# USING THE SHARP EL 738 FINANCIAL CALCULATOR

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2 GETTING STARTED There are a few things you need to do before we can start with the calculations. FUNCTION SET UP The SHARP EL738 is already set up as a financial calculator so it is not necessary to set a particular mode. SETTING PAYMENTS PER PERIOD In these notes, we use the same logic used with manual calculations and set our payments to one payment per period. ON/C 1.00 DECIMAL PLACES To set your calculator to the conventional two decimal places or four decimal places. SET UP SET UP DECIMAL POINT The SHARP EL738 is already set up using a point as the decimal indicator. CLEARING PREVIOUS WORK Every transaction in this document will commence with the following keystrokes. CA is the function to clear all the internal registers of the calculator. 00 SETTING FOR PAYMENTS AT BEGINNING OF THE PERIOD If you are working with an annuity due you must set your calculator to peform caluations from the beginning of the period. If you are doing lump sum calculations or ordinary annuities check to see that your calculator is correctly set and does not dispay BGN SHARP EL738 If it does display BGN ndF BGN Removes this 0.00 Colin C Smith

3 LUMPSUMS FUTURE VALUES AND PRESENT VALUES 1. Simple Future Value (FV) You borrow R5,000 from a friend at 8% p.a. interest to be compounded annually. Capital and interest is repayable in 5 years time. How much will you repay? 00 5,000 +/ PV 5, I/Y N 5.00 COMP FV 7, Future Value (FV) with frequent compounding You have saved R10,000 and invest this in a fixed deposit with a bank at 10.5% compounded quarterly for 4 years. How will you receive in 4 years time? 10,000 +/ PV 10, I/Y x 4 N COMP FV 15, Simple Present Value (PV) You have just turned 20 years of age and your late Uncle Scrooge bequeathed you an amount of R5,000 payable on your 25 th birthday. Your father offers to give you the present value today in cash. At an interest rate of 10% p.a. compounded annually how much must your father give you today? What is the present value of the bequest? The ve amount reflects what should be paid today. 5,000 FV 5, I/Y N 5.00 COMP PV 3, Present Value (PV) with frequent compounding Uncle George is more generous and leaves you a substantial inheritance. You want to set aside and amount to buy your dream car when you complete your trainee contract in 5 years time. Estimates are that the dream car will cost R220,000 at that time. A bank is offering you a 5 year fixed deposit at 11.5% compounded monthly for 5 years. How much should you invest today? The ve amount reflects what should be paid today. 220,000 FV 220, I/Y x 12 N COMP PV 124, Colin C Smith

4 LUMPSUMS INTEREST RATE AND PERIODS, AND NOMINAL AND EFFECTIVE INTEREST RATES These calculations are quite challenging in an equation format but much easier with a financial calculator. 5. Calculating the interest rate An amount of R400,000 is invested in a savings account that compounds interest monthly. After one year the balance in the account is R Calculate the nominal interest rate (i.e. the quoted rate or APR). The R400,000 is shown as a ve as this is the cash outflow required now. 464, FV 464, ,000 +/ PV 400, x12 N COMP I/Y 1.25 X Calculating the periods An amount of R100,000 was invested in an account that accumulates interest at a rate of 14% per annum, compounded quarterly. The balance in the account, immediately after the latest quarter s interest credit is R173, How long ago was the amount invested? Remember that because you have compounded more than once a year (n x m in the formula) N is not years but periods. So the answer is 16 4 = 4 years. 173, FV 173, ,000 +/ PV 100, I/Y 3.50 COMP N Calculating the effective rate Calculate the effective rate of 13% per annum compounded monthly. This reflects the compounding periods per year (m in the formula) and can be changed to any frequency. 2ndF CA 12 (x,y) ndF EFF Calculating the nominal or annual percentage rate (APR) Calculate the nominal rate (APR) of % per annum compounding monthly. This reflects the compounding periods per year (m in the formula) and can be changed to any frequency. 2ndF CA 12 (x,y) ndF APR Colin C Smith

5 ANNUITIES ORDINARY, DUE, FUTURE VALUE, PRESENT VALUE 9. Simple Future Value of an Ordinary Annuity (FVA) Assume you put R1,000 into a savings account at the end of every year for 10 years at 9.5% interest compounded annually. How much will you have in the account after 10 years? 1,000 +/ PMT 1, I/Y N PV 0.00 COMP FV 15, Simple Future Value of an Annuity Due (FVA due ) Assume you put R1,000 into a savings account at the beginning of every year for 10 years at 9.5% interest compounded annually. How much will you have in the account after 10 years? *Must display BGN 2ndF BGN/END BGN ,000 +/ PMT 1, I/Y N PV 0.00 COMP FV 17, Present Value of an Annuity Due (PVA due ) An overseas benefactor has offered to sponsor new Care Centre for Aids Orphans in Cape Town and they have pledged to provide the equivalent of R25,000 per month for the next four years payments starting immediately. The benefactor will make a single investment lump sum investment into a bank account paying 9.5% interest. How large will this initial investment be? *Must display BGN 2ndF BGN/END BGN 0.00 ON/C ,000 +/ PMT 25, I/Y x 12 N FV 0.00 COMP PV 1,002, Colin C Smith

6 ANNUITIES ORDINARY, DUE, FUTURE VALUE, PRESENT VALUE 12. Calculating the payment (PMT) for a normal financial transaction Annuity Due You buy a new car today for R and obtain finance for 80% of the purchase price (R96,000) over four years. The bank quotes you a finance rate of 12% per annum (nominal rate). Instalments are payable monthly in advance. Calculate the monthly instalment. *Must display BGN 2ndF BGN/END BGN 0.00 ON/C ,000 +/ PV 25, = I/Y x12 = N FV 0.00 COMP PMT 2, You can also solve for the interest rate and for the number of periods using the same functions. 13. Calculating the interest rate for a normal financial transaction Annuity Due A bank offers you a personal loan of R20,000 repayable in 24 easy instalments of R1,050 per month starting immediately. What nominal interest rate (APR) is being charged? *Must display BGN 2ndF BGN/END BGN 0.00 ON/C ,000 PV 24, FV ,050 +/ PMT 1, N COMP PMT 2.12 X Additional notes: Please also see the Bond Valuation section for similar transactions. Where we have irregular cash flow payments, we cannot use the annuity functionality and instead can use the NET PRESENT VALUE and INTERNAL RATE OF RETURN functions. Colin C Smith

7 AMORTISATION N.B. ENSURE THAT YOU CORRECTLY IDENTIFY YOUR PAYMENTS AS AN ORDINARY ANNUITY OR AN ANNUITY DUE AND SET YOUR CALCULATOR ACCORDINGLY Calculating the intalment /payment (PMT) for a normal financial transaction Annuity Due with amortisation A company takes a loan of R100,000 loan repayable in equal month instalments, at the beginning of the month, over a period of two years term, an interest rate of 12% per year is quoted by the bank (this is the nominal or Annual Percentage Rate APR. This is your monthly instalment. *Must display BGN 2ndF BGN/END BGN 0.00 ON/C ,000 PV 100, FV I/Y x 12 N COMP PMT 4, THE AMORTISATION SCHEDULE ANNUITY DUE We could derive the interest payments by preparing a manual amortisation schedule (very time consuming) or one below using Microsoft Excel (not allowed in examinations). In an annuity due the entire first payment is applied to capital Year 1 interest R8, Year 2 interest R3, Month Instalment Interest Capital paid off Capital Balance today 100, R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , Year 1 capital R47, Year 2 capital R52, Colin C Smith

8 AMORTISATION 14.3 Amortising the payments using a financial calculator to calculate the amount of capital and interest paid and the balance at the end of each year This step follows directly on your calculation of the instalment above. We enter the first financial period and the number of payments made in that period Note: You can set the amortisation function for any period but here it is for a 12 month period. This is for periods 1 12 Balance at the end of year 1 Capital paid in year 1 Interest paid in year 1 AMRT 1 ENT ENT , , , For the next 12 months (periods 13 24) Balance at the end of year 2 Capital paid in year 2 Interest paid in year 2 13 ENT ENT , , YOU CAN CHECK THESE NUMBERS AGAINST THE AMORTISATION SCHEDULE in section 14.2 that was completed using Microsoft Excel Calculating the intalment /payment (PMT) for a financial transaction Ordinary Annuity with amortisation A company takes a loan of R100,000 loan repayable in equal month instalments, at the end of the month, over a period of two years term, an interest rate of 12% per year is quoted by the bank (this is the nominal or Annual Percentage Rate APR. This is your monthly instalment. ON/C ,000 PV 100, FV I/Y x 12 N COMP PMT 4, Colin C Smith

9 AMORTISATION THE AMORTISATION SCHEDULE ORDINARY ANNUITY As for the schedule at 14.2 this was prepared using Microsoft Excel. Year 1 interest R9, Year 2 interest R3, Month Instalment Interest Capital paid off Capital Balance today 100, R 4, , , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , , R 4, , Year 1 capital R47, Year 1 capital R52, Amortising the payments to calculate the amount of capital and interest paid and the balance at the end of each year This step follows directly on your calculation of the instalment above. We enter the first financial period and the number of payments made in that period. The amortisation function can be for any period but here it is for a 12 month period. This is for periods 1 12 Balance at the end of year 1 Capital paid in year 1 Interest paid in year 1 AMRT 1 ENT ENT , , , For the next 12 months (periods 13 24) Balance at the end of year 2 Capital paid in year 2 Interest paid in year 2 13 ENT ENT , , YOU CAN CHECK THESE NUMBERS AGAINST THE AMORTISATION SCHEDULE ABOVE. Colin C Smith

10 BOND VALUATION 16. Value of an annual payment bond with a single annual payment A company purchases bonds on 1 January of this year. The nominal/face/coupon value is R1,000 and the annual nominal/coupon interest rate is 10%. The bond is redeemable on 31 December 6 years later. The market interest rate for similar bonds is 15%. Assume that the bond payments are made annually in arrears. What price would the company pay for the bond? (i.e. what should the value be on 1 January of this year? 15 I/Y N ,000 FV 1, PMT COMP PV Value of a typical government bond with semi annual payments Assume same information as for 16 above except that the bond is a typical government bond that pays semi annually in arrears. What price would the company pay for the bond? 15 2 I/Y x 2 N ,000 FV 1, PMT COMP PV Calculating the yield to maturity This is extremely difficult to calculate when using a formula approach without a financial calculator. The nominal/face/coupon value is R1,000 and the annual nominal/coupon interest rate is 10% paid semi annually in arrears. You purchased the bond on 1 January of this yearand the bond is redeemable on 31 December 10 years later at a premium of 10%. The bond is priced at R980 on 1 January of this year. What is the yield to maturity on 1 January of this year? This takes a while and your display will be blank. Remember that this is the rate for 6 months. To annualise the convention (from bond trading in the United States) has been to multiply this by x 2 N ,000 x 1.10 FV 1, / PV PMT COMP I/Y 5.45 X Colin C Smith

11 NET PRESENT VALUE and INTERNAL RATE OF RETURN 19 & 20. What is the Net Present Value and IRR of this project? A project has the following cash flows Year Cash Flow (R) 0 1, , , , ,900 If the weighted average cost of capital WACC is 15 % what is the Net Present Value of this project? What is the Internal Rate of Return of the above cash flows? *Must not display BGN CFi ON/C ,000 +/ DATA ,700 +/ DATA ,500 DATA ,800 DATA ,900 DATA 4.00 ON/C ndF CASH 2ndF CA 15 ENT NPV COMP ndF CASH 2ndF CA IRR COMP Colin C Smith

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