FINANCIAL CALCULATIONS


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1 FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N number of periods I periodic interest rate PV present value PMT payment FV Future value These are all at the top row of the HB10bII and HB10bII+ calculator 2 Determine which variable you would like to solve for. You will need four out of the five variables to start, keeping in mind that PMT, PV or FV may be zero Know when to use zero PMT invest a lump sum or owe all of your money at the end of the term PV when you are receiving or making payments FV when a loan or annuity is paid off finished paying out 3 1
2 Keep in mind that the number of periods is usually listed in the same increment as the interest rate, i.e a 30 year mortgage bond would have 360 periods (30 years) If you are uncertain, always use Shift N function. 4 Annually 1 NACA Semi Annually 2 NACSA Quarterly 4 NACQ Monthly 12 NACM Daily 365 NACD 5 Number of periods per year Number of decimals used Begin/end mode Always clear the calculator (Shift C All) before you start any calculation Always practice your calculations well Watch these YouTube training videos:
3 Mrs.BassonwantstotakeherfamilytoDisneyWorld10yearsfromnow. The travel agent has estimated that such a trip would currently cost R150,000.Inflationisexpectedtoaverage8%peryearoverthenext10 years. Mrs. Basson has the following investments available to fund this trip: R20000inasavingsaccount,investedataneffectiverateof7%p.a. AnendowmentpolicywithacurrentvalueofR10000.Mrs.Basson investsalevelamountofr1000permonthintothispolicy.thepolicy willmatureoneyearbeforetheplannedtripandshehasindicated that she will merely reinvest the maturity value for another year without making any further payments. The expected growth rate in this portfolio is 9% per annum, compounded monthly. Mrs.Bassonwouldliketoknowhowmuchshehastoinvestperannumin ordertoensurethatshewouldhaveenoughmoneyfortheholiday,taking into account her current investments earmarked for this purpose. She indicates that she can escalate her annual investment by 5% per year, and thatshebelievesthatanewinvestmentcangrowataneffectiverateof 9% per year. Calculate the annual investment required to make up the shortfall. 7 Brackets Others (indices and integers) Division Multiplication Addition Subtraction Multiplication and division are performed whichever comes first from left to right Addition and subtraction are performed whichever comes first from left to right 8 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) 9 3
4 2/10 6/10 55/100 73/80 60/ / or rdg Converting a fraction to a percentage requires multiplying by 100/1 Therefore: x = = 25% 11 Examples: 32/50 75/100 12/71 25/ /200 64% 75% 16.91% 25% 60% 12 4
5 Bob invests R2,000 at 10%p.a. simple interest for 4 years Amortisation table Year Start 2000 Interest Year End 13 Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Intere st Year End Bob invests R2,000 at 10%p.a. simple interest for 4 years Therefore: 2000 X 10% = x 4 yrs = = 2800 Year Start Interest Year End
6 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? 16 26,600 10,000 = 16,600 15% of 10,000 = 1,500 simple interest per year. 16,600 / 1,500 = (26,600 10,000) / 1,500 = years 10 15% pa annum = R Capital invested = Growth = x years = R R = R 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
7 Bob Invests R2,000 at 10% p.a. compounding Monthly for 1 Year x (1+(0.1/12)) = 2000 x (1+(0.0083)) = x = x = x = Therefore: 2000 x (1.0083) 4 = x (1.0083) 12 = PV x (1 + (I/PY / P/YR) N = FV Future Value = Present Value x (1 + (Int rate / Comp Periods per year)) Power of Total Compounding periods 20 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 21 7
8 Nominal interest rate Simply the stated interest rate of a given bond, loan or investment E.g. if nominal rate on a loan is 5%, then borrowers can expect to pay R5 on every R100 loaned to them Effective interest rate Take the power of compounding into consideration The difference between nominal and effective rates increases with the number of compounding periods within a specific time period 22 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. 23 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% 24 8
9 R1000 invested over a 5 year period with growth at 10%. What will I get at the end? 25 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?
10 If I invest R1000 a month for the next 5 years at 10%, what will the maturity value be? 28 Mr P invested R years ago and receives R now. What is the rate of return on the investment? Show all steps
11 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] 33 11
12 34 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? 35 Alma buys a house & takes a bond of R at an interest rate of 12% for 20 years calculate monthly instalment: 36 12
13 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: End Mode 12 Shift P/YR PV 11 I/YR 20 Shift N PMT? DO NOT CLEAR THE CALCULATOR!! 39 13
14 SHIFT AMORT PRESS = prin  capital amount paid ( ) = int  interest portion paid ( ) = bal balance ( INPUT 24 Shift Amort Capital = R Interest = R Balance = R 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? End Mode 12 Shift P/YR PV 12 I/YR 18 Shift N (remaining years) PMT? R What if after 2 yrs bond holder wants to reduce term by 2 yrs? Use same example as above Answer? 42 14
15 43 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]
16 46 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?
17 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 49 Brad wants to invest 100 per year, escalating at 7% p.a. for 3 years. Growth on the investment is 10% 50 PV FV % for 3 yrs 10% for 2 yrs % for 1 yr 51 17
18 Incorporates both interest and escalation rate: 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 52 PMT PV Resultant Rate Interest Rate PV FV 53 Brad invests R100 pa at the beginning of each year, escalating at 7% pa for 5 years at an interest of 9%. What is the FV? 54 18
19 12mth pmt PMT PV Nominal (Eff Rate) Nominal Interest Resultant Interest Rate Rate Rate 12 P/YR Or 1/py with eff rate PV of annual PV of FV of Payment escalating invest annuity itself! 55 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] 56 Step 1: Calculate PV of the annual contributions 57 19
20 Step 2 calculate resultant rate Step 3 calculate PV of the escalating annual investment 58 Step 4 Calculate the FV of the investment using the interest rate 59 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
21 Step 1 determine the annual equivalent iro the monthly instalments discounted at the nominal rate. 61 Step 2 change to effective rate and calculate resultant rate. Resultant rate 62 Step 3 discount the annual equivalent to PV using resultant rate
22 Step 4 calculate the FV of the instalment using the nominal rate. 64 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?
23 Calculate NPV if discounted at 12% 67 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:
24 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? Mrs Waterman invests R The nominal rate of interest is 10% and the interest is compounded halfannually. What is her FV after 2 years? 72 24
25 73 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% 74 FV of the investment will be: 75 25
26 Capital needed to buy an annuity? 76 FV OF R2886? 77 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. How much will he receive after 5 years if he invests the R800 at the beginning of each month? 78 26
27 STEP 1 PV OF ANNUAL CONTRIBUTIONS 79 STEP 2 CALCULATE RESULTANT RATE 80 STEP 3 PV OF ESCALATING PAYMENTS 81 27
28 STEP 4 CALCULATE FV 82 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?
29 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? 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
30 88 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? 89 STEP 1  WHAT IS THE PV OF WHAT I WANT? 90 30
31 STEP 2 DETERMINE THE RESULTANT RATE 91 STEP 3 CALCULATE ESCALATION RATE 92 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? 93 31
32 94 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?
33 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? 97 Level Annual Investment Amount 98 Step 1 Equivalent Lump Sum (PV) 99 33
34 Step 2 Discounted PMT at Esc 10% 100 Mrs.BassonwantstotakeherfamilytoDisneyWorld10yearsfromnow. The travel agent has estimated that such a trip would currently cost R150,000.Inflationisexpectedtoaverage8%peryearoverthenext10 years. Mrs. Basson has the following investments available to fund this trip: R20000inasavingsaccount,investedataneffectiverateof7% p.a. AnendowmentpolicywithacurrentvalueofR10000.Mrs.Basson investsalevelamountofr1000permonthintothispolicy.thepolicy willmatureoneyearbeforetheplannedtripandshehasindicated that she will merely reinvest the maturity value for another year without making any further payments. The expected growth rate in this portfolio is 9% per annum, compounded monthly. Mrs.Bassonwouldliketoknowhowmuchshehastoinvestperannumin ordertoensurethatshewouldhaveenoughmoneyfortheholiday,taking into account her current investments earmarked for this purpose. She indicates that she can escalate her annual investment by 5% per year, and thatshebelievesthatanewinvestmentcangrowataneffectiverateof 9% per year. Calculate the annual investment required to make up the shortfall. 101 Need Provision Surplus / Shortfall
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37 Step 2 Equivalent escalating annual cash flow for PV Lump Sum 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%
38 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) 112 Calculate the pretax income required monthly Then grow from now to retirement (30 years) 113 Effective rate for monthly conversion to annual Resultant rate (use effective)
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40 118 Step 1 convert shortfall to current day equivalent lump sum (Monthly, so use Nominal rate and 12 P/YR) 119 Step 2 convert current lump sum value needed to an equivalent annual escalating premium
41 Step 3 convert first year s annual premium to an equivalent monthly premium
CARMEN VENTER COPYRIGHT www.futurefinance.co.za 0828807192 1
Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q 5.3.1 Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) 5.3.2 Calculate the capital
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