9.86

50 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915

BABS SEM 1 Page 9


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Present Value Interest Factors for One Annuity Discounted at k Percent for n Periods:

PVIFA = 1 (contd)

(1 + k0)

Annuity Table

Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

12

34

5

.9011.713

2.4443.102

3.696

.8931.690

2.4023.037

3.605

.8851.668

2.3612.974

3.517

.8771.647

2.3222.914

3.433

.8701.626

2.2832.855

3.352

.8621.605

2.2462.798

3.274

.8551.585

2.2102.743

3.199

.8471.566

2.1742.690

3.127

.8401.547

2.1402.639

3.058

.8331.528

2.1062.589

2.991

678

910

4.2314.7125.146

5.5375.889

4.1114.5644.968

5.3285.650

3.9984.4234.799

5.1325.426

3.8894.2884.639

4.9465.216

3.7844.1604.487

4.7725.019

3.6854.0394.344

4.5074.833

3.5893.9224.207

4.4514.659

3.4983.8124.078

4.3034.494

3.4103.7063.954

4.1634.339

3.3263.6053.837

4.0314.192

1112

1314

15

6.2076.492

6.7506.982

7.191

5.9386.194

6.4246.628

6.811

5.6875.918

6.1226.302

6.462

5.4535.662

5.8426.001

6.142

5.2345.421

5.5835.724

5.847

5.0295.197

5.3425.468

5.575

4.8364.988

5.1185.229

5.324

4.6564.793

4.9105.008

5.092

4.4864.611

4.7154.802

4.876

4.3274.439

4.5334.611

4.675

16

1718

1920

7.379

7.5497.702

7.8397.963

6.974

7.1207.250

7.3667.469

6.604

6.7296.840

6.9387.025

6.265

6.3736.467

6.5506.623

5.954

6.0476.128

6.1986.259

5.668

5.7495.818

5.8775.929

5.405

5.4755.534

5.5845.628

5.162

5.2225.273

5.3165.353

4.938

4.9905.033

5.0705.101

4.730

4.7754.812

4.8434.870

2122

2324

25

8.0758.176

8.2668.348

8.4223

7.5627.645

7.7187.784

7.843

7.1027.170

7.2307.283

7.330

6.6876.743

6.7926.835

6.873

6.3126.359

6.3996.434

4.464

5.9736.011

6.0446.073

6.097

5.6655.696

5.7235.746

5.766

5.3845.410

5.4325.451

5.467

5.1275.149

5.1675.182

5.195

4.8914.909

4.9254.937

4.948

30 8.694 8.055 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.97935 8.855 8.176 7.586 7.070 6.617 6.215 5.858 5.539 5.251 4.992

40 8.9515 8 .244 7.634 7.105 6.642 6.233 5.874 5.548 5.258 4.997

45 9.008 8.283 7.661 7.123 6.654 6.242 5.877 5.552 5.261 4.999

50 9.047 8.304 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999

BABS SEM 1 Page 10


11/13


Future Value Interest Factors for One-Dollar Annuity Compounded at k Percent for n Periods:

PVIA = (1 + k)

Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1

23

4

5

1.100

2.0103.030

4.060

5.101

1.000

2.0203.060

4.122

5.204

1.000

2.0303.091

4.184

5.309

1.000

2.0403.122

4.246

5.416

1.000

2.0503.152

4.310

5.526

1.000

2.0703.184

4.375

5.637

1.000

2.0703.215

4.440

5.751

1.000

2.0803.246

4.506

5.867

1.000

2.0903.278

4.573

5.985

1.000

2.103.31

4.64

6.10

6

7

8

9

10

6.152

7.214

8.286

9.368

10.462

6.308

7.434

8.583

9.755

10.950

6.468

7.662

8.892

10.159

11.464

6.633

7.898

9.214

10.583

12.006

6.802

8.142

9.549

11.027

12.578

6.975

8.394

9.897

11.491

13.181

7.153

8.654

10.260

11.978

13.816

7.336

8.923

10.637

12.488

14.487

7.523

9.200

11.028

13.021

15.193

7.71

9.48

11.4

13.5

15.9

11

12

13

14

15

11.567

12.682

13.809

14.947

15.097

12.169

13.412

14.680

15.974

17.293

12.808

14.192

15.618

17.086

18.599

13.486

15.026

16.627

18.292

20.023

14.207

15.917

17.713

19.598

21.578

14.972

16.870

18.882

21.015

23.276

15.784

17.888

20.141

22.550

25.129

16.645

18.977

21.495

24.215

27.152

17.560

20.141

22.953

26.019

29.361

18.53

21.38

24.52

27.97

31.7

16

17

18

1920

17.258

18.430

19.614

20.81122.019

18.639

20.012

21.412

22.84024.297

20.157

21.761

23.414

25.11726.870

21.824

23.697

25.645

27.67129.778

23.657

25.840

28.132

30.53933.066

25.672

28.213

30.905

33.76036.785

27.888

30.840

33.999

37.37940.995

30.324

33.750

37.450

41.44645.762

33.003

36.973

41.301

46.01851.159

35.95

40.54

45.55

51.1557.27

21

22

23

24

25

23.239

24.471

25.716

26.973

28.243

25.783

27.299

28.845

30.421

32.030

28.675

30.536

32.452

34.426

36.459

31.969

34.248

36.618

39.082

41.645

35.719

38.505

41.430

44.501

47.726

39.992

43.392

46.995

50.815

54.864

44.865

49.005

53.435

58.176

63.248

50.422

55.456

60.893

66.764

73.105

56.754

62.872

69.531

76.789

84.699

64.00

71.40

79.54

88.49

98.34

30 34.784 40.567 47.575 56.084 66.438 79.057 94.459 113.282 136.305 164.4

35 41.659 49.994 60.461 73.651 90.318 111.432 138.234 172.314 215.705 271.0

40 48.885 60.401 75.400 95.024 120.797 154.758 199.630 259.052 337.872 442.5

45 56.479 71.8915 92.718 121.027 159.695 212.737 285.741 386.497 525.840 718.8

50 64.461 84.577 112.794 152.664 209.341 290.325 406.516 573.756 815.051 1163.000

BABS SEM 1 Page 11


12/13


Future Value Interest Factors for One-Dollar Annuity Compounded at k Percent for n Periods:

PVIA = (1 + k) (contd)

Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

12

345

1.0002.110

3.3424.7106.228

1.0002.120

3.3744.7796.353

1.0002.130

3.4074.8506.480

1.0002.140

3.4404.9216.610

1.0002.150

3.4724.9936.742

1.0002.160

3.5065.0666.877

1.0002.170

3.5395.1417.014

1.0002.180

3.5725.2157.154

1.0002.190

3.6065.2917.297

1.0002.200

3.6405.7.

678910

7.9139.78311.85914.16416.722

8.11510.08912.30014.77617.549

8.32310.40512.75715.41618.420

8.53510.73013.23316.08519.337

8.75411.06713.72716.78620.304

8.97711.41414.24017.51821.321

9.20711.77214.77318.28522.393

9.44212.14115.32719.08623.521

9.68312.52315.90219.92324.709

9.93012.91616.49920.79925.959

1112131415

19.56122.71326.21130.09534.405

20.65524.13328.02932.39237.280

21.81425.65029.98434.88240.417

23.04427.27132.08837.58143.842

24.34929.00134.35240.50447.580

25.73330.85036.78643.67251.659

27.20032.82439.40447.10256.109

28.75534.93142.21850.81860.965

30.40337.18045.24454.84166.260

32.15039.58048.49659.19672.035

1617181920

39.19044.50050.39656.93964.202

42.75348.88355.74963.43972.052

46.67153.73861.72470.74880.946

50.98059.11768.39378.96891.024

55.71765.07575.83688.211102.443

60.92571.67384.14098.603115.379

66.64878.97893.404110.283130.031

72.93887.067104.739123.412146.626

79.85096.021115.265138.165165.417

87.442105.930128.116154.739185.687

2122232425

72.26481.21391.147102.173114.412

81.69892.502104.602118.154133.333

92.468105.489120.203136.829155.616

104.767120.434138.295158.656181.867

118.809137.630159.274184.166212.790

134.840157.414183.600213.976249.212

153.136180.169211.798248.803292.099

14.019206.342244.483289.490342.598

197.846236.436282.359337.007402.038

225.024271.028326.234392.480471.976

30 199.018 241.330 293.192 356.778 434.738 530.306 617.423 790.932 966.698 1181.865

35 341.583 431.658 546.663 693.552 881.152 120.699 1426.448 1816.607 2314.173 2948.294

40 581.812 767.080 1013.667 1341.979 1779. 048 2360.724 3134.412 4163.094 5529.711 7343.715

45 986.613 1358.208 1874.086 2590.464 3585. 031 4965.191 6879.008 9531.258 13203.105 18280.914

50 1668.723 2399.975 3459.334 4994.301 7217.488 10435.449 15088.805 21812.273 31514.492 45496.094

BABS SEM 1 Page 12


13/13


Area of a Standard Normal Distribution

An entry in the label is the proportion under the entire curve which is between z = 0 and a positive value of

z. areas for negative values of z are obtained by symmetry.

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

0.0

0.1

0.20.3

0.4

0.5

0.6

0.7

0.8

0.9

1.01.1

1.2

1.31.4

1.5

1.6

1.7

1.81.9

2.0

2.1

2.2

2.3

2.4

2.5

2.62.7

2.82.9

3.0

.0000

.0398

.0793

.1179

.1554

.1915

.2257

.2580

.2881

.3159

.3413

.3643

.3849

.4032

.4192

.4332

.4452

.4554

.4641

.4713

.4772

.4821

.4861

.4893

.4918

.4938

.4953

.4965

.4974

.4981

.4987

.0040

.0438

.0832

.1217

.1591

.1950

.2291

.2611

.2910

.3186

.3438

.3665

.3869

.4049

.4207

.4345

.4463

.4564

.4649

.4719

.4778

.4826

.4864

.4896

.4920

.4940

.4955

.4966

.4975

.4982

.4987

.0080

.0478

.0871

.1255

.1628

.1985

.2324

.2642

.2939

.3212

.3461

.3686

.3888

.4066

.4222

.4357

.4474

.4573

.4656

.4726

.4783

.4830

.4868

.4898

.4922

.4941

.4956

.4967

.4976

.4982

.4987

.0120

.0517

.0910

.1293

.1664

.2019

.2357

.2673

.2967

.3238

.3485

.3708

.3907

.4082

.4236

.4370

.4484

.4582

.4664

.4732

.4788

.4834

.4871

.4901

.4925

.4943

.4957

.4968

.4977

.4983

.4988

.0160

.0557

.0948

.1331

.1700

.2054

.2389

.2703

.2995

.3264

.3508

.3729

.3925

.4099

.4251

.4382

.4495

.4591

.4671

.4738

.4793

.4838

.4875

.4904

.4927

.4945

.4959

.4969

.4977

.4984

.4988

.0199

.0596

.0987

.1368

.1736

.2088

.2422

.2734

.3023

.3289

.3531

.3749

.3944

.4115

.4265

.4394

.4505

.4599

.4678

.4744

.4798

.4842

.4878

.4906

.4929

.4946

.4960

.4970

.4978

.4984

.4989

.0239

.0636

.1026

.1406

.1772

.2123

.2454

.2764

.3051

.3315

.3554

.3770

.3962

.4131

.4279

.4406

.4515

.4608

.4686

.4750

.4803

.4846

.4881

.4909

.4931

.4948

.4961

.4971

.4979

.4985

.4989

.0279

.0675

.1064

.1443

.1808

.2157

.2486

.2794

.3078

.3340

.3577

.3790

.3980

.4147

.4292

.4418

.4525

.4616

.4693

.4756

.4808

.4850

.4884

.4911

.4932

.4949

.4962

.4972

.4979

.4985

.4989

.0319

.0714

.1103

.1480

.1844

.2190

.2517

.2823

.3106

.3365

.3599

.3810

.3997

.4162

.4306

.4429

.4535

.4625

.4699

.4761

.4812

.4854

.4887

.4913

.4934

.4951

.4963

.4973

.4980

.4986

.4990

.0359

.0753

.1141

.1517

.1579

.2224

.2549

.2852

.3133

.3389

.3621

.3530

.4015

.4177

.4319

.4441

.4545

.4633

.4706

.4767

.4817

.4857

.4890

.4916

.4936

.4952

.4964

.4974

.4981

.4986

.4990

BABS SEM 1 Page 13

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