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Topic 1 & 2 Introduction to financial management and the Australian Taxation system Financial Markets 2 Learning Objectives Describe what the subject of financial management is about and why it is studied Compare the three typical forms of business and explain why the company is the most logical choice for a firm that is large or growing Understand the goal of the financial manager Explain the 10 principles that form the basis for financial management Identify what has led to the era of the multinational corporation Appreciate some of the themes associated with the Global Financial Crisis and its aftermath 3 Learning Objectives Calculate the taxable income and tax payable for Australian individual and company taxpayers Understand the basic components of the Australian dividend imputation system and the implications for the after-tax wealth of shareholders Appreciate some of the implications of the Australian taxation system for the financial decisions of Australian individuals and businesses Understand the basic elements of Australian capital-gains taxation Appreciate some of the implications of income tax and capital-gains tax on rates of return for shareholders 4 1 Learning Objectives Define financial markets Explain the role of financial markets in a developed economy Describe financial intermediaries in a developed financial market Discuss movement of funds to finance business activities Describe the various component market groups that make up the overall Australian financial markets Outline the main pattern of fund flows underlying the financing of businesses in Australia 5 What is financial management Financial management is the study of how people and businesses evaluate investments and raise funds to finance them The three questions addressed by the study of financial management are: 1. What long-term investments should the firm undertake? - Referred to as capital budgeting 1. How should the firm raise money to fund these investments? - 1. Referred to as capital structure decisions How can the firm best manage its cash flows as they arise in its day-to-day operations? - Referred to as working capital management 6 Three types of business organisation Sole proprietorship A business owned by a single individual Partnership An association of two or more individuals joining together as coowners to operate a business for profit Company An entity that legally functions separately and apart from its owners 7 2 Comparison of organisational forms 8 Role of a company's financial manager 9 The goal of the financial manager Profit maximisation? Problems: Timing of returns Uncertainty of returns 10 3 The goal of the financial manager Maximisation of shareholder wealth? This goal is consistent with: maximising firm value maximising share value BUT...is not without its difficulties! 11 The goal of the financial manager Interaction between the company and the financial markets making investment decisions (capital budgeting decisions) making decisions on how to finance these investments (capital structure decisions) managing funding for the company's day-to-day operations (working capital management) 12 The goal of the financial manager 13 4 10 principles of financial management Principle 1: The risk return trade-off We won't take on additional risks unless we expect to be compensated with additional return 14 10 principles of financial management Principle 2: The time value of money A dollar received today is worth more than a dollar received in the future Principle 3: Cash - not profits - is king Cash flows, not accounting profits, are used for measuring wealth 15 10 principles of financial management Principle 4: Incremental cash flows It's only what changes that counts Incremental cash flow is the difference between the cash flows if a new project was taken on and the cash flows if the project was not taken on 16 5 10 principles of financial management Principle 5: The curse of competitive markets Why it's hard to find exceptionally profitable projects The two most common ways of making markets less competitive are to: differentiate the product achieve a cost advantage over competitors 17 10 principles of financial management Principle 6: Efficient capital markets The markets are quick and the prices are right Efficient markets are markets in which the values of all assets and securities at any instant in time fully reflect all available information. 18 10 principles of financial management Principle 7: The agency problem Managers won't work for owners unless it's in the managers' best interest Agency costs represent the cost, such as reduced share price, associated with potential conflict between managers and investors, when these are not the same 19 6 10 principles of financial management Principle 8: Taxes bias business decisions Principle 9: All risk is not equal Some risk can be diversified away, and some cannot 20 10 principles of financial management Principle 10: Ethical behaviour is doing the right thing... ethical errors end careers businesses need the public's confidence firms have a social responsibility ... and ethical dilemmas are everywhere in finance! 21 Financial management and the new multinational firm Changes which have led to the era of the multinational corporation: Acceptance of free market systems in developing countries Deregulation of local markets Internationalisation of the Australian economy 22 7 Why are taxes relevant? Taxation is usually a mandatory cash outflow The real-world wealth of business owners is always after-tax wealth Taxation affects the amount of the firm's cash flows available to its owners 24 Introduction to income taxation Depends on: Type of taxpayer Taxable income Tax rate Company Individual Fiduciary / Partnership Assessable income minus Allowable deductions Marginal (individuals) vs Flat (companies) 25 Introduction to income taxation Tax 1:Determine net profit before tax 2: Calculate taxable income (likely to be different to profit) 3: Multiply taxable income by tax rate to compute tax 4: Determine net profit after tax 5: Pay tax to government (cash outflow) Taxable income Profit Net Profit 26 8 Tax rate: other taxpayers Fiduciary: beneficiaries taxed at relevant rate Partnership: partners taxed at relevant rate Superannuation fund: depends on members usually 15% may be 0% if pension exists 27 Tax rate: company 30% 28 Dividend imputation A classical tax system has one major drawback: DOUBLE TAXATION Occurs when profits are taxed at both source, and on receipt 29 9 Dividend imputation The solution: Dividend Imputation Introduced in 1987 Ensures that company net income paid to shareholders as dividends is taxed only once, at the shareholders' personal income tax rates 30 Dividend imputation: mechanics Tax paid by the company is \"imputed\" to the shareholders Allowed as a credit in the shareholders' tax payable computation Shareholders' tax payable = prima facie tax less imputation credit 31 Dividend imputation: mechanics Dividends can be fully franked, partially franked, or not franked at all Franking percentage is dependent on company's available franking credits Franking credits are dependent upon tax paid by the company 32 10 Implications of dividend imputation for business decision making Categories of companies Taxation Category 1: Companies that are well integrated with their shareholders by the dividend imputation system, plus non-taxpaying entities Company income tax is largely irrelevant to business decisions 33 Implications of dividend imputation for business decision making Taxation Category 2: Businesses that are not integrated with their owners by the dividend imputation system Business income tax is relevant to business decisions 34 Implications of dividend imputation for business decision making Taxation Category 3: Companies that are only partially integrated with their shareholders by the dividend imputation system Company income tax is partially relevant to business decisions 35 11 Capital-gains taxation A capital gain is assessed as the difference between the sale value of the asset and its purchase value A capital loss occurs when the sale value of the asset is less than its purchase value. Capital losses can be used as offsets against assessable capital gains but not as offsets against other assessable income Taxpayers are required to include these gains/losses in their tax returns and pay tax on net (positive) difference 36 What are financial markets? A complex of institutions, procedures and arrangements that facilitate a transfer of funds from one entity in the economy to another Examples of financial sub-markets: debt market & share market 37 Role of financial markets Net savers of funds Surplus savings Suppliers of funds FINANCIAL INTERMEDIARY Facilitation Net users of funds Shortage of savings Demanders of funds 38 12 Development of a financial market system Stage 1 Real assets = net worth Stage 2 Cash + Real assets = net worth Stage 3 Cash + Real assets + other financial assets = financial liabilities + net worth Stage 4 The addition of loan brokers, security underwriters, and secondary markets Stage 5 The addition of financial intermediaries 39 Types of assets Real assets Tangible assets Houses, equipment, inventory Financial assets Securities (e.g. shares, debentures, bills, notes) Claims for future payments Owners anticipate earning a future rate of return 40 Financial intermediaries Financial intermediaries facilitate the movement of money from savers to borrowers: commercial banks non-bank authorised deposit-taking institutions investment banks insurance companies superannuation funds investment companies private equity firms 41 13 Movement of funds Examples: Banks, building societies, credit unions, life insurance companies, trust funds Sell indirect securities to net savers Use the proceeds to purchase direct securities with increased size and maturity This process is called asset transformation - - e.g. Fixed term deposits, life insurance policies e.g. Debentures, shares 42 Direct transfer of funds: 43 Indirect transfer of funds: 44 14 Components of Australian financial markets Stock market and Bond market public offerings and private placements primary and secondary markets Foreign-exchange markets Derivatives markets Money and capital markets 46 Foreign-exchange markets Transfer of purchasing power from one currency to another Networks of licensed foreign-exchange dealers Very efficient markets Major types of transactions - Spot transactions - Forward transactions 47 15 Derivatives markets Derivatives are financial instruments that are derived from, or based on, the value of an underlying asset. They are often used to manage risk Examples of derivatives: Futures, options, & swaps Derivatives may be traded through an organised exchange or over-the-counter (OTC) 48 Derivatives markets Futures markets A futures contract is a legally binding agreement to buy or sell the underlying financial instrument or commodity specific quantity specific quality deliverable at an agreed location deliverable at an agreed future time at an agreed price 49 Derivatives markets Options markets An options contract is an agreement that gives the holder the right (but not the obligation) to buy or sell the specified commodity or financial instrument on or before a specified date Call option: the right to buy an asset Put option: the right to sell an asset There is a large variety of options-type products 50 16 Money and capital markets Capital markets Markets in long-term financial instruments By convention: terms greater than one year Long-term debt and equity markets Bonds, debentures, shares, leases, convertibles Money markets Markets in short-term financial instruments By convention: terms less than one year Treasury notes, certificates of deposit, commercial bills, promissory notes 52 Continues ... 17 Continued ... Continues ... Continued ... Continues ... Continued ... Continues ... 18 Public offerings and Private Placements Public offerings New securities offered to the public Securities issued through a share-broking firm or a syndicate of firms Examples: shares, bonds Private placements New securities only offered to some investors Often only to existing investors in the company Examples: shares, bonds 57 Primary & Secondary Markets Primary markets Selling of new securities Funds raised by governments and businesses Secondary markets Reselling of existing securities Adds marketability and liquidity to primary markets Reduces risk on primary issues Funds raised by existing security holders 58 The Australian Securities Exchange Major primary and secondary equity market Secondary market for debentures, notes and bonds Publicly listed company ASX listing rules Aim: To provide an efficient, honest, competitive and informed market for trading 60 19 Topic 3 Financial Mathematics 1 Learning Objectives Explain the mechanics of compounding: how money grows over time when it is invested Determine the future or present value of a sum of money Discuss the relationship between compounding (future value) and bringing money back to the present (present value) Calculate the effective annual rate of interest and then explain how it differs from the nominal or stated interest rate 2 Learning Objectives Define an ordinary annuity and calculate its future value and present value Apply the annuity present value model to the process of loan amortisation Understand the notion of a general annuity and the concept of equivalent interest rates Determine the present value of an annuity due Understand how perpetuities work Deal with complex cash flows and deferred annuities 3 1 Learning Objectives Determine how bond values change in response to changing interest rates Interpolate values within financial tables Formulate multi-part and non-standard problems 4 The One-Period Case If you were to invest $10,000 at 5% interest for one year, your investment would grow to $10,500. $500 would be interest ($10,000 .05) $10,000 is the principal repayment ($10,000 1) $10,500 is the total due. It can be calculated as: $10,500 = $10,000(1.05) The total amount due at the end of the investment is call the Future Value (FV). 5 Multi period case: the future value The future value at the end of the nth period, FVn, can be determined using the following equation: FVn = PV(1 + i)n Where PV can be considered as PV0 which is cash flow today (time zero), and i is the appropriate interest rate. 6 2 Future Value Suppose a stock currently pays a dividend of $1.10, which is expected to grow at 40% per year for the next five years. What will the dividend be in five years? FV = PV0(1 + i)n $1.10(1.40)5 $5.92 7 Present value The present value is the current value of a sum of money representing a future payment that is discounted at an appropriate interest rate to reflect the time value of money and other factors The discount rate is the interest rate that converts a future value to the present value The discount factor is the quantity that converts a particular future sum of money to its present value Discounting is the process of converting a future value to its present value 8 Present Value If you were to be promised $10,000 due in one year when interest rates are 5%, how much would you need to invest today? $10,000 $9,523.81 1.05 The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the Present Value (PV). Note that $10,000 = $9,523.81(1.05). In the one-period case, the formula for PV can be written as: Where FV1 is cash flow at date 1, and i is the appropriate interest rate. 9 PV0 FV1 1 i 3 Multi period case: present value To determine an unknown PV, the following equation is used: To reach a savings target of $3,000 after two years at 8% p.a. compounded quarterly, how much would we have to invest today? Answer Substitute FV=$3000, i =2% per quarter and n = 8 quarters (two years) into Equation 4-5: PV = $3,000 / (1.02)8 = $3,000 / 1.17166 $2,560.47 PV = FVn / (1 + i)n 10 Compound interest concepts Compound interest is where interest paid on an investment during the first period is added to the principal, and during the second period interest is earned on the original principal plus the interest earned during the first period Money invested at compound interest accumulates at an increasing rate each period: 'exponential behaviour' 11 Future Value and Compounding Recall previous problem of a stock currently pays a dividend of $1.10, which is expected to grow at 40% per year for the next five years. Notice that the dividend in year five, $5.92, is considerably higher than the sum of the original dividend plus five increases of 40% on the original $1.10 dividend: This is due to compounding. $5.92 > $1.10 + 5[$1.10.40] = $3.30 12 4 Compound interest rates The periodic rate of compound interest, is found by dividing the annual rate of compound interest or the nominal annual rate or Annual Percentage rate (APR) i with m, where m is the number of times that interest is compounded each year. So periodic rate of compound interest = i /m The total number of compounding periods is number of year n multiply by m So total number of compounding periods = m x n Where interest is compounded m times per year for n years. 13 What rate is enough To determine an unknown i, rearrange equation PV = FVn / (1 + i)n and you would get If you invest $10,000 for 2 years you will get $12,544. What is the interest rate? Answer: Substituting in Equation 4-8: i = (FV/PV)1 - 1 i = ($12 544/$10 000)1/2- 1 = (1.2544).5 - 1 = 12% per pa 14 What rate is enough i = (FV/PV)1 - 1 If you invest $10,000 for 2 years you will get $12,668. The interest was compounded quarterly. What is interest rate? Substituting in above Equation: i = ($12 668/$10 000)1/8 - 1 = (1.2688).125 - 1 = .03 = 3% per quarter So, nominal rate = 3% x 4 = of 12% pa 15 5 Finding the Number of Periods To determine an unknown n, you need to use log n = log(FV/PV) / log(1 + i) If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000? $10,000 $5,000 (1.10) n FV PV0 (1 i) n (1.10) n $10,000 2 $5,000 n log(1.10) n log( 2) log( 2) 7.2725 years log(1.10) 16 The number of periods, n To determine an unknown n, you need to use log How many months did it take to repay a loan of $300 if the sum repaid was $358.84 at an interest rate of 12% p.a. compounded monthly? Answer: n = log(FV/PV) / log(1 + i) n = log(358.84 / 300) / log1.01 = log1.19613 / log1.01 18 months 17 Compounding Periods if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to: .12 FV $50 1 2 23 $50 (1.06) 6 $70.93 18 6 Effective Annual Rates of Interest A reasonable question to ask in the example is \"what is the effective annual rate of interest on that investment?\" FV $50 (1 .12 23 ) $50 (1.06) 6 $70.93 2 The Effective Annual Rate (EAR) of interest is the annual rate that would give us the same end-ofinvestment wealth after 3 years: $50 (1 EAR) 3 $70.93 19 Effective Annual Rates of Interest FV $50 (1 EAR) 3 $70.93 (1 EAR) 3 $70.93 $50 13 $70.93 EAR $50 1 .1236 So, investing at 12.36% compounded annually is the same as investing at 12% compounded semi-annually. 20 Making interest rates comparable effective annual interest rate (EAR) = EAR = (1 + i/m)m - 1 What is the effective annual rate if 12% p.a. is compounded twice per year? Answer: Substituting in Equation 4-9a: EAR = (1 + 12/2)2 - 1 = (1.06)2 - 1 = 12.36% (greater than the nominal interest rate!) 21 7 The Rate of simple interest Simple interest: is often used in short-term investing and borrowing is not compounded: interest is only paid on the original 'principal' borrowed or invested is directly proportional to the time of the investment where P = principal, i = interest rate and t = time SI = P x i x t 22 Simplifications Perpetuity A constant stream of cash flows that lasts forever Growing perpetuity A stream of cash flows that grows at a constant rate forever Annuity A stream of constant cash flows that lasts for a fixed number of periods Growing annuity A stream of cash flows that grows at a constant rate for a fixed number of periods 23 Annuities An annuity is a series of equal dollar payments for a specified number of periods - e.g. payments on a housing loan, pension receipts from a superannuation pension fund or interest payments on bonds An ordinary annuity is an annuity whose payments are made at the end of each period 24 8 Ordinary annuity The future value of an ordinary annuity = FVn = PMT [(1+ i) n -1] i The present value of an ordinary annuity = PV0 Pmt1 1 (1 i) n i 25 Future value of an ordinary annuity What is the FV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? PMT = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) Answer: 26 Present value of an ordinary annuity What is the PV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? Pmt = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) 27 9 Present Value of an Ordinary Annuity What is the PV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? Pmt = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) 28 Amortising a loan Loan amortisation is the process of \"paying off\" a loan Term loans are amortised in equal instalments over a specified number of periods (terms) 29 Loan Amortization It is an annuity where PV is the amount of loan 1 (1 i ) n PV Pmt i So consider a $10,000, 2 year loan at 12% interest compounded monthly. What would be the monthly payment on this loan? n = 2 12 = 24 i = .12 / 12 = .01 1 (1 .01) 24 $10,000 Pmt Pmt 21.2444 .01 $10,000 Pmt $470.7123 21.2444 30 10 Annuity due Annuity due is an annuity where payments are made at the beginning of each period To determine the present value of an annuity due: (4.20) 1 (1 i ) PVdue Pmt Pmt i ( n 1) 31 Ordinary annuity vs. annuity due the timing of the payments in these two types of annuity differ: 32 Annuity Interest Rate PV and FV of annuity formula: PV Pmt [1 (1 i ) n ] i FVn Pmt [(1 i ) n 1] i To find annuity interest rate: Use trial and error - we can use trial and error method (finding the interest rate r that corresponds with the given payment PMT, time n and PV or FV) Use Interpolation formula to solve for i 33 11 Annuity Interest Rate For future value of an annuity, we know that FV increases when r increases. For present value of an annuity, PV decreases when r increases. John puts equal amounts of $1,000 into a bank account at the end of each year for the next 20 years. He will receive $100,000 at the end of the investment period. To find the interest rate for the deposits, [(1 r ) t 1] r [(1 r ) 20 1] Simplify the equation as far as possible 100000 1000 r 20 There are several ways to solve this: 100 [(1 r ) 1] r $100,000 is FV, use FV formula, pmt = 1000 n = 20 FVt Pmt Annuity Interest Rate Use trial and error - insert different values of r into the Right Hand Side of the equation (interest factor) until it equals 100. 100 [(1 r ) 20 1] r For example, If r = 12% the interest factor is 72.0524 If r = 15% the interest factor is 102.4436 So interest rate must be between 12% and 15% At r = 12%, FV is $72,052.44 at r = 15%, FV = $102,443.53 You need r that will make FV = $100,000 Annuity Interest Rate Interpolation looks at how far along the interval (72.0524 to 102.4436) 100 lies as a proportion of the whole interval, and assumes that the unknown r lies in the same position in the interval 12% to 15%. r 12% ? 15% FVIAF 72.0524 100 102.4436 Difference = 27.9475 Difference = 30.3912 r 12% + [27.9475/30.3012](15% - 12%) 14. 75879% A good result but because this is an approximating method you should use intervals of 1% as the smaller the interval the greater the accuracy and the better the result. Actually r = 14.79625% giving FV of $100,000 12 Perpetuity Perpetuity is an annuity with an infinite life e.g. the dividend stream on preference shares To determine the present value of a perpetuity, the following equation is used: PV = PMT/i (4.22) 37 Complex cash flows Complex cash flows are cash flows that are irregular To determine the PV of an irregular cash flow, the PV of each individual cash flow are added To determine the overall FV of unequal cash flows, the FV of the sum of the PV of each individual cash flow is calculated - e.g. revenue tapering off as a product is outdated 38 Solving multi-part and nonstandard problems 1. Draw a timeline Identify what is known and needs to be known 2. Determine what unknown(s) the problem involves 3. Identify the class of problem Compounding or discounting? Annuity? Perpetuity? 4. Identify any traps in the problem 5. Formulate the problem Which equation to use? How to set up spreadsheet? 41 13 Topic 4 Credit management and Short-term financing 1 Learning Objectives Understand the nature and importance of working capital Appreciate the nature of the risk-return trade-off in managing current assets and current liabilities Explain the hedging principle and the factors that determine the appropriate level of working capital for a firm Understand how to determine the cost of short-term financial management Describe the typical sources of short-term finance used by the firm 2 Working capital Working capital is made up of a firm's current assets and current liabilities Current assets Current liabilities cash marketable securities accounts receivable inventories bank overdraft accounts payable notes payable accrued expenses 3 1 Net working capital Net working = Current assets - Current liabilities capital Managing net working capital is concerned with managing the firm's liquidity: managing investment in current assets managing the use and amount of short-term finance 4 Managing current assets and liabilities Investing in current assets: improves liquidity reduces the firm's rate of return on investment Using current liabilities to finance assets: This is the 'risk-return trade-off' reduces liquidity 5 Finance option 1 - Principle of self-liquidating debt Finance all current assets with current liabilities, and finance all fixed assets with long-term financing Balance sheet Current assets Fixed assets Current liabilities Long-term debt Preference shares Ordinary shares 6 2 Finance option 2 - excess liquidity Use long-term financing to finance some of our current assets Less risky, more expensive Balance sheet Current assets Fixed assets Current liabilities Long-term debt Preference shares Ordinary shares 7 Finance option 3 - more profitability Use current liabilities to finance some of our fixed assets Less expensive, more risky Balance sheet Current assets Fixed assets Current liabilities Long-term debt Preference shares Ordinary shares 8 The risk-return trade-off 9 3 The hedging principle and the appropriate level of working capital The cash-flow-generating characteristics of an asset should be matched with the maturity of the source of financing used for its acquisition 10 Assets Permanent assets Assets which will not be liquidated or replaced within a 12-month period Temporary current assets Assets which the firm plans to sell / liquidate within a 12-month period 11 Spontaneous, temporary and permanent sources of financing Spontaneous finance Accounts payable that arise spontaneously in day-today operations Trade credit, wages payable, accrued interest Temporary (short-term) finance Unsecured bank loans, commercial bills, promissory notes, loans secured by accounts receivable and inventories Permanent finance Intermediate-term loans, long-term debt, preference shares, ordinary shares 12 4 Short-term financing and its cost How much short-term financing should the firm use? The hedging principle How should sources of short-term financing be selected? Effective cost of credit Credit availability: quantity and period available Influence on the cost and availability of other sources of finance 13 Cost of short-term credit Interest = principal x rate x time Example What interest do you pay for borrowing $10,000 at 8.5% p.a. for 9 months? Interest = $10,000 x 0.085 x 9/12 = $637.50 14 Cost of credit Nominal annual interest rate (RATE) Interest = principal x RATE x time RATE = interest / (principal x time) 15 5 Cost of short-term credit ANNUAL PERCENTAGE RATE (APR) = Interest principal x time Example If you pay $637.50 in interest on $10,000 principal for 9 months, what is the Annual percentage rate? RATE = $637.50 /($10 000 x 9/12) = 8.50% 16 Cost of short-term credit Effective Interest Rate (EAR) EAR = (1 + i/m)m -1 Example What is the effective rate of interest on a 9% loan with monthly payments? EAR = (1 + 0.09 / 12 )12 - 1 = 9.38% 17 Sources of short-term finance Unsecured loans Only security is the lender's faith in the ability of the borrower to repay the funds Sources: trade credit, promissory notes, bills of exchange Secured loans Involves the pledge of specific assets as collateral Sources: banks, finance companies, factors 18 6 Sources of short-term finance Accrued wages and taxes Trade credit Bank overdrafts Promissory notes Bills of exchange Accounts receivable loans Inventory loans 19 Accrued wages and taxes Most firms accrue wages payable in the interval between employees providing service and salary actually being paid Most firms accrue taxes payable e.g. GST, income tax Typically rise and fall spontaneously with level of firm's sales 20 Trade credit Spontaneously generated as part of day-to-day operations No formal agreements are generally involved in obtaining credit The amount of credit expands and contracts in line with the firm's needs Discounts for early repayment are sometimes available 21 7 'Cost' of credit terms and cash discounts Example What is the penalty of delaying repayment of trade credit until 60 days have passed when the credit terms offered are 3/20, net 60? Work on a notional loan of $1 Penalty for missing discount is 3 cents We're effectively borrowing $0.97 for 40 days and being charged 3 cents interest RATE = Interest / (Principal x Time) = 0.03 / (0.97 x 40 / 365 ) = 28.22% 22 Bank overdrafts The bank allows a customer to write cheques for more finance than is in the cheque account Overdraft limits Two approaches: secured lending cash-flow lending Prime/indicator interest rates Unused-limit fee 23 Promissory notes A short-term financial instrument whereby the borrower (or 'issuer' or 'drawer') promises to repay the face value, at maturity, to the holder (or 'investor' or 'lender') Discount (or Interest) = V - P where V = face value to be repaid at maturity (after n days) P = original sum borrowed 24 8 Bills of exchange A short-term financial instrument that requires the face value to be repaid on demand or at a specified date A bill used as a form of financing is called an accommodation bill Three parties involved: drawer/borrower discounter/lender acceptor/guarantor 25 Bills of exchange Bank accepted bills are called bank bills Cost of bill finance: maintenance/activity fees establishment fees acceptance fees Successive bills can be arranged on a 'rollover' basis 26 Accounts receivable loans Loans secured with accounts receivable used as collateral Pledging of accounts receivable General line on all accounts Loan a percentage of accounts receivable pledged Specific invoices as security Factoring of accounts receivable Outright sale of accounts receivable to a factor The factor bears the risk of collection of accounts The factor is often a finance company 27 9 Inventory loans Inventory used as collateral for short-term secured loans Size of loan depends on marketability and perishability of inventory Quality risk for lender Collateral management companies Field warehousing Costs are usually high 28 10 Topic 5 Introduction to risk and rates of return 1 Learning Objectives Describe the relationship between investors' average returns and the riskiness of those returns Explain the effect of inflation on rates of return Describe the term structure of interest rates Define and measure the expected rate of return of an individual investment Define and measure the riskiness of an individual investment Explain how diversifying investments affects the riskiness and expected rate of return of a portfolio of assets 2 Learning Objectives Measure the market risk of an individual asset Calculate the market risk of a portfolio Calculate the expected return and risk of a two-asset portfolio Explain the relationship between an investor's required rate of return on an investment and the risk of the investment Understand the fundamental principles of portfolio theory Explain the notion of efficient markets and its importance to share prices 3 1 Return The relationship between risk and rates of return Almost always true: The greater the expected return, the greater the risk Risk 4 Risk Risk The potential variability in future cash flows Can be measured by the standard deviation of the expected return Default risk The possibility the borrower will not repay the debt in the future Risk premium The additional return expected for assuming risk 5 The effect of inflation on rates of return - The Fisher effect (1 + Nominal) = (1 + Real) (1 + Inflation) Nominal interest rate The actual rate of return paid or earned without making any allowance for inflation Real interest rate The nominal rate of return adjusted for the effect of inflation 6 2 Calculating the real rate of return What is the real rate of return if the nominal return is 10% per annum and inflation is 3% per annum? Answer: (1 + Nominal) = (1 + Real) (1 + Inflation) (1 + 0.10) = (1 + Real) (1 + 0.03) Real = 6.7961% p.a. 7 Measuring return Realised or Historical return The return that an asset has already produced over a specified period of time Expected return The return that an asset is expected to produce over some future period of time Required return The return that an investor requires an asset to produce if he/she is to be a future investor in that asset 9 Realised Return HPR = Ending Price - Beginning Price + Income Beginning Price Also known as the holding-period return 10 3 Calculating holding period return You bought an investment property last year for $350,000. This year the value of the property has gone up to $400,000. You also received $12,000 in rental income for the year. What is your holding-period return on the investment? Answer: HPR = 400,000 - 350,000 + 12,000 350,000 = 17.71% 11 Geometric Rates of Return 4 Historical Return You are given the following three years for the ASX200 index: Year HPR / TR 2013 -8.09% 2014 13.62% 2015 26.33% Calculate the average return ACC515 Risk return calculations document. Calculating expected returns State of economy Probability P A Returns B Recession 0.20 4% -10% Normal 0.50 10% 14% Boom 0.30 14% 30% Expected return is just a weighted average R* = P(R1) x R1 + P(R2) x R2 + ... + P(Rn) x Rn 15 Calculating expected returns Example: R* = P(R1) x R1 + P(R2) x R2 + ... + P(Rn) x Rn Company A RA* = 0.2 x 4% + 0.5 x 10% + 0.3 x 14% = 10% Company B RB* = 0.2 x -10% + 0.5 x 14% + 0.3 x 30% = 14% 16 5 Measuring risk Risk can be measured using the standard deviation of an investment's returns Standard deviation is a measure of the dispersion of possible outcomes The greater the standard deviation, the greater the risk SD of Historical returns ACC515 Risk return calculations document. 17 Measuring Expected Risk (9-7) where n = the number of possible outcomes or different rates of return on the investment Ri = the value of the ith possible rate of return R* = the expected return P(Ri) = the chance or probability that the ith outcome or return will occur 18 Measuring risk Company A ( 4% - 10% )2 ( 0.2 ) = 7.2 ( 10% - 10% )2 ( 0.5 ) = 0.0 ( 14% - 10% )2 ( 0.3 ) = 4.8 Variance = 12.0 = s2 Standard deviation = 12.0 = 3.46% 19 6 Measuring risk Company B ( -10% - 14% )2 ( 0.2 ) = ( 14% - 14% )2 ( 0.5 ) = 0.0 ( 30% - 14% )2 ( 0.3 ) = 76.8 Variance = = s2 Standard deviation = 115.2 192.0 192.0 = 13.86% 20 Measuring risk Share A 10% 14% 3.46% 13.86% Expected return Standard deviation Share B Which share would you prefer? 21 Return of a two-asset portfolio Depends on: the realised / expected return of each of the assets the amount of money invested in each of the assets Rp = w1R1 + w2R2 Where, Rp is the realised / expected return on the portfolio w1 is the weight of the first asset w2 is the weight of the second asset R1 is the expected return of the first asset R2 is the expected return of the second asset 22 7 Risk using realised returns Portfolio Risk Portfolio (comprising two assets) risk depends on: - The proportion of funds invested in each asset (w). - The riskiness of the individual assets (s2). - The relationship between each asset in the portfolio with respect to risk, correlation (. - For a two-asset portfolio the variance is: 2 2 2 s p w12s 12 w2s 2 2w1w2 1, 2s 1s 2 where: wi = the proportion of the portfolio invested in asset i s i = the standard deviation of asset i ij correlation between asset i and j returns Portfolio Risk and Return Measurement Expected returns of A is 8% and B is 12% 60% of the portfolio is invested in A and 40% in B. Standard Deviation of of A is 4% and B is 6% and the correlation between a & B (pA,B) is -0.5 Calculate the expected return and risk of portfolio? E(rp) = (0.6 .08) + (0.4 .12) =.096 = 9.6% Portfolio = [(0.6 0.04 2)+(2 0.6 0.4 (- 0.5) .04 .06)+ (0.4 .06 2 )] = 0.024 = 2.4% 8 Risk and diversification If securities are perfectly positively correlated Investing in two securities to reduce risk No effect on risk If securities are perfectly negatively correlated Perfect diversification. Risk is minimised 26 Risk of a two-asset portfolio Perfect negative correlation removes risk Returns A Portfolio B Time 27 Risk and diversification Diversifiable risk Firm-specific risk Company-unique risk Unsystematic risk Can be eliminated by diversification Non-diversifiable risk Market-related risk Market risk Systematic risk Cannot be eliminated by diversification 28 9 How much diversification? Portfolio risk Diversifiable risk Almost all possible gains from diversification are achieved with a carefully chosen portfolio of 20 - 25 shares Nondiversifiable risk 1 No of different shares 29 Measuring market risk Many factors affect market/systemic risk Unexpected changes in interest rates Unexpected changes in economic condition foreign competition tax changes overall business cycle Investors are only compensated for accepting market risk How do we measure??? 30 Beta: A measure of market risk Beta The relationship between an investment's returns and the market returns A firm with Beta = 1 has average market risk. It has the same volatility as the market A firm with Beta > 1 is more volatile than the market A firm with Beta $1.10 + 5[$1.10.40] = $3.30 12 4 Compound interest rates The periodic rate of compound interest, is found by dividing the annual rate of compound interest or the nominal annual rate or Annual Percentage rate (APR) i with m, where m is the number of times that interest is compounded each year. So periodic rate of compound interest = i /m The total number of compounding periods is number of year n multiply by m So total number of compounding periods = m x n Where interest is compounded m times per year for n years. 13 What rate is enough To determine an unknown i, rearrange equation PV = FVn / (1 + i)n and you would get If you invest $10,000 for 2 years you will get $12,544. What is the interest rate? Answer: Substituting in Equation 4-8: i = (FV/PV)1 - 1 i = ($12 544/$10 000)1/2- 1 = (1.2544).5 - 1 = 12% per pa 14 What rate is enough i = (FV/PV)1 - 1 If you invest $10,000 for 2 years you will get $12,668. The interest was compounded quarterly. What is interest rate? Substituting in above Equation: i = ($12 668/$10 000)1/8 - 1 = (1.2688).125 - 1 = .03 = 3% per quarter So, nominal rate = 3% x 4 = of 12% pa 15 5 Finding the Number of Periods To determine an unknown n, you need to use log n = log(FV/PV) / log(1 + i) If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000? $10,000 $5,000 (1.10) n FV PV0 (1 i) n (1.10) n $10,000 2 $5,000 n log(1.10) n log( 2) log( 2) 7.2725 years log(1.10) 16 The number of periods, n To determine an unknown n, you need to use log How many months did it take to repay a loan of $300 if the sum repaid was $358.84 at an interest rate of 12% p.a. compounded monthly? Answer: n = log(FV/PV) / log(1 + i) n = log(358.84 / 300) / log1.01 = log1.19613 / log1.01 18 months 17 Compounding Periods if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to: .12 FV $50 1 2 23 $50 (1.06) 6 $70.93 18 6 Effective Annual Rates of Interest A reasonable question to ask in the example is \"what is the effective annual rate of interest on that investment?\" FV $50 (1 .12 23 ) $50 (1.06) 6 $70.93 2 The Effective Annual Rate (EAR) of interest is the annual rate that would give us the same end-ofinvestment wealth after 3 years: $50 (1 EAR) 3 $70.93 19 Effective Annual Rates of Interest FV $50 (1 EAR) 3 $70.93 (1 EAR) 3 $70.93 $50 13 $70.93 EAR $50 1 .1236 So, investing at 12.36% compounded annually is the same as investing at 12% compounded semi-annually. 20 Making interest rates comparable effective annual interest rate (EAR) = EAR = (1 + i/m)m - 1 What is the effective annual rate if 12% p.a. is compounded twice per year? Answer: Substituting in Equation 4-9a: EAR = (1 + 12/2)2 - 1 = (1.06)2 - 1 = 12.36% (greater than the nominal interest rate!) 21 7 The Rate of simple interest Simple interest: is often used in short-term investing and borrowing is not compounded: interest is only paid on the original 'principal' borrowed or invested is directly proportional to the time of the investment where P = principal, i = interest rate and t = time SI = P x i x t 22 Simplifications Perpetuity A constant stream of cash flows that lasts forever Growing perpetuity A stream of cash flows that grows at a constant rate forever Annuity A stream of constant cash flows that lasts for a fixed number of periods Growing annuity A stream of cash flows that grows at a constant rate for a fixed number of periods 23 Annuities An annuity is a series of equal dollar payments for a specified number of periods - e.g. payments on a housing loan, pension receipts from a superannuation pension fund or interest payments on bonds An ordinary annuity is an annuity whose payments are made at the end of each period 24 8 Ordinary annuity The future value of an ordinary annuity = FVn = PMT [(1+ i) n -1] i The present value of an ordinary annuity = PV0 Pmt1 1 (1 i) n i 25 Future value of an ordinary annuity What is the FV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? PMT = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) Answer: 26 Present value of an ordinary annuity What is the PV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? Pmt = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) 27 9 Present Value of an Ordinary Annuity What is the PV of an annuity of $100 per quarter for one and a half years if the interest rate is 8% per annum compounded quarterly? Pmt = $100 per quarter, n = 6 quarters, and i = 2% per quarter (.02 as a decimal) 28 Amortising a loan Loan amortisation is the process of \"paying off\" a loan Term loans are amortised in equal instalments over a specified number of periods (terms) 29 Loan Amortization It is an annuity where PV is the amount of loan 1 (1 i ) n PV Pmt i So consider a $10,000, 2 year loan at 12% interest compounded monthly. What would be the monthly payment on this loan? n = 2 12 = 24 i = .12 / 12 = .01 1 (1 .01) 24 $10,000 Pmt Pmt 21.2444 .01 $10,000 Pmt $470.7123 21.2444 30 10 Annuity due Annuity due is an annuity where payments are made at the beginning of each period To determine the present value of an annuity due: (4.20) 1 (1 i ) PVdue Pmt Pmt i ( n 1) 31 Ordinary annuity vs. annuity due the timing of the payments in these two types of annuity differ: 32 Annuity Interest Rate PV and FV of annuity formula: PV Pmt [1 (1 i ) n ] i FVn Pmt [(1 i ) n 1] i To find annuity interest rate: Use trial and error - we can use trial and error method (finding the interest rate r that corresponds with the given payment PMT, time n and PV or FV) Use Interpolation formula to solve for i 33 11 Annuity Interest Rate For future value of an annuity, we know that FV increases when r increases. For present value of an annuity, PV decreases when r increases. John puts equal amounts of $1,000 into a bank account at the end of each year for the next 20 years. He will receive $100,000 at the end of the investment period. To find the interest rate for the deposits, [(1 r ) t 1] r [(1 r ) 20 1] Simplify the equation as far as possible 100000 1000 r 20 There are several ways to solve this: 100 [(1 r ) 1] r $100,000 is FV, use FV formula, pmt = 1000 n = 20 FVt Pmt Annuity Interest Rate Use trial and error - insert different values of r into the Right Hand Side of the equation (interest factor) until it equals 100. 100 [(1 r ) 20 1] r For example, If r = 12% the interest factor is 72.0524 If r = 15% the interest factor is 102.4436 So interest rate must be between 12% and 15% At r = 12%, FV is $72,052.44 at r = 15%, FV = $102,443.53 You need r that will make FV = $100,000 Annuity Interest Rate Interpolation looks at how far along the interval (72.0524 to 102.4436) 100 lies as a proportion of the whole