TABLE OF CONTENTS: PART A: EXAMPLES Compound interest calculations Example 1: Determine the future value of a single payment (lump sum)... 3 Example 2: Determine the annual rate of interest earned by an investor on a lump sum investment... 3 Example 3: The determination of the term (in years) for which a lump sum amount has been invested... 3 Example 4: The calculation of the lump sum that must be invested to mature at a given future value... 4 Example 5: Calculate the future value of an annuity due (payable in advance)... 4 Example 6: The calculation of the annual amount to be invested at the beginning of every year to mature at a given future value... 5 Example 7: The calculation of the annual rate of interest earned on an investment where a fixed annual recurring amount was invested, at the beginning of every year... 5 Example 8: The calculation to determine the instalment payable in respect of a bank loan where instalments are paid at the end of every year... 6 Example 9: Calculation of the future value of an investment where the investor invests firstly, a lump sum, and secondly a recurring annual investment (fixed amount)... 6 Example 10: The calculation of the future value where a lump sum is invested in the beginning of the term and annual withdrawals are taken... 7 Example 11: Calculate the term of an investment if the annual recurring investment (PMT), made at the beginning of every year... 7 Example 12: Calculate the future value of a recurring investment made at the beginning of every month and interest accrues monthly... 8 Example 13: Calculate the monthly instalment on a loan, the outstanding balance of the loan at any particular time, as well as the interest and capital content of instalments... 9 Example 14: Calculate the new monthly instalment on a loan if the rate of interest changes at any particular point in time... 10 Example 15: Calculate the increased monthly instalment that must be paid on a loan in order to shorten the remaining payment period... 11 Example 16: Calculate nominal and effective rates of return... 12 Example 17: Calculate the future value of a monthly instalment where interest accrues quarterly... 13 Example 18: The calculation of the present value of an annuity payable in the beginning of every year and that grows by a fixed percentage every year... 15 Example 19: The calculation of the present value of a growing annuity... 17 Example 20: The present value of a growing annuity payable at the end of every year... 17 vii
FINANCIAL CALCULATIONS Example 21: The calculation of the future value of a growing annuity... 21 Example 22: The calculation of the future value of an annuity that grows (increases) by a fixed percentage every year.... 22 Example 23: Calculation of the first annual instalment that must be invested in the beginning of the first year to mature at a given future value in a case where the annual instalment (annuity) will escalate by a fixed percentage every year... 25 Example 24: Calculate the annual rate at which an investor must increase (escalate) his annual instalments to achieve his capital investment goal.... 25 Example 25: Calculate the internal rate of return of an irregular cash flow... 28 Example 26: Calculate the future value (FV) of an irregular cash flow... 28 Example 27: The calculation of the capital amount (present value) needed to provide a growing annuity every year and that will preserve the capital at the end of the term... 29 Example 28: Calculate the amount that must be invest as the first recurring payment in the beginning of the first year to achieve a particular goal if the annual investment is increased every year... 30 Example 29: The calculation of the total amount of premiums paid where the payments ncreased every year... 30 Example 30: How to calculate the future value of a growing annuity which is paid in monthly instalments (beginning of every month)... 31 Example 31: The calculation of the after-tax rate of return on a fixed interest rate investment (i.e. a fixed deposit). The affect of the section 10(1)(i)(i) interest exemption is not taken into account... 32 Example 32: The calculation of the after-tax rate of return on a fixed interest rate investment (fixed deposit). The affect of the section 10(1)(i)(i) exemption is taken into account... 33 Income tax calculations Example 33: How to determine the pre-tax rate of interest that an investor must earn in order to get a better return than he will receive than by redeeming his outstanding debts... 56 Example 34A: Should one take a withdrawal from a retirement fund in order to repay one s debts?... 56 Example 34B: Calculate whether capital should be invested or rather be used to redeem a debt... 61 Example 35: Key person Insurance... 117 viii
TABLE OF CONTENTS PART A: WORKSHEETS Compound interest calculations Worksheet 1: The calculation of the present value of a growing (escalating) annuity by using a financial calculator... 16 Worksheet 2: Calculation of the future value of an annual recurring investment (annuity) which escalates by a fixed percentage every year... 19 Worksheet 3: Calculation of the first annual instalment that must be invested in the beginning of the first year to mature at a given future value in a case where the annual instalment (annuity) will escalate by a fixed percentage every year... 23 Worksheet 4: The calculation of the capital required to provide a growing annuity payable at the beginning of every year and which will return the capital invested when the term of the annuity expires... 35 Retirement planning calculations Worksheet 5: Calculation of capital need and capital required at retirement date (capital is NOT preserved)... 37 Taxation of lump sum benefits from retirement funds Worksheet 6: The determination of the amount of TAX PAYABLE on a lump sum received on RESIGNATION from a PENSION or a PROVIDENT FUND (including the preservation funds) and where the taxpayer did not previously receive a retirement lump sum benefit... 42 Worksheet 7: The determination of the amount of TAX PAYABLE on a lump received on RESIGNATION from a PENSION FUND, a PROVIDENT FUND (including the preservation funds), or a RETIREMENT ANNUITY FUND where the taxpayer has previously received a withdrawal benefit, a retirement benefit, or a severance benefit... 43 Worksheet 8: The determination of the amount of TAX PAYABLE on a lump benefit received on RETIREMENT from a PENSION FUND, a PROVIDENT FUND (including the preservation funds), or a RETIREMENT ANNUITY FUND (or any combination of the these) where the taxpayer has NOT previously received a benefit from a retirement fund or a severance benefit... 45 Worksheet 9: The determination of the amount of TAX PAYABLE on RETIREMENT FROM a PENSION FUND, a PROVIDENT FUND (including the PRESERVATION FUNDS), or a RETIREMENT ANNUITY FUND (or any combination of these funds) where the taxpayer has previously received a severance benefit (on or after 1 March 2011), a retirement fund lump sum (on or after 1 October 2007), or a retirement fund withdrawal benefit (on or after 1 March 2009)... 46 Worksheet 10: The determination of the amount of TAX PAYABLE on receipt / accrual of a SEVERANCE BENEFIT where the taxpayer has NOT previously received a severance benefit (on or after 1 March 2011), a retirement fund lump sum benefit (on or after 1 October 2007), or a retirement fund withdrawal benefit (on or after 1 March 2009)... 47 Worksheet 11: The determination of the amount of TAX PAYABLE on receipt or accrual of a SEVERANCE BENEFIT where the taxpayer DID previously receive a severance benefit (on or after 1 March 2011), a retirement fund lump sum (on or after 1 October 2007), or a retirement fund withdrawal benefit (on or after 1 March 2009)... 48 ix
FINANCIAL CALCULATIONS Worksheet 12: The determination of the amount of TAX PAYABLE on the DEATH of a member of a PENSION FUND, a PROVIDENT FUND (including the preservation funds) or a RETIREMENT ANNUITY FUND (or any combination of the these) where the member DID previously receive a severance benefit (on or after 1 March 2011), a retirement fund lump sum (on or after 1 October 2007), or a retirement fund withdrawal benefit (on or after 1 March 2009)... 49 Worksheet 13: The determination of the amount of TAX PAYABLE on the DEATH of a member of a PENSION FUND, a PROVIDENT FUND (including PRESERVATION FUNDS), a RETIREMENT ANNUITY FUND, (or any combination of these funds) where the member has previously received a severance benefit (on or after 1 March 2011), a retirement fund lump sum (on or after 1 October 2007), or a retirement fund withdrawal benefit (on or after 1 March 2009); and also when a beneficiary of a compulsory annuity commuted such annuity for a lump sum on the death of the deceased... 51 Worksheet 14: The determination of the amount of TAX PAYABLE on the COMMUTATION amount of a compulsory annuity (including a living annuity) by the annuitant (the former member or his successor) and where the annuity is commuted during his lifetime... 53 Worksheet 15: The determination of the amount of TAX PAYABLE on an amount deducted from the individual reserve or benefit of a pension or provident fund (including preservation funds) or from the fund value of a retirement annuity fund and paid to the non-member spouse under a divorce order dated 13 September 2007 or thereafter... 55 Investment Calculations Worksheet 16: Calculate the true yield on a Banker s Acceptance... 65 Worksheet 17: Valuation of a bond clean price (e.g. Eskom Stock)... 67 Worksheet 18: Calculate the after-tax yield on an insured investment plan... 69 Worksheet 19: Comparing retirement annuities with a pure endowment policy... 71 Estate Planning Calculations Worksheet 20: Calculation of the value of a fiduciary interest for estate duty purposes on the death of the fiduciary... 74 Worksheet 21: Valuation of a usufruct (for estate duty purposes) that passes to another on the death of the usufructuary... 75 Worksheet 22: Valuation (for estate duty purposes) of a usufruct that ceases on the death of the usufructuary... 76 Worksheet 23: Valuation, for estate duty purposes, of an annuity charged upon property, or an annuity not charged upon property that passes to another... 77 Estate Duty Calculations Worksheet 24: Estate duty calculation where the deceased was married out of community of property with the accrual system EXCLUDED and where the residue of his estate does NOT accrue to his surviving spouse... 78 Worksheet 25: Estate duty calculation where the deceased was married out of community of property, with the accrual system EXCLUDED, and where the residue of the estate is bequeathed to the surviving spouse... 81 Worksheet 26: Estate duty calculation where the deceased was married in community of community of property and where the residue of the estate is bequeathed to the surviving spouse... 85 x
TABLE OF CONTENTS Calculations relating to Matrimonial Property regimes Worksheet 27: Calculation of the accrual claim on the death of a person who was married out of community of property and the accrual under the Matrimonial Property Act has not been excluded... 90 Worksheet 28: Estate duty calculation where the deceased was married out of community of property, the accrual system applies and the residue of the estate is NOT bequeathed to the surviving spouse... 93 Worksheet 29: Estate duty calculation where the deceased was married out of community of property, the accrual applies and the residue of the estate IS bequeathed to the surviving spouse... 97 Worksheet 30: The calculation of the estate duty value (deemed property) of a life insurance policy where the person entitled to recover the proceeds (other than the estate) paid a lump sum consideration to acquire ownership of the policy and thereafter paid premiums that became due in respect of the policy... 101 Capital Gains Tax calculations Worksheet 31: Calculation of the Capital Gains Tax payable by a person in the event of his death... 104 Worksheet 32: Determination of the Time Apportionment Base Cost (TABC) of a pre-valuation date asset in the case where no expenditure has been incurred on or after 1 October 2001... 105 Worksheet 33: Determination of the Time Apportionment Base Cost (TABC) of a pre-valuation date asset in the case where expenditure was incurred before, as well as on or after 1 October 2001... 106 Income Tax calculations Worksheet 34: Income tax calculation for a natural person... 108 Worksheet 35: Calculation of the capital (tax-free) element of a voluntary purchased annuity that is payable for a fixed term, or for the lifetime of the annuitant... 111 Worksheet 36: Calculation of the capital (tax-free) element of a voluntary purchased annuity that is payable for the lifetime of the annuitant, but is guaranteed to be paid for a minimum fixed term in the event of the annuitant s death before the expiry of the guaranteed term... 112 Worksheet 37: Calculation of the capital (tax-free) element of a voluntary purchased growing annuity that is payable for a fixed term or for the lifetime of the annuitant without a guaranteed term... 113 Worksheet 38: Calculation of the capital (tax-free) element of a voluntary purchased growing annuity that is payable for the lifetime of the annuitant and that is guaranteed for a minimum term... 115 Business Insurance Calculations Worksheet 39: Calculation to establish the value of a key person and the amount of insurance that should be taken out to replace that key person... 119 Worksheet 40: Calculate the tax payable by (i) the company / employer, and (ii) the director / employee, in respect of the benefits of a deferred compensation scheme funded by a pre-1 March 2012 conforming life insurance policy (with cash value)... 120 xi
FINANCIAL CALCULATIONS PART B: TABLES, RATES AND FORMULAE Table 1: Table to determine the resultant rate where an annuity grows by a fixed percentage every year and earns interest at a certain percentage... 123 Table 2: The first instalment of a growing annuity that if invested will mature at R1 000 after n years if the instalments escalate by e% p.a. and interest of i% p.a.... 124 Table 3: The a (55) tables for annuitants... 127 Table 4: Capital preservation... 128 Table 5: Capital preservation... 132 Table 6: Present value of growing annuity... 133 Table 7: Future value of growing annuity... 136 Table 8: Income tax rates for individuals... 139 Table 9: Rebates individuals... 139 Table 10: Selected exemptions and deductions (individuals)... 140 Table 11: Maximum lump sum that may be taken on the death or retirement of a member of a retirement fund... 141 Table 12: Tax on Retirement Fund lump sums... 141 Table 13: Living annuity drawdown parameters... 145 Table 14: Tax rates other entities... 146 Table 15: Donations tax... 146 Table 16: Capital gains tax... 147 Table 17: Estate duty... 147 Table 18: Rates for the calculation of the value of limited interests Table A... 148 Table B... 149 Table 19: Property transactions... 150 Table 20: Insurance... 150 xii