CA Proficiency 1

PAPER 1 - FINANCE

SUMMER 2010 (Tuesday 25th May 2009 - 3.00 p.m. to 6.00 p.m.)

TABLES AND FORMULAE

CAP1 FIN REF S10 1 5/10/2010

Present Value Tables
Present value of 1, i.e. (1 + r)-n
where r = discount rate
n = number of periods until payment

Periods Discount rates (r)

(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909
2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826
3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751
4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683
5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621
6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564
7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513
8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467
9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424
10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386
11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350
12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319
13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290
14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263
15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239

11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833
2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694
3 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579
4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482
5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402
6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335
7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279
8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233
9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194
10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162
11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135
12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112
13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093
14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078
15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065

21% 22% 23% 24% 25% 26% 27% 28% 29% 30%
1 0.826 0.820 0.813 0.807 0.800 0.794 0.787 0.781 0.775 0.769
2 0.683 0.672 0.661 0.650 0.640 0.630 0.620 0.610 0.601 0.592
3 0.565 0.551 0.537 0.525 0.512 0.500 0.488 0.477 0.466 0.455
4 0.467 0.451 0.437 0.423 0.410 0.397 0.384 0.373 0.361 0.350
5 0.386 0.370 0.355 0.341 0.328 0.315 0.303 0.291 0.280 0.269
6 0.319 0.303 0.289 0.275 0.262 0.250 0.238 0.227 0.217 0.207
7 0.263 0.249 0.235 0.222 0.210 0.198 0.188 0.178 0.168 0.159
8 0.218 0.204 0.191 0.179 0.168 0.157 0.148 0.139 0.130 0.123
9 0.180 0.167 0.155 0.144 0.134 0.125 0.116 0.108 0.101 0.094
10 0.149 0.137 0.126 0.116 0.107 0.099 0.092 0.085 0.078 0.073
11 0.123 0.112 0.103 0.094 0.086 0.079 0.072 0.066 0.061 0.056
12 0.102 0.092 0.083 0.076 0.069 0.063 0.057 0.052 0.047 0.043
13 0.084 0.075 0.068 0.061 0.055 0.050 0.045 0.040 0.037 0.033
14 0.069 0.062 0.055 0.049 0.044 0.039 0.035 0.032 0.028 0.025
15 0.057 0.051 0.045 0.040 0.035 0.031 0.028 0.025 0.022 0.020

CAP1 FIN REF S10 2 5/10/2010

Annuity Table
1 – (1 + r)-n
Present value of an annuity of 1, i.e. r

where r = discount rate

n = number of periods

Periods Discount rates (r)

(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909
2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736
3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487
4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170
5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791
6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355
7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868
8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335
9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759
10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145
11 10.37 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495
12 11.26 10.58 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814
13 12.13 11.35 10.63 9.986 9.394 8.853 8.358 7.904 7.487 7.103
14 13.00 12.11 11.30 10.56 9.899 9.295 8.745 8.244 7.786 7.367
15 13.87 12.85 11.94 11.12 10.38 9.712 9.108 8.559 8.061 7.606

11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833
2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528
3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106
4 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589
5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991
6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326
7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605
8 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837
9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031
10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192
11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327
12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439
13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533
14 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611
15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675

21% 22% 23% 24% 25% 26% 27% 28% 29% 30%
1 0.826 0.820 0.813 0.806 0.800 0.794 0.787 0.781 0.775 0.769
2 1.509 1.492 1.474 1.457 1.440 1.424 1.407 1.392 1.376 1.361
3 2.074 2.042 2.011 1.981 1.952 1.923 1.896 1.868 1.842 1.816
4 2.540 2.494 2.448 2.404 2.362 2.320 2.280 2.241 2.203 2.166
5 2.926 2.864 2.803 2.745 2.689 2.635 2.583 2.532 2.483 2.436
6 3.245 3.167 3.092 3.020 2.951 2.885 2.821 2.759 2.700 2.643
7 3.508 3.416 3.327 3.242 3.161 3.083 3.009 2.937 2.868 2.802
8 3.726 3.619 3.518 3.421 3.329 3.241 3.156 3.076 2.999 2.925
9 3.905 3.786 3.673 3.566 3.463 3.366 3.273 3.184 3.100 3.019
10 4.054 3.923 3.799 3.682 3.571 3.465 3.364 3.269 3.178 3.092
11 4.177 4.035 3.902 3.776 3.656 3.543 3.437 3.335 3.239 3.147
12 5.278 4.127 3.985 3.851 3.725 3.606 3.493 3.387 3.286 3.190
13 4.362 4.203 4.053 3.912 3.780 3.656 3.538 3.427 3.322 3.223
14 4.432 4.265 4.108 3.962 3.824 3.695 3.573 3.459 3.351 3.249
15 4.489 4.315 4.153 4.001 3.859 3.726 3.601 3.483 3.373 3.268

CAP1 FIN REF S10 3 5/10/2010

CAP 1 - FORMULAE
Adjusted present value

APV = Vu + Dt – PV of issue costs

Capital asset pricing model

rj = rf + β(rm - rf)

Dividend valuation model (no growth – finding the value of equity)

P0 = D1
Ke

Dividend valuation model (no growth – finding the cost of equity)

Ke = D1
P0

Dividend valuation model (with growth – finding the cost of equity)

Ke = D0(1 + g) +g
P0

Dividend valuation model (with growth – finding the value of equity)

D0(1 + g)
P0 =
Ke - g

Economic batch quantity

2FU
EBQ = CP (1-d/r)

CAP1 FIN REF S10 4 5/10/2010

Economic order quantity model

2FU
EOQ = CP

Equivalent annual annuity

i
Annual annuity equivalent of the NPV = NPV x 1 – (1 + i)-n

Growth in dividends (using historic actual dividend information)

Dt0
g= y ------- -1
Dt0-y

Growth (using retentions)

g = br

Interpolation (IRR)

NPV 1 (Rate 2 – Rate 1)

IRR rate = Rate 1 + NPV 1 - NPV 2

Irredeemable debt (market value of debt)

D= i
Kd

CAP1 FIN REF S10 5 5/10/2010

Irredeemable debt (cost of debt)

Kd = i(1-t)
D

Nominal discount rate

Nominal discount rate = ((1 + Real rate) x (1 + Inflation rate)) - 1

Preference share (cost)

KP = D1
Pp

Redeemable bonds (market value)

I1 I2 Rn
P0 = -------- + -------- + … --------
(1 + Kd) (1+Kd)2 (1+Kd)n

Redeemable bonds (cost/return)

I1 + (R – P0)/n
Kd =
P0 P0

Standard deviation
The square root of the variance (σ2), which is:

σ2 = (X1 – Y)2p1 + (X2 – Y)2p2……..(Xn – Y)2pn

Untraded debt (cost)

Kdt = i(1 - t)

CAP1 FIN REF S10 6 5/10/2010

Weighted average cost of capital (WACC)

WACC = E(Ke) + D(Kd(1-t))

(D + E) (D + E)

Annualised cost of discount

d___ x ____________365_______________
100 - d (reduction in receivables/debtors days)

CAP1 FIN REF S10 7 5/10/2010