 |
FMA712S - FINANCIAL MANAGEMENT AGRICULTURE - 2ND OPP - NOV 2024 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA unlVERSITY
OF SCIEnCE Ano TECHn OLOGY
FACULTY OF HEAL TH, NATURAL RESOURCES AND APPLIED SCIENCES
SCHOOL OF AGRICULTURE AND NATURAL RESOURCE SCIENCES
DEPARTMENT OF AGRICULTURAL SCIENCES AND AGRIBUSINESS
QUALIFICATION: BACHELOR OF AGRICUL TURE/BSc: AGRICULTURE
QUALIFICATION CODE: 07BAGR/07BAGA
COURSE CODE: FMA712S/FMA720S
SESSION: JANUARY 2025
LEVEL:?
COURSE NAME: FINANCIAL MANAGEMENT-
AGRICULTURE
PAPER: THEORY AND CALCULATIONS
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
Lameck Odada
MODERATOR Dr Kennedy Sean Kalundu
INSTRUCTIONS
1. This examination question paper consists of FOUR (4) questions
2. Answer ALL the questions in blue or black ink only. NO PENCIL.
3. Start each question on a new page and number the answers correctly and clearly.
4. Write clearly and neatly, showing all your workings/assumptions.
5. Work with at least four (4) decimal places in all your calculations and round off only final
answers 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 errors or ambiguities, and any assumptions the candidate makes should be
clearly stated.
PERMISSIBLE MATERIALS
1. Silent, non-programmable calculators
THIS QUESTION PAPER CONSISTS OF _8_ PAGES (including this front page)
|
|
2 Page 2 |
▲back to top |
QUESTION 1
[25 MARKS]
Suppose a loan of N$25 000 is made to an individual at 6% interest compounded quarterly.
The loan is repaid in 6 instalments. The loan provider requires a down payment of 20% of the
loan's value.
REQUIRED: use the information above to answer the following questions MARKS
a} Define an annuity and differentiate between the two (2) types of annuities.
6
b} Identify any four (4) examples of annuities.
4
c} Determine the size of the payments to the nearest dollar. Work with at
5
least 4 decimal places throughout your calculations
d} Prepare an amortization table to determine the total amount of interest 10
paid and the balance on the loan after five (5) installments. Work with
whole numbers throughout the amortization table
QUESTION 2
[31 MARKS]
Sanden Ltd wishes to expand its operations. Six possible capital investments have been
identified, but the company only has access to a total of N$620 000. The projects are not
divisible and may not be postponed until the future. After the projects end, it is unlikely that
similar investment opportunities will occur:
Expected net cash inflows, including salvage value
Project Initial outlay Year1
Year2
Year3
Year4
Year5
N$
N$
N$
N$
N$
N$
A
246 000
70 000
70 000
70 000
70 000
70 000
8
180 000
75 000
87 000
64 000
-
-
C
175 000
48 000
48 000
63 000
73 000
-
D
180 000
62 000
62 000
62 000
62 000
-
E
180 000
40 000
50 000
60 000
70 000
40 000
F
150 000
35 000
82 000
82 000
Projects A and E are mutually exclusive. All projects are believed to be of similar risk to the
company's existing capital investments. Any surplus funds may be invested in the money
n:iarketto earn a return of 9% per year. The money market may be assumed to be an efficient
market. Banden's cost of capital is 12% per year.
1
|
|
3 Page 3 |
▲back to top |
REQUIRED: use the information above to answer the following questions.
Work with whole numbers in all your calculations
a) Define capital rationing and differentiate between the two types of
capital rationing
b) Calculate the expected net present value of each project
c) Calculate the expected profitability index associated with each of the six
projects. Answer to three (3) decimal places.
d) Rank the projects according to the investment appraisal methods in b)
and c) above.
e) Explain briefly why these rankings differ.
MARKS
5
12
6
6
2
QUESTION 3
[29 MARKS]
Bader (Pty) Ltd must prepare its cash budget for three months. The following information is
available:
Month
Estimates sales (N$)
Estimates purchases (N$)
June
25 000
6 900
July
27 200
7 560
August
34 000
5 780
September
33 600
6 300
Additional information
• Direct wages amount to N$13 000 per month
• Bader sells 20% of all goods on cash; the remainder of customers have one month of
credit.
• Suppliers are paid in the month after purchase.
• Wages are paid in cash as they occur.
• Overheads are N$6 400 per month, and Bader is allowed one month's credit on
overheads. Depreciation of N$600 is included in the amount for overhead.
• Selling, distribution, and administrative costs are N$3 780 per month and are paid in
cash in the month they occur.
• Bader wishes to purchase a new vehicle in August with a cash payment of N$120 000.
• The cash balance for the end of June is expected to be N$90 500.
2
|
|
4 Page 4 |
▲back to top |
REQUIRED:
a) Calculate the total collections for the three months (July to September)
b) Calculate the total payments for the three months (July to September)
c) Prepare a cash budget for the three months (July to September)
MARKS
6
13
10
QUESTION 4
[15 MARKS]
Troublesome Ltd produces a single product. The company uses a standard absorption
costing system, and at the beginning of the year, a budget was drawn up to produce 9 000
units at the following standard cost per unit:
Direct material 0.10 kg at N$50 per kg
Direct labour hours at N$25 per hour
Variable overheads ½ machine hour at N$16 per hour
The actual costs recorded were as follows:
• Total direct material was 800 kg at N$49 per kg.
• 7 700 direct labour hours at N$26 per direct labour hour
• Variable overheads, N$60 750
• Actual machine hours, 4 050 hours.
• Actual production, 7 800 units.
5
25
§.
-3..8
REQUIRED:
a) Direct material quantity variance
b) Direct material price variance
c) Direct labour efficiency variance
d) Direct labour rate variance
e) Variable production overhead expenditure variance
MARKS
3
3
3
3
3
END OF EXAMINATION QUESTION PAPER
3
|
|
5 Page 5 |
▲back to top |
FORMULA SHEET
Portfolio Expected Return
Portfolio standard deviation
ERp= "i._WXA ERA+Ws X ERs
O"As=vWixcr 2A+ Ws2xcr2s+ 2xWAxWsxCoVAB
Beta(~)
Covariance of the company with the market)/variance of the
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)]1•m
Payment
Internal Rate of Return
PMT=PV x r/[1-1/(l+rJt]
IRR= R1+ [N1x (R2-R1)]/N1+N2
Profitability Index
Profitability Index
Accounting Rate of Return
Expected return (discrete distribution)
Expected
return
(continuous
distribution)
Standard deviation (discrete distribution)
Present value of future cash flows (excluding
Initial investment
..
NPV
1+ Initial l, --L,Pnt
Average annual i::1rofit
Average investment
IP;X R;
211
N
v"i._[R-; E(R)]2x ( P;)
initial
outlay)
Standard
deviation
(continuous v"i._(R;- E(R)2
distribution)
n
Covariance (discrete distribution)
= I: Pi [RA- E(RA)][Rs- E(Rs)]
Coefficient of variation
= Standard deviation
Expected return
Correlation coefficient
= Covariance of the assets 1 and 2
Amortization table
0-1X 0-2
I I I I I Year Payment Interest Principal
End balance
I
Material usage variance
= (AQ - SQ) x SP
Material price variance
= (AP-SP) xAQ
Labour efficiency variance
= (SH- AH) x SR
Labour rate variance
= (SR- AR) x AH
Variable overhead expenditure variance = (SR- AR) x AM
Variable overhead efficiency variance
=(MH-AM)xSR
4
|
|
6 Page 6 |
▲back to top |
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
4 1.041
2%
1.020
1.040
1.061
1.082
3%
1.030
1.061
1.093
1.126
4%
1.040
1.082
1.125
1.170
5%
1.050
1.103
1.158
1.216·
6%
1.060
1.124
1.191
1.262
7%
1.070
1.145
1.225
1.311
8%
1.080
1.166
1.260
1.360
9%
1.090
1.188
1.295
1.412
10%
1.100
1.210
1.331
1.464
11%
1.110
1.232
1.368
1.518
12%
1.120
1.254
1.405
1.574
13%
1.130
1.277
1.443
1.630
14%
1.140
1.300
1.482
1.689
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677
1.611
1.772
1.685 ·_ 1.762
1.870 1.974
1.842
2.082
1.925
2.195
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 2.502
8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 2.853
9 1.094 1.195 1.305 1.423 1.551 1.689 1.838- 1.999 2.172
2.358
2.558
2.773
3.004
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 1.710 1.898 2.105 2.332 2.580 2.853 3.152 3.479 3.836 4.226
12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813
3.138
3.498
3.896
4.335
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 i.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.~2
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
20 1.220
1.400
1.428
1.457
1.486
1.653
1.702
1.754
1.806
1.948
2.026
2.107
2.191
2.292
2.407
2.527
2.653
2.693
2.854
3.026
3.207
3.159
3.380
3.617
3.870
3.700
3,996
4.316
4.661
4.328
4.717
5.142
5.604
5.054
5.560
6.116
6.727
5.895
6.544
7.263
8.062
6.866
7.690
8.613
9.646
7.986
9.024
10.197
11.523
9.276
10.575
12.056
13.743
25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.835 13.585 17.000 21.231 26.462
30 1.348 1.811 2.427 3.243
35 1.417 2.000 2.814 3.946
40 1.489 2.208 3.262 4.801
f322
5.516
7.040
5.743
7.686
10.286
7.612
10.677
14.974
10.063
14.785
21.725
13.268
20.414
31.409
17.449
28.102
45.259
22.892
38.575
65.001
29.960
52.800
93.051
39.116
72.069
132.782
50.950
98.100
188.884
50 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902 74.358 117.391 184.565 289.002 450.736 700.233
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%
17%
1.160
1.170
1.346
1.369
1.561
1.602
1.811
1.874
2.100
2.192
2.436
2.565
2.826
3.001
3.278
3.511
3.803
4.108
4.411
4.807
5.117
5.624
5.936 · 6.580
6.886
7.699
7.988
9.007
9.266
10.539
10.748
12.330
12.468
14.426
14.463
16.879
16.m
19.748
19.461
23.106
40.874
50.658
85.850 111.065
180.314 243.503
378.721 533.869
1,670.704 2.566.215
18%
19%
1.180
1.190
1.392
1.416
1.643
1.685
1.939
2.005
2.288
2.386
2.700
2.840
3.185
3.379
3.75_9
4.021
4.435 . 4.785
5.234
5.695
6.176
6.m
7.288
8.064
8.599
9.596
10.147
11.420
11.974
13.590
14.129
16.172
16.672
19.244
19.673
22.901
23.214 . 27.252
27.393
32.429
62.669
77.388
143.371 184.675
327.997 440.701
750.378 1,051.668
3.927.357 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 i0/o for n periods, PVIF(i,n).
Period
1
2
3
4
5
6
7
8
1%
0.990
0.980
0.971
0.961
0.951
0.942
0.933
0.923
2%
0.980
0.961
0.942
0.924
0.906
0.888
0.871
0.853
3%
0.971
0.943
0.915
0.888
0.863
0.837
0.813
0.789
4%
0.962
0.925
0.889
0.855
0.822
0.790
0.760
0.731
5%
0.952
0.907
0.864
0.823
0.784
0.746
0.711
0.677
6%
0.943
0.890
0.840
0.792
0.747
0.705
0.665
0.627
7%
0.935
0.873
· 0.816
0.763
0.713
0.666
0.623
0.582
8%
0.926
0.857
0.794
0.735
0.681
0.630
0.583
0.540
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 Q.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
9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194
10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 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 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135
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
0.788
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
0.701
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'
0.625 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
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
0.444
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
0.397
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
0.356
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
0.319
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
0.286
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
0.257
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
0.231
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
0.208
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
0.187
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
0.168
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
0.152
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
0.137 0.124
0.116 0.104
0.099 0.088
0.084 0.074
0.071 0.062
0.060 0.052
0~051 0.044
0.043 0.037
0.037 0.031
0.016 0.013
0.007 0.005
0.003 0.002
0.001 0.001
0.000 0.000
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
y
|
|
7 Page 7 |
▲back to top |
TABLE C
t-uture vatue interest tacmr OT an orarnarv annurtv OT :.,1cer oenoa at 1°10ror n cenoas. r-vir·AIJ.nl.
Period
I
I
1%
2%
3%
4~{,
5%1 6%
7%
8%
9% 10%1 11% 12% 13% 14% 15%1 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 1.000 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 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 21.321 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
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 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
8
9
10
11
12
13
14
15
1%
0.990
1.970
2.941
3.902
4.853
5,795
6:728
7.652
8.566
9.471
10.368
11.255
12.134
13.004
13.865
2%
0.980
1.942
2.884
3.808
4.713
5.601
6.472
7.325
8.162
8'983
9,787
10.575
11.348
12.106
12.849
3%
0.971
1.913.
2.829
3.717
. 4.580
5.417
6,230
7.020
7.786
8,530
9.253
9.954
10.635
11.296
11.938
4%
0.962
1.886
2.775
3,630
4.452
5.242
6.002
6,733
7.435
8.111
8.760
9.385
9.986
10.563
11.118
5%
0.952
1.859
2.723
3.546
4.329
5.076
5.786
6.463
7.108
7.722
8.306
8,863
9.394
9,899
10.380
6%
0.943
1.833
2.673
3.465
4.212
4.917
5.562
6.210
6.802
7.360
7.887
8.384
8,853
9.295
9.712
7%
0.935
1.808
2.624
3.387
4.100
4.767
5.389
5.971
6.515
7.024
7.499
7,943
8.358
8.745
9,108
8%
0.926
1.783
2.577
3.312
3.993
4.623
5.206
5.747
6,247
6.710
7.139
7.536
7.904
8.244
8.559
9%
0.917
1.759
2.531
3.240
3.890
4.486
5.033
5.535
5.995
6.418
6.805
7.161
7.487
7.786
8.061
10%
0.909
1.736
2.487
3.170
3.791
4.355
4.868
5,335
5.759
6.145
6.495
6.814
7.103
7.367
7.606
11%
0.901
1,713
2.444
3.102
3,696
4.231
4.712
5.146
5.537
5.889
6.207
6.492
6.750
6.982
7.191
12%
0.893
1,690
2.402
3.037
3.605
4.111
4.564
4.968
5.328
5.650
5.938
6.194
6.424
6.628
6,811
13%
o.a05
1.668
2.361
2.974
3.517
3.998
4.423
4.799
5.132
5.426
5.667
5.918
6.122
6.302
6.462
14%
0.877
1.647
2.322
2.914
3.433
3.889
4.288
4.639
4.946
5.216
5.453
5.660
5.842
6.002
6.142
15%
0.870
1.626
2.283
2.855
3.352
3.784
4.160
4.487
4.772
5.019
5.234
5.421
5.583
5.724
5.847
16%
0.862
1.605
2.246
2.798
3.274
3,665
4.039
4.344
4.607
4.833
5.029
5.197
5.342
5.468
5.575
17%
0.855
1.585
2.210
2.743
3.199
3.589
3.922
4.207
4.451
4.659
4.836
4.988
5.118
5.229
5.324
18%
0.847
1.566
2.174
2.690
3.127
3.498
3.812
4.078
4.303
4.494
4.656
4.793
4.910
5.008
5.092
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
3.954 3.837
4.163 4.031
4.339 4.192
4.486 4.327
4.611 4.439
4.715 4.533
4.802 4.611
4.876 4.675
16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 Jl.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
18 16.398 14.992
19 17.226 15.678
13.166
13.754
14,324
12.166
12.659
13.134
11.274
11.690
12,085
10.477
10.828
11.158
9.763
10.059
10.336
9.122
9.372
9,604
8.544
8.756
8.950
8.022
8.201
8.365
7.549
7.702
7,839
7.120 6.729
7.250 6.840
7.366 · 6.938
6.373
6.467
6.550
6.047
6.128
6.198
5.749
5.818
5.877
5.475
5.534
5.584
5.222
5.273
5.316
4.990
5.033
5.070
4.775
4.812
4.843
20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.618 9.129 8.514 7.963 7.469 7.025 6,623 6.2°59 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 17.292 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 10.757 9.779 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 18.256 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
4.035
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
4.263
4.279
4.323
4.339
4,345
4,347
4,348
"'