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1 Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) Calculate the capital available at retirement (2) Calculate the shortfall at retirement. (2) Calculate the increasing monthly investment that Makhensa should make/save at the beginning of each month, in his retirement annuity fund to make up for the shortfall. He wants to increase the premium at 6% p.a. 1 3 Mr Makhensa, born 20 January Wants to receive a monthly income of at least R35,000 (after tax 40%) in today s value, when he retires at the age of 60. The monthly income should last for 25 years from the date of retirement and escalate by the rate of inflation per annum. (Given as 6% currently) His Current retirement savings only consist of a pension preservation fund at R350,000 current value. Growth on all investments 10% 714 Sept 2012 Q5.3 Addition Subtraction Multiplication Division Arithmetic
2 Fractions Fractions to Percentages A number that is anything from 0 to 1 Therefore a fraction is less than 1, but greater than 0 ¼ 1 divide by 4 (Long Division) Converting a fraction to a percentage requires multiplying by 100/1 Therefore: ¼ x 100/1 ¼ x 100/1 = 100/4 = 25% 5 7 2/10 6/10 55/100 73/80 60/ /200 Fractions as Decimal points Fractions to Percentages 32/50 75/100 12/71 25/ /200 Examples:
3 Simple Interest Simple Interest Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start 2000 Interest Year End Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Interest Year End 9 Therefore: 2000 X 10% = x 4 yrs = = Simple Interest For how many years does one have to invest a lump sum of R at 15% pa simple interest in order to receive R at the end of the term? Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Interest Year End Practice
4 Compound Interest  Monthly Bob Invests R2,000 at 10% p.a. compounding Monthly for 1 Year. Suggested Solution Compound Interest Bob Invests R2,000 at 10% p.a. compounding annually for 4 Years 2000 x (1+0.1) = 2200 x 1.1 = 2420 x 1.1 = 2662 x 1.1 = Year Start Int End Compounding Periods Per Year Annually 1 NACA Semi Annually 2 NACSA Quarterly 4 NACQ Monthly 12 NACM Daily 365 NACD
5 Compound Interest Mathematical Formula Future Value = Present Value x (1 + (Int rate / Comp Periods per year)) Total Compounding periods PV x (1 + (I/PY / P/YR) N = FV Power of A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates once a year: Capital Invested R 100 Plus interest R 15 Nominal and effective the same as there is no interest on interest. Effective /Nominal Rates Calculator N = TOTAL number of compounding periods in the calculation. I/YR = Nominal per annum interest / growth rate applicable PV = Present Value PMT = Any Regular payment (same as periods per year) 2 nd F P/YR= Number of compounding periods in 1 Year. FV = Future Value PV x (1 + (I/PY / P/YR) N = FV A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates monthly: Capital invested R100 Plus interest R p/yr 15 shift Nom % Shift eff% = 16.08% Effective/Nominal Rates
6 R1000 invested over a 5 year period with growth at 10%. What will I get at the end? Lump Sum Suggested Solution Billy wins the lotto and invest the money for 10 years at an interest rate of 11% per annum. After the 10 years he receives R What is the capital sum that Billy invested? If I invest R1000 a month for the next 5 years at 10%, what will the maturity value be? Extra Practice Recurring payments
7 Elizabeth invests a lump sum amount of R for a period of 5 years. The interest rate is 6.5% per annum which will be credited to the account on a monthly basis. Ignore income tax. At the end of the term she will receive an amount of? Mr A invests R550 at the beginning of each month for 10 years. What is the maturity value if the investment has an 8% effective interest rate? [3] Extra Practice 2008 UFS Preparation Suggested Solution Suggested Solution
8 Tish signed an investment contract where she will invest R a further R1000 pa at beginning of each year for next 5 years at 12% interest: Maturity value will be? Lump sum + instalment Adam Liaw has informed you that he would like to accumulate an amount of R500,000 within the next 5 years. He plans to make (level) payments every 3 months into an account that you have established will pay 11% per year, compounded quarterly. Calculate the amount that he must deposit at the beginning of every 3 month period in order to achieve his goal. (2) Sept Q Alma buys a house & takes a bond of R at an interest rate of 12% for 20 years calculate monthly instalment: A R18,575 B R16,575 C R19,085 D R20,101 Interest accrues monthly Sept Q1.7 cont
9 . Sept Q1.7 cont Suggested Solution Mr N s investment receives an annuity income of R pa in advance for 15 years as well as R at the end of the term. The interest rate is 10% calculated in advance. How much did Mr N invest initially? [4] Bond of R at an interest rate of 11% and term is 20 yrs. Calculate the monthly instalment: DO NOT CLEAR THE CALCULATOR!! 2008 UFS Preparation Bond instalments  Amortisation
10 What if after 2 yrs bond holder wants to reduce term by 2 yrs? use same example as above Answer? Amortisation Reducing term of bond repayment At beg of year 3 rates increase to 12% a) what is new monthly instalments? b) what is the balance at end of year 2? DO NOT CLEAR Change interest Rates Answer
11 Mr Nkosi has a mortgage bond of R repayable over 20 years at an interest rate of 13% 1.1 Calculate monthly repayments [2] 1.2 The interest rate drops from 13% to 11% at the beg of the 2 nd year. Mr Nkosi elects not to reduce his monthly payments. Calculate how long it will now take Mr Nkosi to repay his bond? [4] 2008 UFS PREPARATION Suggested Solution Frans buys a new car for R He pays a deposit of R and takes a loan from the bank for the balance for a period of 3 years. His monthly instalment is R What is the percentage interest that he pays on the loan? Suggested Solution 1.1 Extra Practice
12 Brad wants to invest 100 per year, escalating at 7% p.a. for 3 years. Growth on the investment is 10%. What will the maturity value be of his investment. Suggested Solution Example Problem Scenario Annual premium pd to an investment must increase each year by 7% and the investment s growth is 10% Can we account for 2 growth factors? Only 1 I/YR key no escalation key. Can t add them together! ie can t do a FV calc. Can deduct and get a net effect and thereby do an equivalent PV calc Escalating regular PMT (annuity) and Growth? Incorporates both interest and escalation rate: 1+i 1+e 1 x 100 I = interest or growth rate E = escalation Alternative method: Interest 12% Escalation rate 10% / 1,10 = 1,81818% = resultant rate NB: I AM BEFORE E IS Resultant Rate
13 PMT Resultant Rate PV Interest Rate 12mth pmt PMT PV Nominal (Eff Rate) Nominal Interest Resultant Interest Rate Rate Rate 12 p/yr Or 1/py with eff rate PV FV PV of annual PV of FV of Payment escalating invest annuity itself! Escalating Annuities Annual Escalating Annuities Monthly Carmen invests R175 pa at the beginning of each year, escalating at 7% pa for 5 years at an interest of 9%. What is the FV? Mr J wants to invest R2 500 pm for the next 5 years at an interest rate of 7.5% and wants to increase his premiums by 6% every year. How much will he receive after 5 years if he invests the R2 500 at the beg of each month? [6] Resultant rate example FV of escalating annuity 2008 UFS Preparation
14 Suggested Solution Suggested Solution Ann wants to invest R100 per month for 5 years. This monthly investment must increase by 6% per annum. The investment will earn 8%. What will the future value of this monthly investment be? We want to know the FV of an investment if we are investing MONTHLY. Suggested Solution Practice
15 Suggested Solution Suggested Solution Suggested Solution Suggested Solution
16 Tom pays out an amount of R and receives monthly payments of R3000, R6000, R6000, R22000 and R15000 Calculate internal rate of return If discounted at 12% what will the net present value be? Cash Flows irregular payment Cash Flows irregular payment DO NOT CLEAR CALCULATOR Cash flow irregular payment Your client has been making uneven adhoc contributions into her investment for the past year. Contributions made as follows: March R1000 April R2000 June R1750 September R350 October R900 December R175 January R1000 February R 250 The current value is R8 587 Calculate the annual rate of return, assuming the fund compounds monthly: Cash Flow example assignment
17 Cash Flow Example Assignment 2008 Activity 3.3 Solution Question 1 Activity 3.3 Mr Nel has just taken cession of a life assurance contract. The policy is due to mature in 4 years time. Premiums of R750 pa are payable towards the policy. The estimated maturity value of the policy in 4 years time is R The growth rate is assumed to be 10%. What is the PV of this policy? Financial Calculations Environment Workbook Activities Question 2 Activity 3.4 Mrs Waterman invests R The nominal rate of interest is 10% and the interest is compounded halfannually. What is her FV after 2 years? Financial Calculations Environment Workbook Activities
18 Activity 3.4 solution ACTIVITY 4.1 SOLUTION Question 3  ACTIVITY 4.1 Mrs Van Wyk wants to invest R500 at the beginning of each year for 10 years. The interest payable on this investment will be 15% What will the future value of this investment be? Still using the same figures above, how much capital would she need to buy an annuity of R 500 per annum payable at beg of each year for 10 years, if the life assurer pays 15% on her investment? What is the FV if we take the result from the previous calculation if she invests a lump sum of R for 10 years at 15% Financial Calculations Environment Workbook ActivitiesS 70 Capital needed to buy an annuity? ACTIVITY 4.1 SOLUTION
19 FV OF R2886? BEG MODE 1 shift P/YR PV 15 I/YR 10 shift N FV? ACTIVITY 4.1 SOLUTION ACTIVITY 5.1 SOLUTION Question 4 ACTIVITY 5.1 Mr Verwey wants to invest R800 pm for the next 5 years at an interest rate of 8% and wants to increase his premiums by 5% every year. STEP 2 CALCULATE RESULTANT RATE How much will he receive after 5 years if he invests the R800 at the beginning of each month? Financial Calculations Environment Workbook Activities ACTIVITY 5.1 SOLUTION
20 STEP 3 PV OF ESCALATING PAYMENTS Question 5 ACTIVITY 7.3 Susan has R in a fixed deposit which earns interest of 15%. The inflation rate is 6%. Sue s marginal tax rate is 40%. What effect will this have on her real rate of return? ACTIVITY 5.1 SOLUTION Financial Calculations Environment Workbook Activities STEP 4 CALCULATE FV ACTIVITY 5.1 SOLUTION ACTIVITY 7.3 SOLUTION
21 Question 6 ACTIVITY 7.4 Mpho owns a house. The interest she pays on the bond is 12%. She won R from the lotto. Her marginal tax rate is 40% What taxable rate of interest must she earn on the R to equal the 12% interest rate she is paying on her bond? Financial Calculations Environment Workbook Activities Question 7 ACTIVITY 8.22 Mr Greedy would like to double his inheritance of R within 5 years by speculation on the stock market. He is aware that he will have to give up approximately 40% to tax annually. Calculate the annual pretax yield rate he will have to achieve in order to reach his goal. Financial Calculations Environment Workbook Activities ACTIVITY 7.4 SOLUTION ACTIVITY 8.22 SOLUTION
22 Question 8 Mr R needs R in 5 years time. He will invest by way of annual installments. He will start with an amount Of R8 500 and then increase the Installment by a fixed %. He will earn interest at 7.5% pa. Calculate the % by which he has to increase his installments every year? JUST TO MAKE SURE YOU ARE VERY COMFORTABLE WITH CALCULATIONS..! STEP 2 DETERMINE THE RESULTANT RATE SUGGESTED SOLUTION STEP 1  WHAT IS THE PV OF WHAT I WANT? STEP 3 CALCULATE ESCALATION RATE Suggested solution SUGGESTED SOLUTION
23 Calculation of Retirement Needs: Mr G who is currently 45 years of age would like to retire at the age of 65. His current salary is R pa and he will be happy to receive 75% of his salary. He believes that his salary will increase with 8% pa. What is the first year s income that he will need at the age of 65? Extra Practice Mr G would like this income (75% of his salary ) for at least until his age of 85 but the income he receives must be increased by 6% every year. The capital will be invested and will attract 8% growth. How much Capital will Mr G need to have at the age of 65 to address his needs? Extra practice Ist Yrs Income Required? Capital Required to address needs?
24 Mr G is very concerned as he will under no circumstances have this type of money! He would like to know:  with an investment growth of 12%. a) How much does he have to invest annually assuming it will be a level premium? b) What if he decides to increase the premium by 10% every year? Extra practice Escalating premiums? Level Premiums? Escalating premiums?
25 Mr Makhensa, born 20 January Wants to receive a monthly income of at least R35,000 (after tax 40%) in today s value, when he retires at the age of 60. The monthly income should last for 25 years from the date of retirement and escalate by the rate of inflation per annum. (Given as 6% currently) His Current retirement savings only consist of a pension preservation fund at R350,000 current value. Growth on all investments 10% 714 Sept 2012 Q Q Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) Calculate the capital available at retirement (2) Calculate the shortfall at retirement. (2) Calculate the increasing monthly investment that Makhensa should make/save at the beginning of each month, in his retirement annuity fund to make up for the shortfall. He wants to increase the premium at 6% p.a. (3)
26 PV of the first Years income Q5.3.2 Calculate Provision PV 25 years annualised incomes, discounted for escalation Q5.3.3 Calc Shortfall
27 Q5.3.4 Calculate Investment Monthly. Esc annually. Monthly Starting Prem Q5.3.4 Cont So have you changed at all after these sessions?
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