Answer ALL questions. QUESTION 1 (25 Marks) You have been appointed as the financial director of Remedica Limited (Ltd). They require you to calculate the cost of capital of the company. The following information is available on the capital structure of the company: 1 000 000 Ordinary shares, with a market price of R5 per share. The latest dividend declared was 87 cents per share. A dividend growth of 13% was maintained for the past 5 years. 1 000 000 12%, R1 Preference shares with a market value of R2 per share. R1 000 000 9%, Debentures due in 7 years and the current yield-to-maturity is 10%. R1 300 000 15% Bank loan, due in December 2025. Additional information: 1. The company has a tax rate of 30%. 2. The beta of the company is 1.5, a risk free rate of 5% and the return on the market is 16% Required: 1.1 Calculate the weighted average cost of capital (WACC). Use the Gordon Growth Model to calculate the cost of equity. 1.2 Calculate the cost of equity, using the Capital Asset Pricing Model. (22 marks) (3 marks) QUESTION 2 (25 Marks) 2.1 Selhurst Distributors normal credit terms to Westering Stores are 30 days but is prepared to allow a 2% rebate if it pays the account within 15 days. Calculate the cost to Westering Stores of not accepting the discount. (5 marks) 2.2 Differentiate in detail between accruals and when the bank account has an unfavourable balance. (8 marks) 2.3 Discuss the different types of non-current liabilities. (12 marks) QUESTION 3 (25 Marks) Miley (Ltd), South Africa, is a specialist manufacturer of aluminium products. In seeking to expand its operations, it has the opportunity to acquire an American subsidiary company, Trump Ltd, or set up a new division in its home market. The relevant figures for these two options are: Set up new division at home Rand Cost of setting up premises 15 000 000 Cost of machinery 9 000 000 Annual sales 13 000 000 Annual variable cost 4 000 000 Additional head office expenses 1 000 000 Existing head office expenses 500 000 Depreciation 2 400 000 Acquisition Euro Acquire shares from existing shareholders 6 500 000 Annual sales 4 000 000 Annual variable costs 2 000 000 Annual fixed costs 500 000 Consultant fees 350 000 Additional information: - The project is expected to last for 10 years. - Miley (Ltd), current cost of capital is 12%. - The American inflation is expected to be below the South African inflation by 1% per year, throughout the life of this investment. - The exchange rate is expected to be R12 to the Dollar ($) due to the strengthening of the Rand (R) as a result of an upbeat (positive) economic and political outlook for South Africa. Required: 3.1 Make all necessary calculations for the two options. 3.2 Advise Miley (Ltd) on the viability of these two opportunities. (22 marks) (3 marks) QUESTION 4 (25 Marks) The directors of Axe (Ltd) have appointed you as a merger and acquisition specialist. They are considering the acquisition of Mex (Ltd). You are to advise them whether or not to proceed with the project. The following information is available: Axe (Ltd) Mex (Ltd) Market price per share R20.00 R16.00 Earnings per share R6.00 R4.80 No. of shares issued 4 million 1 million Cash payment to Mex Ltd = R26 million. Synergy benefits of R20 million will accrue through the acquisition. Mex Ltd have just had their assets re valued and the valuation has appreciated quite significantly. Required: Assume the acquisition is based on market values with a cash payment: 4.1 Discuss the possible tax gains from a merger and acquisition (5 marks) 4.2 Calculate the combined value of the proposed acquisition (2 marks) 4.3 Calculate the net present value of the proposal (2 marks) 4.4 Calculate the acquisition premium (2 marks) 4.5 Calculate the post-acquisition market price of the share (3 marks) 4.6 Calculate the post-acquisition increase/decrease price of the share (2 marks) Assume the acquisition is based on earnings per share: 4.7 Calculate the exchange ratio based on earnings per share 4.8 Calculate the total number of shares in the proposed acquisition 4.9 Calculate the post-acquisition earnings per share (3 marks) (2 marks) (4 marks) END OF PAPER APPENDIX 1 1 (1 + K ) Present value of R1: PVFA (k,n) = 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 14% 15% 16% 17% 18% 19% 25% Number of Periods 1 2 3 0.9901 0.9804 0.9803 0.9612 0.9706 0.9423 0.9610 0.9238 0.9515 0.9057 0.9709 0.9426 0.9151 0.8885 0.8626 0.9615 0.9524 0.9434 0.9246 0.9070 0.8900 0.8890 0.8638 0.8396 0.8548 0.8227 0.7921 0.8219 0.7835 0.7473 0.9346 0.9259 0.8734 0.8573 0.8163 0.7938 0.7629 07350 0.7130 0.6806 0.91740.9091 0.9009 0.8929 0.8850 0.8417 0.8264 0.8116 0.7972 0.7831 0.7722 0.7513 0.7312 0.7118 0.6931 0.7084 0.6830 0.6587 0.6355 0.6133 0.6499 0.6209 0.5935 0.5674 0.5428 0.8772 0.7695 0.6750 0.5921 0.5194 0.8696 0.8621 0.8547 0.8475 0.7561 0.7432 0.7305 0.7182 0.6575 0.6407 0.6244 0.6086 0.57180.55230.5337 0.5337 0.5158 0.4972 0.4761 0.4561 0.4371 0.8403 0.8333 0.8000 0.7062 0.6944 0.6400 0.5934 0.5787 0.5120 0.49870.4823 0.4096 0.4190 0.4019 0.3277 4 5 6 7 8 9 10 0.9420 0.9327 0.9235 0.9143 0.9053 0.8880 0.8375 0.8706 0.8131 0.8535 0.7894 0.8368 0.7664 0.8203 0.7441 0.7903 0.7599 0.7307 0.7026 0.6756 0.7462 0.7050 0.7107 0.6651 0.6768 0.6274 0.6446 0.5919 0.6139 0.5584 0.6663 0.6227 0.5820 0.5439 0.5083 0.6302 0.5835 0.5403 0.5002 0.4632 0.5963 0.5645 0.5346 0.5066 0.5470 0.5132 0.4817 0.4523 0.5019 0.4665 0.4339 0.4039 0.4604 0.4241 0.3909 0.3606 0.4224 0.3855 0.3522 0.3220 0.4803 0.4556 0.4251 0.3996 0.3762 0.3506 0.3329 0.3075 0.2946 0.2697 0.4323 0.4104 0.3898 0.3704 0.3759 0.3538 0.3332 0.3139 0.3269 0.3050 | 0.2848 0.2660 0.2843 0.2630 0.2630 0.2434 0.2434 0.2255 0.2472 0.2267 0.2080 0.1911 0.3521 0.3349 0.2621 0.2959 0.2791 0.2097 0.2487 0.2326 0.1678 0.2090 0.1938 0.1342 0.1756 0.1615 0.1074 11 12 13 14 15 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.4289 0.3875 0.3971 0.3555 0.3677 0.3262 0.3405 0.2992 0.3152 0.2745 0.3505 0.3173 0.2875 0.2607 0.3186 0.2858 0.2567 0.2307 0.2897 0.2575 0.2292 0.2042 0.2633 0.2320 0.2046 0.1807 0.2394 0.2090 0.1827 0.1599 0.2366 0.2076 0.1821 0.1597 0.1401 0.2149 0.1869 0.1625 0.1413 0.1229 0.1954 0.1778 0.1619 0.1685 0.15200.1372 0.1452 0.1299 0.1163 0.12520.1110 0.0985 0.1079 0.0949 0.0835 0.1476 0.1346 0.0859 0.1240 0.1122 0.0687 0.1042 0.0935 0.0935 0.0550 0.0876 0.0779 0.0779 0.0440 0.0736 0.0649 0.0352 16 17 18 19 20 0.8528 0.7284 0.6232 0.8444 0.7142 0.6050 0.8360 0.7002 0.5874 0.8277 0.6864 0.5703 0.8195 0.6730 0.5537 0.5339 0.4581 0.3936 0.3387 0.2919 0.5134 0.4363 0.3714 0.3166 0.2703 0.4936 0.4155 0.3503 0.2959 0.2502 0.4746 0.3957 0.3305 0.2765 0.2317 0.4564 0.3769 0.3118 0.2584 0.2145 0.2519 0.2176 0.188 0.1631 0.1415 0.1229 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.2120 0.1799 0.1799 0.1528 0.1300 0.1108 0.0946 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.1069 0.0930 0.0811 0.0929 0.0802 0.0693 0.0808 0.0691 0.0592 0.07030.0596 0.0506 0.0611 0.0514 | 0.0433 0.0708 0.0600 0.0508 0.0431 0.0365 0.0618 0.0541 0.0281 0.0520 0.0451 0.0225 0.0437 0.0376 0.0180 0.0367 0.0313 0.0144 0.0308 0.0261 0.0115 25 30 40 50 60 0.7798 0.6095 0.4776 0.3751 0.2953 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 0.0736 0.0588 0.0471 0.0378 0.0304 | 0.0245 0.0245 0.0197 0.0160 0.7419 0.5521 0.4120 0.3083 0.2314 | 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0090 0.0090 0.0070 0.67170.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 0.01070.0075 0.0053 0.0037 0.0026 0.0019 0.0013 0.6080 0.3715 0.2281 0.1407 0.08720.0543 0.0339 0.0213 0.01340.0085 0.0054 0.0035 0.0022 0.0014 0.0009 0.0006 0.0004 0.0004 0.0003 0.5504 0.3048 0.1697 0.0951 0.0535 0.0303 0.01730.0099 0.00570.0033 0.0019 0.0011 0.00070.0004 0.0002 0.0001 0.0001 0.0129 0.0054 0.0010 0.0002 0.0105 0.0038 0.0042 0.0012 0.0007 0.0001 0.0001 APPENDIX 2 Present value of a regular annuity of R1 per period for n periods : PVFA (k,n) = 1 1 (1 + K) 1 (1+ k ) I'M= k 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Number of Periods 1 2 3 4 5 0.9901 1.9704 2.9410 3.9020 4.8534 0.9804 1.9416 2.8839 3.8077 4.7135 0.9709 1.9135 2.8286 3.7171 4.5797 0.9615 1.8861 2.7751 3.6299 4.4518 0.9524 1.8594 2.7232 3.5460 4.3295 0.9434 1.8334 2.6730 3.4651 4.2124 0.9346 1.8080 2.6243 3.3872 4.1002 0.9259 1.7833 2.5771 3.3121 3.9927 0.9174 0.9091 0.9009 1.7591 1.7355 1.7125 2.5313 2.4869 2.4437 3.2397 3.1699 3.1024 3.88973.7908 3.6959 0.8929 1.6901 2.4018 3.0373 3.6048 0.8850 1.6681 2.3612 2.9745 3.5172 0.8772 1.6467 2.3216 2.9137 3.4331 0.8696 0.8621 1.6257 1.6052 2.2832 2.2459 2.8550 2.7982 3.3522 3.2743 0.8547 0.8475 0.8403 0.8333 1.5852 1.5656 1.54651.5278 2.2096 2.1743 2.1399 2.1065 2.7432 2.6901 2.6386 2.5887 3.1993 3.1272 3.0576 2.9906 6 7 8 9 5.7955 6.7282 7.6517 8.5660 9.4713 5.6014 6.4720 7.3255 8.1622 8.9826 5.4172 6.2303 7.0197 7.7861 8.5302 5.2421 6.0021 6.7327 7.4353 8.1109 5.0757 5.7864 6.4632 7.1078 7.7217 4.9173 5.5824 6.2098 6.8017 7.3601 4.7665 5.3893 5.9713 6.5152 7.0236 4.6229 5.2064 5.7466 6.2469 6.7101 4.48594.3553 4.2305 5.0330 4.8684 4.7122 5.5348 5.33495.1461 5.99525.7590 5.5370 6.4177 6.1446 5.8892 4.11143.9975 4.5638 4.4226 4.9676 4.7988 5.3282 5.1317 5.6502 5.4262 3.8887 3.7845 3.68473.5892 3.4976 3.4098 4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 4.6389 4.48734.3436 4.2072 4.0776 3.9544 4.9464 4.7716 4.6065 4.4506 4.3038 4.1633 5.2161 5.01884.8332 4.6586 4.4941 4.3389 3.3255 3.6046 3.8372 4.0310 4.1925 10 7.4987 7.9427 11 12 13 14 15 10.3676 11.2551 12.1337 13.0037 13.8651 9.7868 10.5753 11.3484 12.1062 12.849 9.2526 9.9540 10.6350 11.2961 11.9379 8.7605 9.3851 9.9856 10.5631 11.1184 8.3064 8.8633 9.3936 9.8986 10.3797 7.8869 8.3838 8.8527 9.2950 9.7122 8.3577 7.1390 1.5361 7.9038 8.2442 8.5595 6.80526.4951 6.2065 7.1607 6.81376.4924 7.48697.1034 6.7499 7.78627.3667 6.9819 8.0607 7.6061 7.1909 5.9377 6.1944 6.4235 6.6282 6.8109 5.6869 5.9176 6.1218 6.3025 6.4624 5.4527 5.2337 5.0286 4.8364 4.6560 4.6560 4.4865 4.3271 5.6603 5.42065.1971 4.9884 4.7932 4.6109 4.4392 5.8424 5.5831 5.3423 5.11834.9095 4.7147 4.5327 6.0021 5.72455.4675 5.2293 5.0081 4.8023 4.6106 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759 4.6755 8.7455 9.1079 16 17 18 19 20 14.7179 15.5623 16.3983 17.2260 18.0456 13.5777 12.5611 14.291913.1661 14.9920 13.7535 15.6789 14.3238 16.3514 14.877 11.6523 10.8378 10.1059 12.1657 11.2741 10.4773 12.6593 11.6896 10.8276 13.1339 12.0853 11.158 13.590 12.4622 11.4699 9.4466 9.7632 10.0591 10.3356 10.5940 8.8514 9.1216 9.3719 9.6036 9.8181 8.3126 7.8237 7.3792 8.5436 8.0216 7.5488 8.7556 8.2014 7.7016 8.9501 8.3649 7.8393 9.1285 8.5136 7.9633 6.97406.6039 7.1196 6.7291 7.2497 6.8399 7.3658 6.9380 7.4694 7.0248 6.2651 6.3729 6.4674 6.5504 6.6231 5.9542 5.6685 5.4053 5.1624 4.9377 4.7296 6.04725.7487 5.4746 5.2223 4.9897 4.7746 6.12805.81785.5339 5.2732 5.0333 4.8122 6.1982 5.8775 5.5845 5.3162 5.0700 4.8435 6.25935.9288 5.62785.3527 5.1009 4.8696 25 30 40 50 60 22.0232 19.5235 17.4131 15.6221 14.0939 12.7834 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 32.834727.3555 23.1148 19.7928 17.1591 15.0463 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 44.9550 34.7609 27.6756 22.6235 18.9293 16.1614 11.6536 12.4090 13.3317 13.8007 14.0392 10.6748 9.82269.0770 8.4217 11.2578 10.27379.4269 8.6938 11.9246 10.7574 9.7791 8.9511 12.2335 10.9617 9.9148 9.0417 12.3766 | 11.0480 9.96729.0736 7.8431 7.3300 6.8729 8.0552 7.4957 7.0027 8.2438 7.6344 7.1050 8.3045 7.6752 7.1327 8.3240 7.68737.1401 6.4641 6.0971 5.7662 5.4669 5.1951 4.9476 6.56606.1772 5.8294 5.51685.2347 4.9789 6.64186.2335 5.8713 5.5482 5.2582 4.9966 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995 6.6651 6.2402 5.8819 5.5553 5.2630 4.9999 Answer ALL questions. QUESTION 1 (25 Marks) You have been appointed as the financial director of Remedica Limited (Ltd). They require you to calculate the cost of capital of the company. The following information is available on the capital structure of the company: 1 000 000 Ordinary shares, with a market price of R5 per share. The latest dividend declared was 87 cents per share. A dividend growth of 13% was maintained for the past 5 years. 1 000 000 12%, R1 Preference shares with a market value of R2 per share. R1 000 000 9%, Debentures due in 7 years and the current yield-to-maturity is 10%. R1 300 000 15% Bank loan, due in December 2025. Additional information: 1. The company has a tax rate of 30%. 2. The beta of the company is 1.5, a risk free rate of 5% and the return on the market is 16% Required: 1.1 Calculate the weighted average cost of capital (WACC). Use the Gordon Growth Model to calculate the cost of equity. 1.2 Calculate the cost of equity, using the Capital Asset Pricing Model. (22 marks) (3 marks) QUESTION 2 (25 Marks) 2.1 Selhurst Distributors normal credit terms to Westering Stores are 30 days but is prepared to allow a 2% rebate if it pays the account within 15 days. Calculate the cost to Westering Stores of not accepting the discount. (5 marks) 2.2 Differentiate in detail between accruals and when the bank account has an unfavourable balance. (8 marks) 2.3 Discuss the different types of non-current liabilities. (12 marks) QUESTION 3 (25 Marks) Miley (Ltd), South Africa, is a specialist manufacturer of aluminium products. In seeking to expand its operations, it has the opportunity to acquire an American subsidiary company, Trump Ltd, or set up a new division in its home market. The relevant figures for these two options are: Set up new division at home Rand Cost of setting up premises 15 000 000 Cost of machinery 9 000 000 Annual sales 13 000 000 Annual variable cost 4 000 000 Additional head office expenses 1 000 000 Existing head office expenses 500 000 Depreciation 2 400 000 Acquisition Euro Acquire shares from existing shareholders 6 500 000 Annual sales 4 000 000 Annual variable costs 2 000 000 Annual fixed costs 500 000 Consultant fees 350 000 Additional information: - The project is expected to last for 10 years. - Miley (Ltd), current cost of capital is 12%. - The American inflation is expected to be below the South African inflation by 1% per year, throughout the life of this investment. - The exchange rate is expected to be R12 to the Dollar ($) due to the strengthening of the Rand (R) as a result of an upbeat (positive) economic and political outlook for South Africa. Required: 3.1 Make all necessary calculations for the two options. 3.2 Advise Miley (Ltd) on the viability of these two opportunities. (22 marks) (3 marks) QUESTION 4 (25 Marks) The directors of Axe (Ltd) have appointed you as a merger and acquisition specialist. They are considering the acquisition of Mex (Ltd). You are to advise them whether or not to proceed with the project. The following information is available: Axe (Ltd) Mex (Ltd) Market price per share R20.00 R16.00 Earnings per share R6.00 R4.80 No. of shares issued 4 million 1 million Cash payment to Mex Ltd = R26 million. Synergy benefits of R20 million will accrue through the acquisition. Mex Ltd have just had their assets re valued and the valuation has appreciated quite significantly. Required: Assume the acquisition is based on market values with a cash payment: 4.1 Discuss the possible tax gains from a merger and acquisition (5 marks) 4.2 Calculate the combined value of the proposed acquisition (2 marks) 4.3 Calculate the net present value of the proposal (2 marks) 4.4 Calculate the acquisition premium (2 marks) 4.5 Calculate the post-acquisition market price of the share (3 marks) 4.6 Calculate the post-acquisition increase/decrease price of the share (2 marks) Assume the acquisition is based on earnings per share: 4.7 Calculate the exchange ratio based on earnings per share 4.8 Calculate the total number of shares in the proposed acquisition 4.9 Calculate the post-acquisition earnings per share (3 marks) (2 marks) (4 marks) END OF PAPER APPENDIX 1 1 (1 + K ) Present value of R1: PVFA (k,n) = 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 14% 15% 16% 17% 18% 19% 25% Number of Periods 1 2 3 0.9901 0.9804 0.9803 0.9612 0.9706 0.9423 0.9610 0.9238 0.9515 0.9057 0.9709 0.9426 0.9151 0.8885 0.8626 0.9615 0.9524 0.9434 0.9246 0.9070 0.8900 0.8890 0.8638 0.8396 0.8548 0.8227 0.7921 0.8219 0.7835 0.7473 0.9346 0.9259 0.8734 0.8573 0.8163 0.7938 0.7629 07350 0.7130 0.6806 0.91740.9091 0.9009 0.8929 0.8850 0.8417 0.8264 0.8116 0.7972 0.7831 0.7722 0.7513 0.7312 0.7118 0.6931 0.7084 0.6830 0.6587 0.6355 0.6133 0.6499 0.6209 0.5935 0.5674 0.5428 0.8772 0.7695 0.6750 0.5921 0.5194 0.8696 0.8621 0.8547 0.8475 0.7561 0.7432 0.7305 0.7182 0.6575 0.6407 0.6244 0.6086 0.57180.55230.5337 0.5337 0.5158 0.4972 0.4761 0.4561 0.4371 0.8403 0.8333 0.8000 0.7062 0.6944 0.6400 0.5934 0.5787 0.5120 0.49870.4823 0.4096 0.4190 0.4019 0.3277 4 5 6 7 8 9 10 0.9420 0.9327 0.9235 0.9143 0.9053 0.8880 0.8375 0.8706 0.8131 0.8535 0.7894 0.8368 0.7664 0.8203 0.7441 0.7903 0.7599 0.7307 0.7026 0.6756 0.7462 0.7050 0.7107 0.6651 0.6768 0.6274 0.6446 0.5919 0.6139 0.5584 0.6663 0.6227 0.5820 0.5439 0.5083 0.6302 0.5835 0.5403 0.5002 0.4632 0.5963 0.5645 0.5346 0.5066 0.5470 0.5132 0.4817 0.4523 0.5019 0.4665 0.4339 0.4039 0.4604 0.4241 0.3909 0.3606 0.4224 0.3855 0.3522 0.3220 0.4803 0.4556 0.4251 0.3996 0.3762 0.3506 0.3329 0.3075 0.2946 0.2697 0.4323 0.4104 0.3898 0.3704 0.3759 0.3538 0.3332 0.3139 0.3269 0.3050 | 0.2848 0.2660 0.2843 0.2630 0.2630 0.2434 0.2434 0.2255 0.2472 0.2267 0.2080 0.1911 0.3521 0.3349 0.2621 0.2959 0.2791 0.2097 0.2487 0.2326 0.1678 0.2090 0.1938 0.1342 0.1756 0.1615 0.1074 11 12 13 14 15 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.4289 0.3875 0.3971 0.3555 0.3677 0.3262 0.3405 0.2992 0.3152 0.2745 0.3505 0.3173 0.2875 0.2607 0.3186 0.2858 0.2567 0.2307 0.2897 0.2575 0.2292 0.2042 0.2633 0.2320 0.2046 0.1807 0.2394 0.2090 0.1827 0.1599 0.2366 0.2076 0.1821 0.1597 0.1401 0.2149 0.1869 0.1625 0.1413 0.1229 0.1954 0.1778 0.1619 0.1685 0.15200.1372 0.1452 0.1299 0.1163 0.12520.1110 0.0985 0.1079 0.0949 0.0835 0.1476 0.1346 0.0859 0.1240 0.1122 0.0687 0.1042 0.0935 0.0935 0.0550 0.0876 0.0779 0.0779 0.0440 0.0736 0.0649 0.0352 16 17 18 19 20 0.8528 0.7284 0.6232 0.8444 0.7142 0.6050 0.8360 0.7002 0.5874 0.8277 0.6864 0.5703 0.8195 0.6730 0.5537 0.5339 0.4581 0.3936 0.3387 0.2919 0.5134 0.4363 0.3714 0.3166 0.2703 0.4936 0.4155 0.3503 0.2959 0.2502 0.4746 0.3957 0.3305 0.2765 0.2317 0.4564 0.3769 0.3118 0.2584 0.2145 0.2519 0.2176 0.188 0.1631 0.1415 0.1229 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.2120 0.1799 0.1799 0.1528 0.1300 0.1108 0.0946 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.1069 0.0930 0.0811 0.0929 0.0802 0.0693 0.0808 0.0691 0.0592 0.07030.0596 0.0506 0.0611 0.0514 | 0.0433 0.0708 0.0600 0.0508 0.0431 0.0365 0.0618 0.0541 0.0281 0.0520 0.0451 0.0225 0.0437 0.0376 0.0180 0.0367 0.0313 0.0144 0.0308 0.0261 0.0115 25 30 40 50 60 0.7798 0.6095 0.4776 0.3751 0.2953 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 0.0736 0.0588 0.0471 0.0378 0.0304 | 0.0245 0.0245 0.0197 0.0160 0.7419 0.5521 0.4120 0.3083 0.2314 | 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0090 0.0090 0.0070 0.67170.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 0.01070.0075 0.0053 0.0037 0.0026 0.0019 0.0013 0.6080 0.3715 0.2281 0.1407 0.08720.0543 0.0339 0.0213 0.01340.0085 0.0054 0.0035 0.0022 0.0014 0.0009 0.0006 0.0004 0.0004 0.0003 0.5504 0.3048 0.1697 0.0951 0.0535 0.0303 0.01730.0099 0.00570.0033 0.0019 0.0011 0.00070.0004 0.0002 0.0001 0.0001 0.0129 0.0054 0.0010 0.0002 0.0105 0.0038 0.0042 0.0012 0.0007 0.0001 0.0001 APPENDIX 2 Present value of a regular annuity of R1 per period for n periods : PVFA (k,n) = 1 1 (1 + K) 1 (1+ k ) I'M= k 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Number of Periods 1 2 3 4 5 0.9901 1.9704 2.9410 3.9020 4.8534 0.9804 1.9416 2.8839 3.8077 4.7135 0.9709 1.9135 2.8286 3.7171 4.5797 0.9615 1.8861 2.7751 3.6299 4.4518 0.9524 1.8594 2.7232 3.5460 4.3295 0.9434 1.8334 2.6730 3.4651 4.2124 0.9346 1.8080 2.6243 3.3872 4.1002 0.9259 1.7833 2.5771 3.3121 3.9927 0.9174 0.9091 0.9009 1.7591 1.7355 1.7125 2.5313 2.4869 2.4437 3.2397 3.1699 3.1024 3.88973.7908 3.6959 0.8929 1.6901 2.4018 3.0373 3.6048 0.8850 1.6681 2.3612 2.9745 3.5172 0.8772 1.6467 2.3216 2.9137 3.4331 0.8696 0.8621 1.6257 1.6052 2.2832 2.2459 2.8550 2.7982 3.3522 3.2743 0.8547 0.8475 0.8403 0.8333 1.5852 1.5656 1.54651.5278 2.2096 2.1743 2.1399 2.1065 2.7432 2.6901 2.6386 2.5887 3.1993 3.1272 3.0576 2.9906 6 7 8 9 5.7955 6.7282 7.6517 8.5660 9.4713 5.6014 6.4720 7.3255 8.1622 8.9826 5.4172 6.2303 7.0197 7.7861 8.5302 5.2421 6.0021 6.7327 7.4353 8.1109 5.0757 5.7864 6.4632 7.1078 7.7217 4.9173 5.5824 6.2098 6.8017 7.3601 4.7665 5.3893 5.9713 6.5152 7.0236 4.6229 5.2064 5.7466 6.2469 6.7101 4.48594.3553 4.2305 5.0330 4.8684 4.7122 5.5348 5.33495.1461 5.99525.7590 5.5370 6.4177 6.1446 5.8892 4.11143.9975 4.5638 4.4226 4.9676 4.7988 5.3282 5.1317 5.6502 5.4262 3.8887 3.7845 3.68473.5892 3.4976 3.4098 4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 4.6389 4.48734.3436 4.2072 4.0776 3.9544 4.9464 4.7716 4.6065 4.4506 4.3038 4.1633 5.2161 5.01884.8332 4.6586 4.4941 4.3389 3.3255 3.6046 3.8372 4.0310 4.1925 10 7.4987 7.9427 11 12 13 14 15 10.3676 11.2551 12.1337 13.0037 13.8651 9.7868 10.5753 11.3484 12.1062 12.849 9.2526 9.9540 10.6350 11.2961 11.9379 8.7605 9.3851 9.9856 10.5631 11.1184 8.3064 8.8633 9.3936 9.8986 10.3797 7.8869 8.3838 8.8527 9.2950 9.7122 8.3577 7.1390 1.5361 7.9038 8.2442 8.5595 6.80526.4951 6.2065 7.1607 6.81376.4924 7.48697.1034 6.7499 7.78627.3667 6.9819 8.0607 7.6061 7.1909 5.9377 6.1944 6.4235 6.6282 6.8109 5.6869 5.9176 6.1218 6.3025 6.4624 5.4527 5.2337 5.0286 4.8364 4.6560 4.6560 4.4865 4.3271 5.6603 5.42065.1971 4.9884 4.7932 4.6109 4.4392 5.8424 5.5831 5.3423 5.11834.9095 4.7147 4.5327 6.0021 5.72455.4675 5.2293 5.0081 4.8023 4.6106 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759 4.6755 8.7455 9.1079 16 17 18 19 20 14.7179 15.5623 16.3983 17.2260 18.0456 13.5777 12.5611 14.291913.1661 14.9920 13.7535 15.6789 14.3238 16.3514 14.877 11.6523 10.8378 10.1059 12.1657 11.2741 10.4773 12.6593 11.6896 10.8276 13.1339 12.0853 11.158 13.590 12.4622 11.4699 9.4466 9.7632 10.0591 10.3356 10.5940 8.8514 9.1216 9.3719 9.6036 9.8181 8.3126 7.8237 7.3792 8.5436 8.0216 7.5488 8.7556 8.2014 7.7016 8.9501 8.3649 7.8393 9.1285 8.5136 7.9633 6.97406.6039 7.1196 6.7291 7.2497 6.8399 7.3658 6.9380 7.4694 7.0248 6.2651 6.3729 6.4674 6.5504 6.6231 5.9542 5.6685 5.4053 5.1624 4.9377 4.7296 6.04725.7487 5.4746 5.2223 4.9897 4.7746 6.12805.81785.5339 5.2732 5.0333 4.8122 6.1982 5.8775 5.5845 5.3162 5.0700 4.8435 6.25935.9288 5.62785.3527 5.1009 4.8696 25 30 40 50 60 22.0232 19.5235 17.4131 15.6221 14.0939 12.7834 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 32.834727.3555 23.1148 19.7928 17.1591 15.0463 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 44.9550 34.7609 27.6756 22.6235 18.9293 16.1614 11.6536 12.4090 13.3317 13.8007 14.0392 10.6748 9.82269.0770 8.4217 11.2578 10.27379.4269 8.6938 11.9246 10.7574 9.7791 8.9511 12.2335 10.9617 9.9148 9.0417 12.3766 | 11.0480 9.96729.0736 7.8431 7.3300 6.8729 8.0552 7.4957 7.0027 8.2438 7.6344 7.1050 8.3045 7.6752 7.1327 8.3240 7.68737.1401 6.4641 6.0971 5.7662 5.4669 5.1951 4.9476 6.56606.1772 5.8294 5.51685.2347 4.9789 6.64186.2335 5.8713 5.5482 5.2582 4.9966 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995 6.6651 6.2402 5.8819 5.5553 5.2630 4.9999