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FTP801S- FINANCIAL TECNIQUES FOR PROCUREMENT AND SUPPLY CHAIN MANAGEMENT- 1ST OPP- JUNE 2024 |
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nAm I 8 IA un IVERS ITV
OF SCIEn CE Ano TECHn OLOGY
FACULTY OF COMMERCE, HUMAN SCIENCESAND EDUCATION
DEPARTMENTOF MARKETING, LOGISTICSAND SPORTMANAGEMENT
QUALIFICATION: POST GRADUATE DIPLOMA IN PROCUREMENT MANAGEMENT
QUALIFICATION CODE: 08PDPM
COURSE CODE: FTP801 S
SESSION: APRIL 2024
LEVEL:8
COURSE NAME: FINANCIAL TECHNIQUES FOR
PROCUREMENT AND SUPPLY CHAIN MANAGEMENT
PAPER: THEORY AND CALCULATIONS
DURATION: 3 HOURS
MARKS: 100
FIRST OPPORTUNITY FINAL ASSESSMENT QUESTION PAPER
EXAMINER
MR. LAMECK ODADA
MODERATOR MR. JOHANNES NDJULUWA
INSTRUCTIONS
1. This question paper consists of FOUR (4) questions.
2. Answer ALL FOUR (4) questions in blue or black ink only. NO PENCIL.
3. Start each question on a new page, number the answers correctly and clearly.
4. Write clearly, neatly and show all your workings/calculations/assumptions.
5. Unless otherwise stated, work with four (4) decimal places in all your calculations and
only round off final answers to two (2) decimal places.
6. Questions relating to this assessment may be raised in the initial 30 minutes after the
start of the examination. Thereafter, candidates must use their initiative to deal with any
perceived error or ambiguities and any assumptions made by the candidate should be
clearly stated.
PERMISSIBLE MATERIALS
• Silent, non-programmable calculators
THIS FINALASSESSMENTCONSISTSOF _9_ PAGES(including this cover page, not tables)
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QUESTION 1
[20 MARKS]
For questions 1.1-1.10, write only the answer (the correct letter chosen) in your answer book and not
on the question paper. Do not copy the question again.
(2 marks each)
1.1 Capital rationing comes about because:
a) There are not enough positive NPV projects
b) Companies do not always have accessto all the funds they could make use of
c) Managers find it difficult to decide how to fund projects
d) Banks require very high returns on projects
1.2 In caseswhere capital must be rationed, a firm should rank projects according to their
a) net present values.
b) internal rates of return.
c) profitability indexes.
d) external rates of return.
1.3 Asymmetric information refers to circumstances in which.
a) both parties to a transaction have identical amounts of information.
b) neither party to a transaction has any relevant information.
c) one party to a transaction has more information than the other party.
d) the riskiness of a transaction is greater than its expected return.
1.4 The principal-agent problem may result if
a) a firm is owned and operated by the same person.
b) managers make decisions that are not in the best interest of owners.
c) a firm compensates managers based on the profitability of the firm.
d) All of the above.
1.5 One way to correct a potential principal-agent problem is for stockholders to
a) offer managers "golden parachutes" in the event of a takeover.
b) empower managers to make the decisions they feel are best.
c) ensure that there is no explicit linkage between managers' compensation and the profitability of
the firm.
d) All of the above.
1.6 The coefficient of variation measures
a) the risk per unit of expected payoff.
b) the risk-adjusted expected value.
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c) the payoff per unit of risk.
d) a decision maker's risk-return trade-off.
1.7 Which of the following items describes an index measure of systematic risk?
a) Beta.
b) Standard deviation.
c) Coefficient of variation.
d) Variance.
1.8 This type of risk is avoidable through proper diversification.
a) portfolio risk
b) systematic risk
c) unsystematic risk
d) total risk
1.9 The term "capital structure" refers to:
a) long-term debt, preferred stock, and common stock equity.
b) current assets and current liabilities.
c) total assets minus liabilities.
d) shareholders' equity.
1.10 The after-tax weighted average cost of capital is determined by:
a) Multiplying the weighted average after tax cost of debt by the weighted average cost of equity
b) Adding the weighted average before tax cost of debt to the weighted average cost of equity
c) Adding the weighted average after tax cost of debt to the weighted average cost of equity
d) Dividing the weighted average before tax cost of debt to the weighted average cost of equity
(2 marks each, 2 x 10 = 20 marks)
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QUESTION2
[30 MARKS]
Amagulu Group of companies (hereafter Amagulu) is made up of companies with various business
portfolios. The Group is multifunctional and multidimensional, with subsidiaries and associates that can
provide and sustain the provision of the basic needs and equipment to the Namibian nation at large. It
prides itself as a group of wholly Namibian companies with the right personnel, expertise, and ability to
procure equipment and render services efficiently.
Amagulu is evaluating an investment proposal to manufacture Product W33, which has performed well in
test marketing trials conducted recently by the company's research and development division. The
following information relating to investment proposal has now been prepared.
Initial investment
N$2 million
Selling price (current price terms)
N$20 per unit
Variable operating costs (current price terms)
N$8 per unit
Fixed operating costs (current price terms)
N$170,000 per year
The research and development division has prepared the following demand forecast as a result of its test
marketing trials. The forecast reflects expected technological change and its effect on the anticipated life
cycle of Product W33.
Year
1
2
3
4
Demand (units)
60,000
70,000
120,000
45,000
It is expected that all units of Product W33 produced will be sold, in line with the company's policy of
keeping no inventory of finished goods. No machinery scrap value is expected at the end of four years,
when production of Product W33 is planned to end. For investment appraisal, Amagulu uses a discount
rate of 10% per year and a target return on capital employed of 30% per year. Ignore taxation.
REQUIRED
a) Identify any FOUR (4) factors that Amagulu should consider in evaluating this
investment proposal
MARKS
4
b) Calculate the Net Present Value (NPV) for the investment proposal and advise 14
whether the investment proposal is financially acceptable.
Using a 17% cost of capital, calculate the Internal Rate of Return (IRR) for the
7
c) investment proposal and advise whether the investment proposal is financially
acceptable. Answer to the nearest whole number.
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Calculate the Return on Capital Employed (ROCE)A/ ccounting Rate of Return (ARR) 5
d) for the investment proposal and advise whether the investment proposal is
financially acceptable. Answer to the nearest whole number.
TOTAL
30
QUESTION 3
[25 MARKS]
Oshikoto Country Lodges (hereafter OCL) is a truly Namibian hospitality company. They provide their
guests with unmatched experiences at unique properties with a true sense of place in the landscape.
Staying at one of their lodges is a once-in-a-lifetime experience that is grounded in genuine, warm
hospitality and a love of the land they come from. Developing a passionate and dedicated team is
foremost in their philosophy, as only a great team can provide their guests with a first-class experience.
They continually pursue excellence by enhancing our skills and evolving with the hospitality and tourism
industry of Namibia. OCLis looking to expand its hospitality and tourism interest in Namibia by investing
in two companies in the hospitality and tourism sector. OCL can invest N$4 million in one of the two
companies or a portfolio of the two companies. The following risk/return profiles have been provided.
Estimated Returns (%)
Economic State
Probability (%)
SLM Safaris
ATI Holidays
Market
Recession
30
2
25
-
Boom
50
10
22
-
Depression
20
12
-2
-
Expected return
-
-
12%
Standard deviation
-
-
6%
Covariance with the market
25.2
39.6
-
The risk-free rate is 3% per annum and there is no company or personal taxation.
REQUIRED
MARKS
Calculate the expected returns together with the risk of SLM Safaris and ATI 6
a)
Holidays.
If OCLis to select only one company to invest in, which one would you advise OCL 3
b)
to select? Motivate your answer with appropriate calculations.
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Determine the expected return of the portfolio, assuming that OCL invests N$1.6
2
c)
million in SLM Safaris.
Determine the covariance of SLM Safaris and ATI Holidays and interpret your
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d)
answer.
Determine the standard deviation of the portfolio and advise OCL on whether to
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e)
invest in the portfolio or not.
Calculate the required return for both companies according to the Capital Asset
4
f)
Pricing Model (CAPM)
TOTAL
25
QUESTION 4
[25 MARKS]
Dineo Manufacturing and Supplies {hereafter DMS) is a 100% Namibian custom garment manufacturer,
founded in 2009 and started with operations in 2010. The target audience of DMS is corporate companies,
public services, and schools and is not limited to local and international brands. Below is the summarized
statement of the financial position of DMS and the statement of comprehensive income for the year
ended 31 December 2023.
DMS Statement of financial position as of 31 December 2023
ASSETS
Non-current assets
Property, plant, and equipment
Investments
Current assets
Inventories
Receivables
Cash assets
TOTAL ASSETS
EQUITY AND LIABILITIES
Share capital and reserves
Share capital
Other reserves
Retained earnings
Redeemable -preference shares
Non-current liabilities: Long-term borrowings
Current liabilities
2023
9 450 000
9 450 000
-
36 045 000
20 925 000
12150 000
2 970 000
45 495 000
16 335 000
7 000 000
-250 000
9 585 000
2 700 000
7 425 000
19 035 000
2022
8 640 000
8 640 000
-
29 632 500
14 850 000
9 990 000
4 792 500
38 272 500
15120 000
7 000 000
-250 000
8 370 000
2 700 000
7 425 000
13 027 500
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Trade and other payables
Short term borrowings
TOTAL EQUITY AND LIABILITIES
4 860 000
14175 000
45 495 000
4 320 000
8 707 500
38 272 500
DMS Statement of comprehensive income for the year ended 31 December 2023
2023
2022
Sales
85 320 000
74 250 000
Cost of sales
63 990 000
54 945 000
Gross profit
21330 000
19 305 000
Operating expenses
12 636 000
11070 000
Depreciation
810 000
675 000
Profit before interest and tax
7 884 000
7 560 000
Finance costs
2 430 000
1485 000
Profit before tax
5 454 000
6 075 000
Income tax expense
2 430 000
2160 000
Profit from continuing operations
3 024 000
3 915 000
loss on discontinued operations
1080 000
-
Profit for the year
1944 000
3 915 000
DMS Statement of changes in equity for the year ended 31 December 2023
2023
Balance on 31 December
8 370 000
Comprehensive income for the year
1944 000
10 314 000
Dividends-preference shares
-324 000
Dividends-ordinary shares
-405 000
Balance on 31 December
9 585 000
2022
5 184 000
3 915 000
9 099 000
-324 000
-405 000
8 370 000
REQUIRED
MARKS
Compute the following liquidity ratios for 2022 and 2023 and comment on the
10
overall liquidity position of DMS.
• Current ratio
a)
• Quick ratio
• Debtors' collection period
• Creditors settlement period
Compute the debt ratio of DMS for 2022 and 2023 and comment on your answer.
4
b)
• Debt ratio
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Compute the following profitability ratios for 2022 and 2023 and comment on the
8
overall profitability of DMS.
c)
• Gross profit margin
• Net profit margin
• Return on Assets
d) Explain any three (3) limitations of financial statement/ratio analysis
3
TOTAL
25
END OF QUESTION PAPER
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Portfolio Expected Return
Portfolio standard deviation
FORMULA SHEET
ERp= z...WAX ERA+Ws X ERs
crAs=vW/xcr 2A+ Ws2xcr2s+ 2xWAxWsxCovAs
Beta(~)
Covariance of company with market)/variance of market
Cost of equity capital
Before tax cost of debt
Re= Rf+~ (Rm - Rf) and Re= [D1 +Po]+ g
kd =I+ [Par value - Nd]/n +[Nd+ par value]/2
Frequency of compounding
FV= PV[l + (r/m)fm
Effective Annual Rate
FV= PV[l + (r/m)Jl•m
Payment
PMT=PV x r/[1-1/(l+r)t]
Internal Rate of Return
Profitability Index
Profitability Index
Accounting Rate of Return
IRR= R1+ [N1 x (R2-R1)]/N1+N2
Present value of future cash flows (excluding initial outlay)
Initial investment
NPV
1 + Ini.tia. l .investment
Average investment
Expected return (discrete distribution)
LP;XR;
Expected
distribution)
return
(continuous .l&
N
Standard deviation (discrete distribution) ../"j_[R;-E(R)]2x ( P;)
Standard
deviation
(continuous
distribution)
Covariance (discrete distribution)
../'L.{.&-E(R)2
n
= Pi [RA- E(RA)][RB- E(RB)]
Coefficient of variation
= Standard deviation
Expected return
Correlation coefficient
= Covariance oftbe assets :l and 2
cr1x cr2
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TABLE A
Future value interest factor of $1 per period at i% for n periods, FVIF(i,n).
Period
1%
1 1.010
2 1.020
3 1.030
2%
1.020
1.040
1.061
3%
1.030
1.061
1.093
4%
1.040
1.082
1.125
5%
1.050
1.103
1.158
6%
1.060
1.124
1.19·1
7%
1.070
1.145
1.225
8%
1.080
1.166
1.260
9%
1.090
1.188
1.295
10%
1.100
1.210
1.331
11%
1.110
1.232
1.368
12%
1.120
1.254
1.405
13%
1.-130
1.277
1.443
14%
1.140
1.300
1.482
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412
1.464
1.518
1.574
1.630
1.689
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 i.469 1.539
1.611
1.685
1.762
1.842
1.925
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677
1.772
1.870
1.974 2.082
2.195
7 1.072
8 1.083
9 1.094
1.149
1.172
1.195
1.230
1.267
1.305
1.316
1.369
1.423
1.407
1.477
1.551
1.504
1.594
1.689
1.606
1.718
1.838-
1.714
1.851
1.999
1.828
1.993
2.172
1.949
2.144
2.358
2.076
2.305
2.558
2.211
2.476
2.773
2.353
2.658
3.004
2.502
2.853
3.252
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367
2.594
2.839
3.106
3.395
3.707
11 1.116 1.243 1.384 1.539
12 1.127 1.268 1.426 1.601
1.710
1.796
1.898
2.012
2.105
2.252
2.332
2.518
2.580
2.813
2.853
3.138
3.152
3.498
3.479
3.896
3.836
4.335
4.226
4.818
13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066
3.452
3.883
4.363
4.898
5.492
14 1.149 1.319 1.513 1.732
15 1.161 1.346 1.558 1.801
1.980
2.079
2.261
2.397
2.579
2.759
2.937
3.172
3.342
3.642
3.797
4.177
4.310
4.785
4.887
5.474
5.535
6.254
6.261
7.138
16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970
4.595
5.311
6.130
7.067
8.137
17 1.184
18 1.196
19 1.208
1.400
1.428
1.457
1.653
1.702
1.754
1.948
2.026
2.107
2.292
2.407
2.527
2.693
2.854
3.026
3.159
3.380
3.617
3.700
3.996
4.316
4.328
4.717
5.142
5.054
5.560
6.116
5.895
6.544
7.263
6.866
7.690
8.613
7.986
9.024
10.197
9.276
10.575
12.056
20 1.220
25 1.282
30 1.348
35 1.417
40 1.489
so 1.645
1.486
1.641
1.811
2.000
2.208
2.692
1.806
2.094
2.427
2.814
3.262
4.384
2.t91
2.666
3.243
3.946
4.801
7.107
2.653
3.386
4.322
5.516
7.040
11.467
3.207
4.292
5.743
7.686
10.286
18.420
3.870
5.427
7.612
10.677
14.974
29.457
4.661
6.848
10.063
14.785
21.725
46.902
5.604
8.623
13.268
20.414
31.409
74.358
6.727
10.835
17.449
28.102
45.259
117.391
8.062
13.585
22.892
38.575
65.001
184.565
9.646
17.000
29.960
52.800
93.051
289.002
11.523
21.231
39.116
72.069
132.782
450.736
13.743
26.462
50.950
98.100
188.884
700.233
15%
1.150
1.323
1.521
1.749
2.011
2.313
2.660
3.059
3.518
4.046
4.652
5.350
6.153
7.076
8.137
9.358
10.761
12.375
14.232
16.367
32.919
66.212
133.176
267.864
1.083.657
16%
1.160
1.346
1.561
1.811
2.100
2.436
2.826
3.278
3.803
4.411
5.117
5.936
6.886
7.988
9.266
10.748
12.468
14.463
16.777
19.461
40.874
85.850
180.314
378.721
1,670.704
1i%
1.170
1.369
1.602
1.874
2.192
2.565
3.001
3.511
4.108
4.807
5.624
6.580
7.699
9.007
10.539
12.330
14.426
16.879
19.748
23.106
50.658
111.065
243.503
533.869
2.566.215
18%
1.180
1.392
1.643
1.939
2.288
2.700
3.185
3.759
4.435
5.234
6.176
7.288
8.599
10.147
11.974
14.129
16.672
19.673
23.214
27.393
62.669
143.371
327.997
750.378
3.927.357
19%
1.190
1.416
1.685
2.005
2.386
2.840
3.379
4.021
4.785
5.695
6.777
8.064
9.596
11.420
13.590
16.172
19.244
22.901
27.252
32.429
77.388
184.675
440.701
1,051.668
5,988.914
20%
1.200
1.440
1.728
2.074
2.488
2.986
3.583
4.300
5.160
6.192
7.430
8.916
10.699
12.839
15.407
18.488
22.186
26.623
31.948
38.338
95.396
237.376
590.668
1,469.772
9,100.438
TABLE B
Present value interest factor of $1 per period at i% for n periods, PVIF(i,n).
Period
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
35
40
50
1%
0.990
0.980
0.971
0.961
0.951
0.942
0.933
0.923
0.914
0.905
0.896
0.887
0.879
0.870
0.861
0.853
0.844
0.836
0.828
0.820
0.780
0.742
0.706
0.672
0.608
2%
0.980
0.961
0.942
0.924
0.906
0.888
0.871
0.853
0.837
0.820
0.804
0.788
0.773
0.758
0.743
0.728
0.714
0.700
0.686
0.673
0.610
0.552
0.500
0.453
0.372
3%
0.971
0.943
0.915
0.888
0.863
0.837
0.813
0.789
0.766
0.744
0.722
0.701
0.681
0.661
0.642
0.623
0.605
0.587
0.570
0.554
0.478
0.412
0.355
0.307
0.228
4%
5%
0.962 0.952
0.925 0.907
0.889 0.864
0.855 0.823
0.822 0.784
0.790 0.746
0.760 0.711
0.731 0.677
0.703 0.645
0.676 0.614
0.650 0.585
0.625 0.557
0.601 0.530
0.577 0.505
0.555 0.481
0.534 0.458
0.513 0.436
0.494 ' 0.416
0.475 0.396
0.456 0.377
0.375 0.295
0.308 0.231
0.253 0.181
0.208 0.142
0.141 0.087
6%
0.943
0.890
0.840
0.792
0.747
0.705
0.665
0.627
0.592
0.558
0.527
0.497
0.469
0.442
0.417
0.394
0.371
0.350
0.331
0.312
0.233
0.174
0.130
0.097
0.054
7%
0.935
0.873
· 0.816
0.763
0.713
0.666
0.623
0.582
0.544
0.508
0.475
0.444
0.415
0.388
0.362
0.339
0.317
0.296
0.277
0.258
0.184
0.131
0.094
0.067
0.034
8%
0.926
0.857
0.794
0.735
0.681
0.630
0.583
0.540
0.500
0.463
0.429
0.397
0.368
0.340
0.315
0.292
0.270
0.250
0.232
0.215
0.146
0.099
0.068
0.046
0.021
9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19%1 20%
0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833
0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694
0.772· 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579
0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482
0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402
0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335
0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279
0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233
0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194
0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162
0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135
0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112
0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093
0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.D78
0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065
0.252 0.218 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054
0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045
0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038
0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031
0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026•
0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010
0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004
0.049 0.036 0.026 0.019 0.014 0.010 0.008 0.006 0.004 0.003 0.002 0.002
0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001
0.013 0.009 0.005 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000
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2 Pages 11-20 |
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2.1 Page 11 |
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TABLE C
1-uturev.a1ue1nterest-ractoror an orainarv annu1[Yor ::,1 per p_enooat I roror nnenons, 1--VTFAfl,nl,
Period I 1%
2%
3%
4%
5%
6%
7%
8%
9% l0%
11% 12% 1-3% 14% 15% 16% 17% 18% 19% 20%
1 1,000 1.000 1,000 1.000 1,000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.QQO 1.000 1.000 1.000 1,000 1.000 1.000 I
2 2.010 2.020 2.030 2.040 2.050 2.060 2,070 2.080 2.090 2.100 2.-110 2.120 2.130 2.140 2.15.0 2.160 2.170 2.180 2.190 2.200
3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3,310 3.342 3.374 3.407 3.440 3.473 3.506 3.539 3.572 3.606 3.640
4 4,060 4.12·2 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.710 4.779 4.850 4.921 4.993 5.066 5.141 5.215 5.291 5.368
5 5.101 5.204 5.309 5.416 5,526 5.637 5.751 5.867 5.985 6.105 6.228 6.353 6.480 6:610 6.742 6.877 7.014 7.154 7.297 7.442
6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716 7,913 8.115 8.323 8,536 8.754 8.977 9.207 9.442 9.683 9.930
7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 9.783 10.089 10.405 10.730 11.067 11:414 11.772 12.142 12.523 12:916
8 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.637 11.028 11.436 11.859 12.300 12.757 13,233 13.727 14.240 14.773 15.327 15.902 16.499
9 9.369 9.755 10.159 10.583 11.027 11.491 11.978 1-2,488 13.021 13.579 14.164 14.776 15.416 16.085 16:786 17.519 18.285. 19.086 19.923 20.799
10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15:937 16.722 17.549 18.420 19.337 20.304 21.3.21 22.393 23.521 24.709 25.959
11 11.567 12.169 12.808 130486 14.207 14.972 15,784 16.645 17.560 18.531 19.561 20.655 21.814 23.045 24.349 25.733 27.200 28.755 30.404 32.150
12 12.683 13.412 14.192 15.026 15.917 16.870 17.88_8 18.977 20.141 21.384 22.7l3 24.133 25.650 27.271 29.002 30.850 32.8.24 34.931 37.180 39,581
13 13.809 14.680 15.618 16.627 17.713 18.882 20.-141 21.495 22.953 24.523 26.212 28.029 29.985 32.089 34.352 36.786 39.404 42.219 45:244 48.497
14 14.947 15.974 17.086 18:292 19,599 21.015 22.550 24.215 26.019 27.975 30.095 32,393 34.883 37.581 40.505 43.672 47.103 50.818 54.841 59.196
15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 34.405 37.280 40.417 43.842 47.580 51.660 56.110 60.965 66.261 72.035
16 17.258 18.639 20.157 21.825 23,657 25,673 27.888 30,324 33.003 35.950 39.190 42.753 46.672 50.980 55.717 60.925 66.649 72.939 79.850 87.442
17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33,750 36.974 40,545 44.501 48.884 53.739 59.118 65.075 71.673 78.979 87:068 96.022 105.93
18 19.615 21.412 23.414 25.645 28.132 30.906 33:999 37.450 41301 45.599 50.396 55.750 61.725 68.394 75,836 84.141 93.406 103.74 115.27 .128.12
19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159 56,939 63.440 70.749 78.969 88.212 98,603 110.28 123.41 138.17 154.74
20 22.019 24.297 26,870 29.778 33.066 36.786 40.995 45.762 51.160 57.275 64.203 72.052 80.947 91.025 102.44 115.38 130.03 146.63 165.42 186.69
25 28.243 32.030 36.459 41.646 47.727 54.865 63,249 73.106 84.701 98.347 114.41 133.33 155.62 181.87 212.79 249.21 292.10 342.60 402.04 471.98
30 34.785 40.568 47.575 56.085 66.439 79.058 94.461 113.28 136.31 164.49 199.02 241.33 293.20 356.79 434.75 530.31 647.44 790.95 966.71 1,181.9
35 41.660 49.994 60A62 73.652 90.320 111.43 138.24 172.32 215.71 271.02 341.59 431.6.6 546.68 693.57 881.17 1,120.7 1.426.5 1,816.7 2,314.2 2,948.3
40 48:886 60.402 75.401 95:026 120.80 154.76 199.64 259.06 337.88 442.59 581.83 767.09 1,013.7 1,342.0 1,779.1 2,360.8 3,t34.5 4,163.2 5,529.8 7,343.9
50 64.463 84.579 112.80 152.67 209:35 290.34 406,53 573,77 815.08 1,163.9 1,668.8 2.400:0 3,459.5 4994.5 7,217.7 10436 15090 21,813 31.515 45.497
TABLED
Present value interest factor of an (ordinary) annuity of $1 oer period at i% for n periods, PVIFA(i,n).
P~riod
1
2
3
4
5
6
1%.
0:990
1.970
2.941
3.902
4.853
5,795
2%
3%
0.980 ·0.971
1.942 1.913
2.884 2.829
3,808 3.717
4.713 . 4.580-
5.601 5.417
4%
0,962
Ui86
2.775
3.630
4.452
5.242
5%
0.952
1.859
2.723
3.546
4.329
5,076
6%
0.943
1..833
2.673
3.465
4.212
4.917
7%
0..935
1:808
2,624
3.387
4·_100
4.767
8%
0,,928
1.783
2.577
3.3:12
3.993
4.623
9%
0,917
1.759
2.531
3.240
3.890
4.486
·10% 11%
0.909 - 0,901
1.736 1.713
2.487 2.444
3.170 3.102
3.791 3.696
4.355 4.231
12%
0.893
1.690
2.402
3.037
3.605
4.111
13%
0.8. 85
1.668
2.36_1
2.974
3.517
3.998
14_% 15%
0.877 0.870
1.647 1.626
2,322 2.283
2.914 2.855
3.433 3,352
3.889 3.764
16% 17%
0.862 0.855
1,"60,5 1.5135
2,246 2.210
2.798 2.743
3.274 3.199
3.685 3.589
18%
0:847
1.566
2.174
2.690
3:127
3:498
19%1 20%
0,840 ·0:033
1.547 1.528
2,1.40 2.106
2.639 2:589
3,058 2.991
3.410 3.326
7 6:728 6:472 6,230 6,0_02 5.786 5,582 5.389 5.206 5.033 4.868 4.71°2 4.564 4.423 4.2il8 4.160 4.039 :i.922 3.a12 3.706 3.605
8 7,652
9 8,566
7.325
8.162
7.020
7.786
6.733
7.435
6.463
7.108
6.210
6.802
5.971
6:515
5.747
6.247
5.535 5,335 5.146 4.968 4,799 4.639 4.487 4.344 4.207 4.078 3.954 3:.837
5:995 5.759' 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4,163 4.031
10 9.471 8.:983 8.530 8.111 7.722 7,360 7.024 6. 7-10 6.418 6.145 5.S89 5.650 5.426 5.216 5.019: 4.8'j3 4.659 4.494 4,339 4,192
11 10,368 9,787 9.253 8.760 8.306 7.887 7.499 7.1.39 .6,.805 6.495 6.207 5.938 5,687 .5.453 5.234 5.029 4.836 4,656 4.486 4·,327
12 11.255 10.575 9,954 9.385, 8.,863 8.384 7,943 7.536 7,161 6.814 q.492 6.194 5.9)8 5,660 5.421 5.197 -4:988 4.793 4.611 4.439
13 12.134 11.348' 1b.635 9Jl86 9.394 8.853 8.358 7,_904 7.487 7.1Q3 6,7$0 6.424 6.122 5,842 5.583 5.342 5.118 4.910 4.715 4.533
14 13.004 12:106 1-1.296 10,563 9,899 .9.295 8.745 8,244 7.786 7.367 6.982 6:628· q.302 6.002' 5.724 5.468 5:229 5.008 4.802 4.611
15 13.86.5 12,849 11.938 1Uf8 10,380 9.712 9,108 B,559 8:061 7.606 7.191 6.811 6.462· 6.142 5:847 5.575 5,324 5.092 4.876 4.675
16 14.718 13.578 12.561 11.652 10,838 10,106 9.447 8.851 8.3~3 7.824 7.379 6.974 6,604 6,265 .. 5,954 5.668 5.405 5.162 4,938 4,7.30
17 15.562 14.292 13.166 1-2.16.6 11.274 10.477 9.763 9.122 8:544 8.022' 7.5. 49 7,120 6.729 6,373 6.047 5.749 5.475 -5.222 4,990 4.775
18 16,398 14,992 13.754 12.659 11.690 10:828 10,059 9;372 8.756 8.201 7,702 7.250 6.840 q.467 6.128 5.810 5.534 _5.-273· 5.033 4.812
19 17.226: 15.678 14.324 13.134 12.08_5 11:158 10.336 9.604 8.950 8.365 7.839 7.366 · 6.938 6.550 6.198 5.877 5.584 5.316, 5.070 4.843
20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818. 9,129 8.514 7,963 7.469 7.025 6,623 6,259 5,929 5.628 5,353' 5.101 4,870
25 22.023
30 25:808
35 29.409
40 32.835
19.523
22.396
24.999
27.355
17.413
19.Eioo
21.487
23.115
15.622
17.292
18.665
19.79.3
·14.094
15.372
16,374
17.159
12,783
13.765
14.498
15.046
11,654.
12.409
12,948
13.332
10.675
11.258
11.655
11.925
9.823
10.274
10.567
10.757
9.017
9.427
9.644
9.779
8:422
8,694
8,855
8,951
7.843,. 7.330
8.055 7.496
8.176 7,586
8.244 7.634
6,873
7.003
7.070
7,105
6.464
6:566
6.617
6.642
6,097
6,177
6;215
6,233
5.766
5.829
5.858
5.871
-5:457 5.195
5.5i7 5.235
5_-539 5:251
5;548 5.258
4 ..948
4.979
4:992·
4.997
50 39,196 31-.424 25,730 21.482 18.256 15.762 13'801 12.233 10.962 9.915 9.042 8,304 7.675 7.133 6.661 6.246 5.880 5,554 5.262 4.999
21%
0.826
1.509
2.074·
2.540
2.926
3.245
3.508.
3.726
3.905
4,054
4.177
4.278
4.362
4.432
4.489-
4.536
4.576
4.608
4.635
4.657
4.721
4.746
4.756
4.760
4.762
22%
0.820'
1.492
2.042
'2.494
2.864
3.167
3-.416
3,619
3.786
3:923
4.0.35
4.127
4.203
4.265
4.315
4.357
4_39·1
4.419
4.442
4.460
'4.514
4.534
4.541
4.544
4.545
23%
0.813
1.474
2.011
2.448
2.803
3.092
3.327
3.518
3.67;3.
3'.799
3.902
3.985
4.053
4.108
4.15:3
4.189
4,219
4.243
4,263
4.279
4.320
4.3311.
4.340
4.347
4.a48