Time Value of Money - Simple & Compound Interest - PDF

9. CONCEPTS & MODES OF ANALYSIS 9.1 What is simple interest? Simple Interest: Formula for calculating simple interest: I = Prt Where, I = interest P = principal r = interest rate (per year) t = time (in years or fraction of a year) Example: Therefore, his interest would be:...

9. CONCEPTS & MODES OF ANALYSIS 9.1 What is simple interest? Simple Interest: Formula for calculating simple interest: I = Prt Where, I = interest P = principal r = interest rate (per year) t = time (in years or fraction of a year) Example: Therefore, his interest would be: 9.2 What is compounD interest? Compound Interest: Compound interest means that, the interest will include interest principal sum, and the whole amount is then treated as new principal, for the calculation of compounded yearly: 57 For any loan or borrowing unless simple interest is stated, one should always assume interest Compound interest may involve calculations for more than once a year, each using a new Formula for calculating Compound Interest: C = P (1+i)n Where C = amount P = principal i = Interest rate per conversion period n = total number of conversion periods Example: Therefore, the amount, C, is: 58 Compounding plays a very important role in investment since earning a simple interest and earning an interest on interest makes the amount received at the end of the period for the interest option, then the amount that he would earn is calculated by applying the following formula: S = P (1 + rt), P = 10,000 t=5 Simply put, compounding refers to the re-investment of income at the same rate of return to more is the income which keeps getting added back to the principal regularly generating The table below shows you how a single investment of Rs 10,000 will grow at various rates bank account, 7-8% is typically the rate of return you could expect from a one-year company fixed deposit, 15% - 20% or more is what you might get if you prudently invest in mutual The Impact of Power of Compounding: The impact of the power of compounding with different rates of return and different time periods: At end of Year 5% 10% 15% 20% 1 Rs 10,500 Rs 11,000 Rs 11,500 Rs 12,000 5 Rs 12,800 Rs 16,100 Rs 20,100 Rs 24,900 10 Rs 16,300 Rs 25,900 Rs 40,500 Rs 61,900 15 Rs 20,800 Rs 41,800 Rs 81,400 Rs 1,54,100 25 Rs 33,900 Rs 1,08,300 Rs3,29,200 Rs9,54,000 59 9.3 What is meant by the time value of money? Let us take an example: Suppose you are given two options: future value don’t have time on your side, and the payment received in three years would be your future Let us take an another example: If you choose option A and invest the total amount at a simple annual rate of 5%, the future interest rate of 5% and then adding the 60 Thus, Future value of investment at end of first year: You can also calculate the total amount of a one-year investment with a simple modification of the above equation: Which can also be written as: S = P (r+ 1) Where, S = amount received at the end of period P = principal amount r = interest rate (per year) This formula denotes the future value (S) of an amount invested (P) at a simple interest of 9.3.1 How is time value of money computed? The time value of money may be computed in the following circumstances: (1) Future Value of a Single Cash Flow For a given present value (PV) of money, future value of money (FV) after a period M:’ for which compounding is done at an interest rate of V, is given by the equation FV = PV (1+r)t compounding, the future value is determined using the formula rt Example 1: 61 By discrete compounding: 3 3 By continuous compounding: (2) Future Value of an Annuity done at the rate V is calculated as follows: t-1 t-2 1 + CF = CF ( (1 + r)t – 1 r ( The term ( (1 + r)t – 1 r ( a certain period, to know how much to save annually to reach the targeted amount, to know earn a compound interest rate of 10 per cent, what will be value of this series of deposits (an Future value of this annuity is: 4 3 2 (3) Present Value of a Single Cash Flow Present value of (PV) of the future sum (FV) to be received after a period T for which discounting is done at an interest rate of V, is given by the equation In case of discrete discounting: PV = FV / (1+r)t ”rt 62 (4) Present Value of an Annuity The present value of annuity is the sum of the present values of all the cash inflows of this Present value of an annuity (in case of discrete discounting) PVA = FV [{(1+r)t t }] The term [(1+r)t t ] is referred as the Present Value Interest factor for an annuity Present value of an annuity (in case of continuous discounting) is calculated as: PVa = FVa )/r –rt continuous years /v 9.3.2 What is Effective Annual return? Usually while applying for a fixed deposit or a bond it is stated in the application form, that the annual return (interest) of an investment is 10%, but the effective annual return mentioned quarter, the effect of compounding would become apparent: you would receive another Rs 25 annual interest rate is 10%, because of quarterly compounding, the effective rate of return 63 compounding does not necessarily occur quarterly, or only four times a year, as it does in the 9.4 hoW to go about systematically analyzing a company? You must look for the following to make the right analysis: Industry Analysis: Companies producing similar products are subset (form a part) of an Industry Analysis. Corporate Analysis: information on its current operations, managerial capabilities, growth plans, its past Corporate Analysis. Financial Analysis: If performance of an industry as well as of the company seems good, performance of the company and certain key financial parameters like Earnings Per Share is termed as Financial Analysis. For that you need to understand financial statements of a 9.4.1 What is an Annual Report? report shows assets, liabilities, revenues, expenses and earnings - how the company stood at the close of the business year, how it fared profit-wise during the year, as well as other an annual report of a company is the best source of information about the financial health of 64 9.4.2 Which features of an Annual Report should one read carefully? One must read an Annual Report with emphasis on the following: 9.4.3 What is a Balance Sheet and a Profit and Loss Account Statement? What is the difference between Balance Sheet and Profit and Loss Account Statements of a company? The Balance sheet of a company shows the financial position of the company at a particular point of time. The balance sheet of a company/firm, according to the Companies Act, 1956 should be either in the account form or the report form. Balance Sheet: Account Form Liabilities Assets Share Capital Fixed Assets Reserves and Surplus Investments Secured loans Current Assets, loans and advances Unsecured loans Miscellaneous expenditure Current liabilities and provisions Balance Sheet: Report Form I. Sources of Funds Shareholders’ Funds Share Capital Loan Funds Secured loans Unsecured loans 65 Application of Funds Fixed Assets Investments Current Assets, loans and advances Less: Current liabilities and provisions Net current assets Miscellaneous expenditure and losses The Profit and Loss account (Income Statement), on the other hand, shows the financial 9.4.4 How to interpret Balance Sheet and Profit and Loss Account of a company? BOX-l As at 31st As at 31st Balance sheet as on 31st March, 2005 March, 2005 March, 2004 SOURCES OF FUNDS Schedule Page 1 (a) Capital 1 19 (b) Reserves and Surplus 2 20 2 LOAN FUNDS (a) Secured 3 21 (b) Unsecured 4 21 3 TOTAL FUNDS EMPLOYED 1066.31 971.97 APPLICATION OF FUNDS 4 FIXED ASSETS (a) Gross Block 5 22 (b) Less: Depreciation (c) Net Block (d) Capital Work in Progress 5 INVESTMENTS 6 23 66 BOX-l As at 31st As at 31st Balance sheet as on 31st March, 2005 March, 2005 March, 2004 SOURCES OF FUNDS Schedule Page CURRENT ASSETS, LOANS AND 6 ADVANCES (a) Inventories 7 24 (b) Sundry Debtors 8 24 (c) Cash and Bank Balances 9 25 (d) Loans and Advances 10 25 Less: CURRENT LIABILITIES AND 7 PRIVISIONS (a) Current Liabilities 11 26 (b) Provisions 12 26 8 NET CURRENT ASSETS [(6) less (7)1 9 TOTAL ASSETS (NET) 1066.31 971.97 10 CONTINGENT LIABILITIES 13 27 As per our report attached For and on behalf of the XXXXX AAAA ASDFG Chartered Accountants, Chairman BBBB CCCC TYUB POIUY Directors YYYY NSDF Vice- Chairman Chartered Accountants, and Managing WERT MNBV Director ZZZZZZ Secretary The balance sheet of a company is a record showing sources of funds and their application for everyday due to fund inflow and outflow, balance sheets are drawn on a specific date, say 9.4.5 What do these sources of funds represent? As shown in a sample balance sheet in Box-1, there are two sources of funds: Shareholders’ Fund (also known as Net Worth) is the fund coming from the owners of the company; and Loan Fund When a company/firm starts operations, its owners, called shareholders, contribute funds called Share Capital. 67 Share capital has been further divided into equity capital and preference capital. Equity After distributing dividends, a part of the profit is retained by the company for meeting fund reserves and surplus, 9.4.6 What is the difference between Equity shareholders and Preferential shareholders? Equity Shareholders are supposed to be the owners of the company, who therefore, have right to get dividend, as declared, and a right to vote in the Annual General Meeting for The act defines a preference share as that part of share capital of the Company which enjoys preferential right as to: (a) payment of dividend at a fixed rate during the life time of But Preference shares cannot be traded, unlike equity shares, and are redeemed after a pre- Preferential Shareholders 9.4.7 What do terms like authorized, issued, subscribed, called up and paid up capital mean? Authorized capital Issued capital Subscribed capital is that part of the issued capital which is subscribed (accepted) by Called up capital is a part of subscribed capital which has been called up by the company Paid Up capital refers to that part of the called up capital which has been actually paid 68 9.4.8 What is the difference between secured and unsecured loans under Loan Funds? as creation of charge, which safeguards creditors in the event of any default on the part of 9.4.9 What is meant by application of funds? The funds collected by a company from the owners and outsiders are employed to create following assets: Fixed Assets: These assets are acquired for long-terms and are used for business Investments: The investments are the financial securities created by investing surplus funds into any non-business related avenues for getting income either for long-term or Current Assets, Loans, and Advances: This consists of cash and other resources which are in the form of raw materials, finished goods, cash, debtors, inventories, loans and Miscellaneous Expenditures and Losses: The miscellaneous expenditures represent certain outlays such as preliminary expenses and pre-operative expenses not written 69 9.4.10 What do the sub-headings under the Fixed Assets like ‘Gross block’ ‘Depreciation’, ‘Net Block’ and Capital-Work in Progress’ mean? The total value of acquiring all fixed assets (even though at different points of time) is called ‘Gross Block’ or “Gross Fixed Asset’. ‘Depreciation’. The Companies Act 1956 stipulates different rates of depreciation for different types of assets and different methods calculating depreciation, namely, Straight Line Method (constant annual method) and Written Down Value Method (depreciation rate decreases over The worth of the fixed assets after providing for depreciation is called ‘Net Block’. In case of The capital/funds used for a new plant under erection, a machine yet to be commissioned 9.4.11 What are Current Liabilities and Provisions and Net Current Assets in the balance sheet? A company may receive many of its daily services for which it does not have to pay immediately “Current Liabilities’. Similarly the company may have to provide for certain other expenses (though not required to be paid immediately) like dividend ‘Provisions’. In short, Current Liabilities and Provisions are amounts due to the suppliers of goods and services brought on credit, advances payments received, accrued expenses, unclaimed dividend, provisions for taxes, Current Liabilities and Provisions, therefore, reduce the burden of day-today expenditure on “Net Current Assets’ or “Net Working Capital’. 9.4.12 How is balance sheet summarized? A balance sheet indicates matching of sources of funds with application of funds. In case of 70 Thus in a balance sheet, A Profit and Loss Account shows how much profit or loss has been incurred by a company know how the profit available for appropriation is arrived at by using profit after tax as well BOX- 2 PROFIT AND LOSS ACCOUNT FOR THE YEAR ENDED 31ST MARCH, 2005 RUPEES RUPEES RUPEES PARTICULARS (in crores) (in crores) (in crores) As at 31st As at 31st March, 2005 March, 2004 INCOME EXPENDITURE ACCOUNTS PROFIT BEFORE TAX PROFIT AFTER TAX ACCOUNT RESERVE WRITTEN BACK 71  RUPEES RUPEES RUPEES PARTICULARS (in crores) (in crores) (in crores) As at 31st As at 31st March, 2005 March, 2004 AMOUNT AVAILABLE FOR APPROPRIATIONS (b) General Reserve 100 10 (c) Balance credited to Balance Sheet As per our report attached to the Balance Sheet For and on behalf of the Board AAA Chartered Accountants, Chairman BBB ABC CCC Partner DDD Directors Chartered Accountants, Vice- Chairman and DEF Managing Director Partner STU Secretary 9.4.13 What should one look for in a Profit and Loss account? For a company, the profit and loss statement is the most important document presented to the the other income stems from dividend on the investments or interest from the loans and 72 9.5 conclusion other concept to be learned is Time Value of Money which includes learning about Future value of a single cash flow, Future value of an annuity, Present value of a single cash flow and about balance sheet, profit and loss statement, directors report, auditors report, management 73