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PFI810S- PROJECT FINANCE AND INVESTMENT ANALYSIS-1ST OPP- JUNE 2025 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnDLOGY
FACULTY OF COMMERCE, HUMAN SCIENCES AND EDUCATION
DEPARTMENT OF ECONOMICS, ACCOUNTING AND FINANCE
QUALIFICATION: POST GRADUATE DIPLOMA IN DEVELOPMENT FINANCE
QUALIFICATION CODE: 08PGDD
COURSE CODE: PFl81 OS
SESSION: JUNE 2025
LEVEL:8
COURSE NAME: PROJECT FINANCE & INVESTMENT
ANALYSIS
PAPER: THEORY AND CALCULATIONS
DURATION: 3 HOURS
MARKS: 100
EXAMINERS
MODERATOR
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Lameck Odada
Dr Faeezah Peerbhai
INSTRUCTIONS
1. This question paper consists of FOUR (4) Questions.
2. Answer ALL the FOUR (4) questions in blue or black ink only. NO PENCIL and TIPEX
3. Start each question on a new page and number the answers correctly and clearly.
4. Write clearly and neatly and show all your formulas, workings, and assumptions.
5. Unless otherwise stated, round off final answers only to two (2) decimal places.
6. Questions relating to this examination 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 the candidate makes should be
clearly stated.
PERMISSIBLE MATERIALS
1. Silent, non-programmable calculators
THIS QUESTION PAPER CONSISTS OF _7_ PAGES (including this front page)
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QUESTION 1
[25 MARKS]
Charm Incorporated (hereafter Charm), a software company, has developed a new game,
'Fingo', which it plans to launch in the near future. Sales of the new game are expected to be
strong, following a favourable review by a popular magazine. Charm has been informed that
the review will give the game a 'Best Buy' recommendation. Sales volumes, production
volumes, and selling prices for 'Fingo' over its four-year life are expected to be as follows:
Year
1
2
3
4
Sales and production (units)
150 000
70 000
60 000
60 000
Selling price (N$ per game)
25
24
23
22
Financial information on 'Fingo' for the first year of production is as follows:
Direct material cost
N$5.40 per game
Other variable production cost
N$6.00 per game
Fixed costs
N$4.00 per game
Advertising costs to stimulate demand are expected to be N$650 000 in the first year of
production and N$100 000 in the second year of production. No advertising costs are expected
in the third and fourth years of production. Fixed costs represent incremental cash fixed
production overheads. 'Fingo' will be produced on a new production machine costing N$800
000. Although this production machine is expected to have a useful life of up to ten years,
government legislation allows Charm to claim the capital cost of the machine against the
manufacture of a single product. Capital allowances will therefore be claimed on a straight-
line basis over four years.
Charm pays tax on profits at a rate of 30% per year, and tax liabilities are settled in the year
in which they arise. Charm uses an after-tax discount rate of 10% when appraising new capital
investments. Ignore inflation.
REQUIRED
MARKS
Calculate the Net Present Value (NPV) of the proposed investment and conclude 25
whether the investment is financially viable or not. Show all your figures to the
nearest N$1 000.
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QUESTION 2
[25 MARKS]
DRAB Limited (DRAB) has been allocated N$5 million for capital expansion in the forthcoming
year. The management of DRAB Ltd believes that the company must spread its risk by
investing in projects with different risk profiles and has identified two possible investments
(projects A and B). The capital available to DRAB Ltd is sufficient to invest in only one of the
projects. The following information has been made available:
Economic growth
(annual average)
Zero
3%
6%
Expected return
Standard deviation
Book value
Market value
Probability of
occurrence
0.3
0.4
0.3
Estimated return%
Project
Project
Existing
A
B
investments
14
8
6
10
6
12
8
22
16
11.4%
3.90%
N$5 million N$10 million N$5 million
N$5 million N$15 million N$5 million
As the development finance expert, the division manager has requested you to use portfolio
theory to determine which of the two projects should be accepted.
REQUIRED
MARKS
Based on expected returns and the standard deviations, which project 11
a)
should DRAB invest in?
If DRAB forms a portfolio of the two projects, determine the portfolio's
4
b) expected return and conclude whether DRAB should invest in the
portfolio.
Determine the standard deviation of the portfolio in part b) above and
7
c)
conclude whether DRAB should invest in the portfolio or not.
d) Explain the meaning of the term diversification
3
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QUESTION 3
[25 MARKS]
Fruit Lover's Market (FLM) is a supermarket chain that operates franchised grocery stores and
convenience stores in Southern Africa. FLM currently offers an FLM card to Namibian
customers, which enables consumers to purchase FLM products on credit. FLM does not
currently offer any early settlement discounts. You have also been provided with the following
extracts from the FLM Integrated report as at 29 February 2025:
Trade Receivables
Inventory
Trade payables
Bank Overdraft
Note
2
1
2025
N$
61 969 784
65 580 906
25 270 622
9 929 334
Revenue
Cost of Sales
Gross Profit
Operating profit before finance income and finance expense
Finance income
Finance expenses
Profit for the year from continuinQ operations
3
430 798 744
(257 862 994)
172 935 750
17 829 811
1 785 130
(6 467 307)
9 265 281
Note 1
Merchandise
Merchandise in transit
Impairment of inventory
Inventory
2024
N$
66 620 149
2 966 753
(4 005 996)
65 580 906
Note 2
Trade receivables
Impairment (bad debts)
Trade and other receivables
2024
N$
62 611 923
(642 139)
61 969 784
The impairment allowance has been raised against trade receivables that are considered to
be impaired due to uncollectable amounts and credit claims.
Credit risk.
The FLM's exposure to credit risk is influenced mainly by the individual characteristics of each
customer. The FLM's most significant customer, a domestic retailer, accounts for N$50 681
081 of the trade receivables carrying amount at 29 February 2025. Even though FLM has
significant credit risk exposure to this client, it was noted that this retailer has a great attitude
towards paying their debts and currently always settles their accounts within the credit terms
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as stipulated. Normal trading terms are 50 days, but not always adhered to. Credit clients are
not required to provide collateral for products purchased on credit.
FLM has policies to ensure that sales of products are made to customers with an appropriate
credit history. An established credit policy exists under which each new customer is analysed
individually for creditworthiness before the FLM's standard payment and delivery terms, and
conditions are offered. The FLM's review of creditworthiness includes external ratings when
available and, in some cases, bank references.
Note 3
27% of sales relate to cash sales, while the remaining 73% use the FLM card. FLM does not
offer any early settlement discounts currently.
Future growth strategy
FLM plans to actively market the FLM card to customers to improve its current Namibian cash
flow position. To remain competitive in this market, they are pondering credit terms in line with
the other related credit providers:
• 5% early settlement discounts if accounts are settled within 7 days (corresponding to
the cooling off period for online purchase agreements). 20% of credit sales is expected
to be paid within 7 days.
• 30 days credit if not taking the discount.
• It is expected that bad debts will increase to 5% of trade receivables.
• It is expected that credit sales will increase by 10% should the FLM card be marketed
more actively, whereas cash sales will remain unaffected.
• Gross profit percentages will remain constant.
• Money market investments in Namibia currently offer 6% interest per annum. It is
expected that the increase in credit sales and a quicker debt collection period will result
in a positive cash balance in the future.
Another alternative avenue for improving the current Namibian cash flow situation of FLM is
to consider factoring the company receivables with a banking institution. FLM hopes that the
debt collection will also improve by factoring their debtors' books.
Assumptions
• Assume all payments on credit are received at the end of each month.
• Round up all days to the nearest whole number.
• Assume that there are 365 days in a calendar year.
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REQUIRED
MARKS
Explain five (5) factors credit managers should consider when assessing
10
a)
a potential customer's creditworthiness.
Analyse the cash flow conversion cycle of FLM by assessing the
following ratios for 2025:
• Debtors Days
2
b)
• Inventory Days
2
• Creditors Days
2
• Cash conversion cycle
1
Discuss any four (4) methods of reducing the length of the cash
8
c)
operating cycle
QUESTION 4
[25 MARKS]
Baker Hughes Company (BHC) undertook a project involving the construction of a seawater
desalination plant near Swakopmund. The project was completed on 01 January 2025, for
N$10 million. The directors of BHC believe their multi-million-dollar project shall be able to
supply all the water to be consumed at some 40km into the desert. After 5 years, the company
must dismantle and restore the environment in compliance with the Ministry of Marine
Resources & Fisheries and the Ministry of Environment & Tourism regulations. Management
of BHC has established that the cost of dismantling and restoring the environment was N$4
million on 1 January 2025. BHC would want to evaluate several investment opportunities and
understand the overall risk of their assets as perceived by the market. Accordingly, the
directors have set out to calculate the company's weighted average cost of capital (WACC).
Equity, bonds and preference shares currently finance the assets of the company. The details
are as follows:
Debt: BHC issued 10 000 bonds that are currently outstanding with a 6% annual coupon rate.
The bonds mature in eight years and have a N$1 000 face value. These bonds are currently
trading in the market for N$1 100.
Preference shares: BHC also has in issue 3% Preference shares with a par value of N$100
each amounting to 100 000 shares. These preference shares are perpetual shares that are
not redeemable at any time. The preference shares are currently selling for N$30 per share in
the market.
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Equity: BHC has 500 000 shares currently selling for N$25 each in the market. The shares
have a beta of 1.5. The risk-free rate is 4%, and the expected market return is 12%. Recently,
the company paid a dividend of N$2.32 per share, and management expects the growth in
dividends to be 6% per share forever. The corporate tax rate is 20%.
REQUIRED
MARKS
Describe the weighted average cost of capital (WACC) in your own
5
a)
words.
b) Estimate the BHC after-tax cost of debt.
3
c) Calculate the BHC cost of preference shares.
2
Determine the BHC cost of equity using both the Dividend Growth Model
5
d)
(DGM) and the Capital Asset Pricing Model (CAPM)
Calculate the Weighted Average Cost of Capital of BHC to the nearest 10
e)
whole number. Use the least cost of equity capital
END OF EXAMINATION PAPER
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TABLE A
Future value interest factor of $1 per period at i% for n periods, FVIF(i,n).
Period
1% 2%
1 1.010 1.020
2 1.020 1.040
3 1.030 1.061
4 1.041 1.082
5 1.051 1.104
6 1.062 1.126
7 1.072 1.149
8 1.083 1.172
9 1.094 1.195
10 1.105 1.219
11 1.116 1.243
12 1.127 1.268
13 1.138 1.294
14 1.149 1.319
15 1.161 1.346
16 1.173 1.373
17 1.184 1.400
18 1.196 1.428
19 1.208 1.457
20 1.220 1.486
25 1.282 1.641
30 1.348 1.811
35 1.417 2.000
40 1.489 2.208
50 1.645 2.692
3% 4%
1.030 1.040
1.061 1.082
1.093 1.125
1.126 1.170
1.159 1.217
1.194 1.265
1.230 1.316
1.267 1.369
1.305 1.423
1.344 1.480
1.384 1.539
1.426 1.601
1.469 1.665
1.513 1.732
1.558 1.801
1.605 1.873
1.653 1.948
1.702 2.026
1.754 2.107
1.806 2.191
2.094 2.666
2.427 3.243
2.814 3.946
3.262 4.801
4.384 7.107
5%
1.050
1.103
1.158
1.216
1.276
1.340
1.407
1.477
1.551
1.629
1.710
1.796
1.886
1.980
2.079
2.183
2.292
2.407
2.527
2.653
3.386
4.322
5.516
7.040
11.467
6%
1.060
1.124
1.191
1.262
1.338
1.419
1.504
1.594
1.689
1.791
1.898
2.012
2.133
2.261
2.397
2.540
2.693
2.854
3.026
3.207
4.292
5.743
7.686
10.286
18.420
7%
1.070
1.145
1.225
1.311
1.403
1.501
1.606
1.718
1.838-
1.967
2.105
2.252
2.410
2.579
2.759
2.952
3.159
3.380
3.617
3.870
5.427
7.612
10.677
14.974
29.457
8%
1.080
1.166
1.260
1.360
1.469
1.587
1.714
1.851
1.999
2.159
2.332
2.518
2.720
2.937
3.172
3.426
3.700
3.996
4.316
4.661
6.848
10.063
14.785
21.725
46.902
9%
1.090
1.188
1.295
1.412
1.539
1.677
1.828
1.993
2.172
2.367
2.580
2.813
3.066
3.342
3.642
3.970
4.328
4.717
5.142
5.604
8.623
13.268
20.414
31.409
74.358
10%
1.100
1.210
1.331
1.464
1.611
1.772
1.949
2.144
2.358
2.594
2.853
3.138
3.452
3.797
4.177
4.595
5.054
5.560
6.116
6.727
10.835
17.449
28.102
45.259
117.391
11%
1.110
1.232
1.368
1.518
1.685
1.870
2.076
2.305
2.558
2.839
3.152
3.498
3.883
4.310
4.785
5.311
5.895
6.544
7.263
8.062
13.585
22.892
38.575
65.001
184.565
12%
1.120
1.254
1.405
1.574
1.762
1.974
2.211
2.476
2.773
3.106
3.479
3.896
4.363
4.887
5.474
6.130
6.866
7.690
8.613
9,646
17,000
29.960
52.800
93.051
289,002
13%
1.130
1.277
1.443
1.630
1.842
2.082
2.353
2.658
3.004
3.395
3.836
4.335
4.898
5.535-
6.254
7.067
7.986
9.024
10.197
11.523
21.231
39.116
72.069
132.782
450.736
14%
1.140
1.300
1.482
1.689
1.925
2.195
2.502
2.853
3.252
3.707
4.226
4.818
5.492
6.261
7.138
8.137
9.276
10.575
12.056
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.m
19.461
40.874
85.850
180.314
378.721
1,670.704
17%
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
1%
0.990
0.980
2%
0.980
0.961
3%
0.971
0.943
4%
0.962
0.925
5%
0.952
0.907
6%
0.943
0.890
7%
0.935
0.873
8%
0.926
0.857
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
3 0.971
4 0.961
0.942
0.924
0.915
0.888
0.889
0.855
0.864
0.823
0.840 · 0.816
0.792 0.763
0.794
0.735
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
5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402
6 0.942
7 0.933
0.888
0.871
0.837
0.813
0.790
0.760
0.746
0.711
0.705
0.665
0.666
0.623
0.630
0.583
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
8 0.923
9 0.914
10 0.905
0.853
0.837
0.820
0.789
0.766
0.744
0.731
0.703
0.676
0.677
0.645
0.614
0.627
0.592
0.558
0.582
0.544
0.508
0.540
0.500
0.463
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
11 0.896
12 0.887
13 0.879
14 0.870
15 0.861
16 0.853
17 0.844
18 0.836
19 0.828
20 0.820
25 0.780
30 0.742
35 0.706
40 0.672
50 0.608
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
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
0.650
0.625
0.601
0.577
0.555
0.534
0.513
0.494
0.475
0.456
0.375
0.308
0.253
0.208
0.141
0.585
0.557
0.530
0.505
0.481
0.458
0.436
. 0.416
0.396
0.377
0.295
0.231
0.181
0.142
0.067
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
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
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
0.388
0.356
0.326
0.299
0.275
0.252
0.231
0.212
0.194
0.178
0.116
0.075
0.049
0.032
0.013
0.350
0.319
0.290
0.263
0.239
0.218
0.198
0.180
0.164
0.149
0.092
0.057
0.036
0.022
0.009
0.317
0.286
0.258
0.232
0.209
0.188
0.170
0.153
0.138
0.124
0.074
0.044
0.026
0.015
0.005
0.287
0.257
0.229
0.205
0.183
0.163
0.146
0.130
0.116
0.104
0.059
0.033
0.019
0.011
0.003
0.261
0.231
0.204
0.181
0.160
0.141
0.125
0.111
0.098
0.087
0.047
0.026
0.014
0.008
0.002
0.237
0.208
0.182
0.160
0.140
0.123
0.108
0.095
0.083
0.073
0.038
0.020
0.010
0.005
0.001
0.215
0.187
0.163
0.141
0.123
0.107
0.093
0.081
0.070
0.061
0.030
0.015
0.008
0.004
0.001
0.195
0.168
0.145
0.125
0.108
0.093
0.080
0.069
0.060
0.051
0.024
0.012
0.006
0.003
0.001
0.178
0.152
0.130
0.111
0.095
0.081
0.069
0.059
0.051
0.043
0.020
0.009
0.004
0.002
0.000
0.162
0.137
0.116
0.099
0.084
0.071
0.060
0.051
0.043
0.037
0.016
0.007
0.003
0.001
0.000
0.148
0.124
0.104
0.088
0.074
0.062
0.052
0.044
0.037
0.031
0.013
0.005
0.002
0.001
0.000
0.135
0.112
0.093
0.078
0.065
0.054
0.045
0.038
0.031
0.026'
0.010
0.004
0.002
0.001
0.000,
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9 Page 9 |
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TABLE C
i-uture vaIue interest ractor or an orainarv annu1tv or ::;1oer oenoa at 1"10ror n penoas. F\\711-All.nl.
i
Period I 1%
2%
3%
4~'<> 5%/ 6%
7%
8%
9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%1
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 1.000 1.000 1.000 1.000 1.000 1.000 1.000 !
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 2.150 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 4.122 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 12.488 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 21.321 22.393 23.521 24.709 25.959
11 11.567 12.169 12.808 13.486 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 17.888 18.977 20.141 21.384 22.713 24.133 25.650 27.271 29.002 30.850 32.824 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 41.301 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 60.462 73.652 90.320 111.43 138.24 172.32 215.71 271.02 341.59 431.66 546.68 693.57 881.17 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 3,134.5 4,163.2 5,529.8 7,343.9
so 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 4,994.5 7,217.7 10.436 15,090 21,813 31,515 45,497
TABLED
Present value interest factor of an (ordinary) annuity of $1 per period at i% for n periods, PVIFA(i,n).
Period
1
2
3
4
5
6
7
1%
0.990
1.970
2.941
3.902
4.853
5.795
6.728
2%
0.980
1.942
2.884
3.808
4.713
5.601
6.472
3%
0.971
1.913
2.829
3.717
4.580
5.417
6.230
4~1o
0.962
1.886
2.775
3.630
4.452
5.242
6.002
5%
0.952
1,859
2.723
3,546
4.329
5,076
5.766
6%
0.943
1.833
2.673
3.465
·.;:212
4.917
5.562
7%
0.935
1.808
2.624
3.387
4.100
4.767
5.389
8%
0.926
1.783
2.577
3.312
3.993
4.623
5.206
9%
0.917
1.759
2.531
3.240
3.890
4.486
5.033
10%
0.909
1.736
2.487
3.170
3.791
4.355
4.868
11%
0.901
1.713
2.444
3.102
3.696
4.231
4.712
12% 13%
0.893 0.885
1.690 1.668
2.402 2.361
3.037 2.974
3.605 3.517
4.111 3.998
4.564 4.423
14%
0.877
1.647
2.322
2.914
3.433
3.889
4.288
15%
0.870
1.626
2.283
2.855
3.352
3.784
4.160
16%
0.862
1.605
2.246
2.798
3.274
3.665
4.039
17%
0.855
1.585
2.210
2.743
3.199
3.589
3.922
18%
0.847
1.566
2.174
2.690
3.127
3.498
3.812
19%1 20%
0.840 0.833
1.547 1.528
2.140 2.106
2.639 2.589
3.058 2.991
3,410 3.326
3.706 3.605
6 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
11 10.368
12 11.255
8,983
9.787
10.575
8.530
9.253
9.954
8.111
8.760
9.38.5
7.722
8.306
8.863
7.360
7.887
8.384
7.024
7.499
7.943
6.710
7.139
7.536.
6.418
6.805
7.161
6.145
6.495
6.814
5.a89
6.207
6.492
5.650
5.938
6.194
5.426
5.661
5.918
5.216
5.453
5.660
5.019
5.234
5.421
4.833
5.029
5.197
4.659
4.836
4.986
4.494
4.656
4.793
4.339
4.486
4.611
4.192
4.327
4.439
13 12.134 11.348 10.635 9.986 9,394 : 8.853 8.358 7.904 7.487 7.103 6.750 6.424 6,122 5.842 5.583 5.342 5.118 4.910 4.715 4.533
14 13.004 12.106 11.296 10.563 9.899 "9.295
15 13.865 12.849 11.938 11.118 10.380 ·9,i12
8.745
9.108
8,244
8.559
7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611
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 11.552 10.838 10.106 9.447 8.851 8,313 7.824 7.379 6.974 6.604 6.265 5.954 5.668 5.405 5.162 4,938 4.730
17 15.562 14.292 13.166 12.166 11.274 10.477 9.763
18 16.398 14.992 13.754 12.659 11.690 10.828 10.059
9.122
9.372
8.544 8.022 7.549 7.120 6.729 6,373 6.047 5.749 5.475 5.222 4.990 4.775
8.756 8.201 7.702 7.250 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812
19 17.226 15.678 14.324 13.134 12.085 11.158 10.336
20 18.046 16.351 14.877 13.590 12.462 11.470 10.594
9.504
9.816
8.950 8,365 7.839 7.366 6.938 6.550 6.198 5,877 5.584 5.316 5.070 4.843
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 19.523 17.4.13 15.622 14.094 _12.783 11.654 10.675 9.823 9.077 8.422 7.843,. 7.330 6.873 6.464 6,097 5.766 5.467 5.195 4.948
30 25.808 22.396 19.600 i7.292 15.372 13.765 12.409 11.258 10.274 9.427 8.694 8.055 7.496 7.003 6.566 6,177 5.829 5.517 5.235 4.979
35 29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567 9.644 8.855 8.176 7.586 7 070 6.617 6.215 5.858 5.539 5.251 4.992
40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 'l0.757 9.7i9 8.951 8,244 7,634 7.105 6.642 6.233 5.871 5.548 5.258 4.997
50 39.196 31.424 25.730 21.482 18.25if ·,5_752 ·13 601 12.233 i0.962 9.915 9,042 8.304 7.575 7.133 6.661 6.246 5.860 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
4.035
4.127
4.203
4.265
4.315
4.357
4.391
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
3.673
3.799
3.902
3.985
4.053
4.108
4.153
4.189
4.219
4.243
4.253
4.279
4.323
4.339
4.345
4.347
4.348