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4 COMPONENTS OF FINANCE 1.Public Finance – deals with govt expenditure and income including on public projects, National Budgets and the Tax systems 2.Corporate Finance – is the financial management of assets, liabilities, revenues and expenditures in companies, often ones with numerous shareholders 3.Personal Finance – addresses financial matters of you and me, either as an individual or as a family commonly known as a household 4.These three broad areas forms an identifiable structure called the Financial system Financial System • The financial system consists of 5 components namely Financial markets, Financial Institutions, Financial Instruments/securities, Money and the Central bank 1.Financial Markets include Money Markets, Capital Markets and Foreign exchange markets 7 8 08/09/2024 5 2.Financial Institutions are Banks and Non-Bank Financial Institutions supervised by Bank of Botswana (BoB) supervisory Unit and NBFIRA respectively 3.Financial Securities are long term vs short term exchange instruments used to raise funds in the financial markets. Common examples are shares, bonds and foreign currency accounts 4.Money is the oil that lubricate the whole financial system so that it operates smoothly and is controlled by the central bank (BoB) through monetary policy 5.Central Bank – overarching authority over the financial system and is responsible for overseeing the stability and soundness of this system largely through controlling the supply of money which in turn affects demand and thus the value of a country’s currency 9 10 08/09/2024 6 Overview of Financial Management •Financial management •It is primarily about financial decisions made in a Business. •It can be defined as the acquisition, application and disbursement of funds by the organisation. •Most of these funds are acquired and used in financial markets • Many a times the whole process is facilitated by financial institutions such as brokerage and investment banking houses as this involves large sums of money 11 CORPORATE FINANCE •Financial management – Defined as the sourcing, use and distribution of funds in a company •Financial management activities and decisions fall under three broad areas of (i) financing, (ii) investment and (iii) operations i. Financing Activities – This means that a company first has to raise funds. These funds have to be raised in the most cost effective and efficient manner 11 12 08/09/2024 7 •At times one doesn’t look only at thecostof raising these funds but rather considerthe convenience in terms ofmatchingrepaymentincometo theinstalmentsto bepaid. •In some cases, supplementary features of the financing process willhave the upper hand such as less stringentconditionsof the funds beingraised •Examples of Financing activities – issuing of shares, long term Bonds or Short-term borrowing (commercial paper) 2.Investment Activities – refers to expenditure on capital assets such as Property, Plant and Equipment (PPE), independent projects and acquisition of other businesses. 13 14 08/09/2024 8 • Investment of excess funds in market securities is also included in this category 3.Operating Activities – deals with daily activities of the core business of a company in order to produce and sell its products. The main focus is in managing expenditure and generating revenue •Examples are procurement of material, payment of salaries and wages, payment of factory or warehouse rent, utilities etc Duties in Financial Management •To conduct a splendid financing process a lot goes into planning, appraisal and risk assessment •The scope of financial management is therefore quite broad. It involves: ▪Financial appraisal of business opportunities ▪Assessment of the cost-effective means of sourcing capital ▪Securities evaluation ▪Assessment of risk and returns 15 16 08/09/2024 9 Role of a financial manager The goal of financial manager: ▪Forecasting and planning for the firm’s future financial requirements. ▪Undertake investment and financing decisions. Assets must be acquired, replaced, maintained or hired and funds must be sourced to achieve these objectives. ▪Dealing with financial markets in raising funds. A financial manager needs to understand the workings of both the money and capital markets. ▪Risk management. Risk is an integral part of any business venture, be it from natural disasters or security markets. 17 Primary objective in Finance The objective of the firm : ➢Primary Goal: Maximize shareholder wealth i.e. stock price ➢Other Goals: Corporate Social Responsibility (CRS): a firm has a responsibility for the welfare of its employees, customers and the community at large. ➢This is an ethical objective that ensures a safe workplace, production of safe products and a pollution free environment respectively. ➢Other stakeholders are Creditors, Govt, Trade Unions Recent Business Trends: ➢Increased globalization of business ➢Improvements in Information Technology (IT) ➢Corporate Governance and Business Ethics 18 17 18 08/09/2024 10 Capital Formation…Fundamental Model 19 Classification of Financial Markets •Financial markets are trading places or platforms that create a conducive environment for effective capital formation and capital transfer of funds from Savings Surplus Units (SSUs) = Investors to Savings Deficit Units (SDUs) = businesses. •Overall, the role of Financial Markets is to: •bridge the gap between savings surplus units and savings deficit units (facilitates an enabling environment) •Capital formation ensure efficacy (creation of appropriate securities) •Integrity- ensure effective capital transfer (regulation, legalities, processes and procedures) 20 19 20 08/09/2024 11 ▪Types Financial Markets I. Physical vs Financial Markets 1.Physical Asset Markets ➢trade in tangible products that can be seen, touched and physically valued, e.g. equipment, computers, agricultural produce, oil, steel etc 2.Financial Asset Market ➢trade in either claims on real assets (shares, bonds, mortgages) or derivative securities (hedges on stock/economic movements)(GIY) 21 II. Money Markets vs Capital Markets a)Money Markets ➢Trade in short-term finance (normally up to 1 year) e.g. treasury bills ➢Highly liquid and marketable securities ➢Facilitate transactions between savers with temporarily idle funds and businesses temporarily short of funds (working capital) b)Capital Markets ➢Trade in long-term finance, e.g. shares, bonds, debentures (GIY) ➢Mechanism through which long-term finance is pooled and made available to corporations ➢Higher in risk and return 21 22 08/09/2024 12 III. Mortgage Markets vs Consumer Credit Markets a)Mortgage Markets ➢Markets for immovable property such as real estates –Commercial, Industrial, Residential and Land ➢Financial instruments linked to real estate (mortgages) are created by financial institutions ➢These instruments are then Securitized and traded in secondary markets b)Consumer Credit Markets ➢Personal Debt taken to purchase products for personal use and immediate consumption. ➢Examples are credit cards, personal loans, bank overdraft, auto loans 23 iv. PRIMARY VS SECONDARY MARKETS Primary Market •The shares/stock are issued by the company directly to investors •Achieved by either private placement or initial public offering (IPO)(GIY) •The company receives the funds and issues share certificates (nowadays not physical) •Funds used as start-up (IPO) or expansion capital(FPO) •New capital is formed in the economy •E.g. BTC listing 24 23 24 08/09/2024 13 Secondary Market •Trade in existing or already outstanding securities •Transaction between the security (share) holder and a third-party investor •Proceeds from the sale doesn’t accrue to the owner company V. ORGANISED EXCHANGES VS OVER THE COUNTER MARKETS(OTC) Organised Stock Market – Formal Stock exchange markets •Has physical location exchanges e.g NYSE, BSE, JSE •Tangible entities where outstanding securities are resold (nowadays done electronically) •Limited number of members (brokers) and governed by set of rules and regulations •Account for 62% of the volume of financial securities traded (by dollar volume) 26 25 26 08/09/2024 14 •Over the Counter (OTC) Stock Market •Intangible markets that trade in securities not traded in the organised exchanges •Also referred to as Dealer Markets •Has few dealers, compared to organised exchanges •Dealers hold inventory of securities and create markets for them •Uses an extensive computerised communication network, i.e. Nasdaq, Primary dealer (banks) trading in Botswana etc VI. SPOT VS FUTURES MARKETS •Spot market is where assets are bought or sold ‘on-the spot/Immediate’ delivery (normally T+2 for currency, T+3 for bonds and stocks) •Futures markets are whereby participants make an agreement today, to buy or sell an asset at a specified future date. •The deal is concluded today but the delivery is done at some future date usually 3 months or so 28 27 28 08/09/2024 15 Direct Transfer BUSINESS SAVINGS DEFICIT UNITS (SDU) SAVERS (INVESTORS) SAVINGS SURPLUS UNITS(SSU) Capital (Pula) Securities (Shares & Bonds) 29 I. Direct Transfer •Businesses (SDUs) directly solicit and acquire funds from investors •Limited capacity to raise finance •Slow process •Cuts the involvement and costs of the go-between such as an intermediary •i.e. private equity firms like CEDA, Venture Capital, unlisted credit lending 29 30 08/09/2024 16 II. Direct Transfer Through Investment Banks or brokers 31 •The security ‘passes through’ an investment bank to investors •Investment banks underwrite the issue, an assurance that the issued securities will be fully subscribed •Investment banks create conducive conditions for the successful floatation of securities and transfer of funds between businesses and investors •In Botswana this service is offered by companies like RMB 31 32 08/09/2024 17 Indirect Capital Transfer 33 Indirect Transfer Through Financial Intermediaries •financial intermediaries directly trade with both savings surplus and deficit units • in the process, Financial Intermediaries can create and float their own securities to savers to create a pool of funds •Thereafter amounts from this pool is invest in Business organisations or companies’ securities that have productive projects 33 34 08/09/2024 18 •Note, two separate security flotations could be necessary before a company finally gets its capital •Financial Intermediaries enjoy economies of scale in terms of expertise in analysing creditworthiness of potential borrowers • They also minimise the risk of its shareholders through a diverse pool of investments. •Eg Unit trusts offered by companies like Stanlib, BIFM, Afinitas, Vunani etc. 36 35 36 08/09/2024 19 Financial Institutions 1. Commercial Banks (ABSA, Stanbic, FNB, StanChart etc) •Custodians of the savers’ funds, administered through current, savings and fixed deposit accounts •Offer a wide range of consumer credit products, e.g. credit/debit cards, short/long term loans, investment packages/advice •Offer corporate financial products • In recent decades has branched to investment finance, stock brokerage, insurance, 2. Investment Banks (RMB only local company) •Help corporations design securities with features currently attractive to investors •They help companies sell their securities to investors •Also called underwriters since they guarantee that the companies will raise needed capital 37 3. Financial Services Corporations (BIHL, African Alliance etc) •Large conglomerates that combine many different financial institutions within a single corporation •Services include investment banking, brokerage operations, insurance and commercial banking •E.g. BIHL (insurance, lending, asset management), African Alliance (broking, asset management) 4. Savings and Loan Associations (BSB etc) •Receive savings from individual (small) savers and in turn lend accumulated funds to individuals and businesses through short and long term (mortgage) loans •Advantage: they make professional services on investment and make finance readily available to small savers overlooked by commercial banks, e.g. BSB 38 37 38 08/09/2024 20 5.Mutual Savings Banks •Localised financial institutions that have a depository functionary for individuals and small scale operators •The institution creates short and long-term securities for home ownership and other purposes e.g BBS 6.Credit Unions (BOPEU owned SACCOS) •Have well-defined membership •Operate at a much smaller scale 39 •Savings accumulated from periodic member contributions •Pooled funds are lent within the membership at concessionary interest rates •Credit unions are very common among labour organisations, e.g. Teachers’ Union, UBASSU 39 40 08/09/2024 21 Pension Funds (BPOPF,UBDCPF) •A pool of savings in the form of premiums is collected from members •Employers may contribute to members’ funds •Appointed fund managers oversee fund investment, creating suitable portfolios •Rules and regulations govern how the funds ought to be invested •Members are only entitled to the funds in case of occurrence of an event stipulated in the policy document or after a defined time lapse, e.g. retirement, disability or death •Member borrow short-term against their entitlements 41 8. Insurance Companies (Botswana Life, Metropolitan etc) •A pool of savings in the form of premiums is collected from members •Insurance can be life or Non-life Insurance •Non-life include Home, disability, health, auto, Professional Indemnity etc •Rules and regulations govern how the funds ought to be invested •Members are only entitled to the funds in case of occurrence of an event stipulated in the policy document or after a defined time lapse, e.g death, accident etc •Member can borrow short-term against their entitlements 41 42 08/09/2024 22 9. Mutual Funds (BIFM, IMARA, Unit Trusts etc) •Create portfolios of securities from a pool of funds invested by savers •Investors effectively invest in ‘slices’ of created portfolios, rather than individual shares or securities, i.e. Unit trusts •Small investors enjoy the benefit of diversification, and thus reduced risk •Small investors benefit from the economies of scale enjoyed by mutual funds companies 43 10. Exchange Traded Funds (ETFs) •Similar to mutual funds and often operated by mutual funds companies •EFTs buy a portfolio of stocks of a certain type (e.g. top 40 companies in JSE) and then sell their own shares to the public •ETFs are generally traded in the public markets and follow a specific index or set of securities e.g betta beta and Gold ETF in BSE •Other Examples in BW are NewFunds, NewGold, NewPlat, New Pall 43 44 08/09/2024 23 11.Hedge Funds •Similar to mutual funds in that they accept money from savers and buy various securities •Unlike mutual funds, hedge funds are largely unregulated as they target high-net-worth(HNW) individuals and institutional Investors •Used by individuals who want to hedge risks (or economic conditions) 45 12.Private Equity Companies •Examples are CEDA Venture Capital, CMA Private Equity etc •Unlike hedge funds which purchase some of the stocks, private equity firms buy entire firms •They buy and manage those entire firms •Most of the money used to buy firms is borrowed •NOTE: With exception of hedge funds and private equity companies, financial institutions are regulated to protect investors 45 46 08/09/2024 24 Exercises a. What are the key aspects involved in corporate financial management? a. Discuss the responsibilities performed by the Finance Manager or Finance Director of a listed company. a. Distinguish between: Direct capital transfer and Indirect capital transfer, with relevant hypothetical examples. b. Distinguish between: i) Money and Capital markets; ii)Primary and Secondary markets; iii) organised and over the counter (OTC) stock markets; and iv) spot and futures markets giving relevant hypothetical examples of each. c. What would you consider to be a ‘conducive economic environment’ for a business to borrow debt? Use any three of the factors that determine interest rate to explain your answer. d. How does the interest rate of short-term securities differ from that of the long-term securities issued by the Central Bank? e. A three-month BOB bond carries a nominal interest rate of 6.2%. A comparable (in Liquidity) three-month bond of a lowly rated company’s carries a nominal interest rate of 7.6%. What is the default risk premium for the company 47 Interest Rates Introduction ➢Cost of Capital: Interest Rate is a reflection of the cost of capital, and in particular is the price of borrowed debt ➢Compensation: Interest rate is a compensation paid by the borrower of funds to the lender ➢Rationing: Interest rate rations available capital funds, thereby allocating funds prudently among alternative investment opportunities i.e. profitable ventures attract most capital away from inefficient ones ➢Opportunity Cost: It represents the opportunity cost of capital 48 47 48 08/09/2024 25 Determinants of Interest Rates •Interest Rate levels in any given economy is influenced by 4 major macro economic factors that determine the supply and demand of investment capital: • Productions Opportunities – competition by way of variety of investment opportunities available in an economy stimulates a sense of eagerness and urgency, hence higher interest rates •Time Preference for Consumption - propensity for high current consumption starves savings, hence increases the price for lending. ▪Capital formation would be difficult, supply low, therefore demand is high, interest rate level would be high 49 •Risk – volatility of the returns, uncertainty about the outcome, instability of the markets. Increased risk heightens required returns (interest rate) •Rate of Inflation - the percentage amount by which prices in general, increase over time. Inflation erodes the purchasing power of money and hence an important factor to be incorporated when considering interest rates (time value of money). The expected future rate of inflation determines interest rate 50 49 50 08/09/2024 26 • Other Determinants of Interest Rates •Foreign Trade Balance - Foreign trade deficit (net-importation) requires finance and increased borrowing increases interest rates. ▪ Interest rate levels for securities held by foreign investors must remain competitive with those investors’ comparative domestic rates, otherwise there will be no economic incentive to hold (invest) •Business cycles - The general trading conditions and business activity influence the general levels of interest rates, i.e. recessions, depressions, booms and bubbles ▪Also called Troughs and Peaks of a Business Cycles when Business Expand and Contract 51 Monetary vs Fiscal Policies •Monetary Policy -Deals with the management of the supply or amount of money in the economy through the central Bank to achieve certain objectives •Central Bank Policy •Economic activity, the rate of inflation, and hence interest rates, can be controlled using money supply–Increase in money supply increases expected inflation rate, thereby pushing interest rates up–Reduction in money supply has the opposite effect–Central bank also has direct control over interest rate 52 51 52 08/09/2024 27–Short term rates are most adversely impacted by Central Bank intervention. Long-term rates may remain unchanged, or indicate slight change–Read BoB 2023 Monetary Policy Statement (MPS) (GIY – Google It Yourself) •Fiscal Policies - Deals with Govt expenditures through Treasury –Min Of Finance •Budget Deficits or Surpluses–Governments borrow to supplement budgets, thereby increasing the demand (competition) for money–Interest rates increase as a direct result of such expenditure–Debt security buy-backs reduce interest rates Nominal (Quoted) Market Interest Rate (k) •The nominal market interest rate of a security (k) is the actual interest rate that is quoted on the face of a security as charged by the lender and paid by the borrower •‘k’ will vary across situations, depending largely on the riskiness of both the security and the borrower •Determinants of nominal interest rate: •k = k* + IP + DRP + LP + MRP Or •k = krf + DRP + LP + MRP • where: krf = k* + IP 54 53 54 08/09/2024 28 Nominal vs Real risk-free Interest Rate 1. Real Risk-Free Rate of Interest (k*) •The real compensation (return) an investor demands for foregoing the use of his/her money, assuming a perfect world: •The investor is guaranteed a stipulated return, hence risk-free •Inflation-free economy 55 Nominal Risk-Free Rate (kRF) •Inflation erodes the purchasing power of money •Inflation lowers the real rate of return on an investment •Inflation Premium (IP) is the (simple) average expected inflation rate over the lifespan/duration of a security, serves the purpose of protecting returns •Inflation premium is not necessarily equal to current rate of interest •kRF is normally equated to a short-term central bank (Bank of Botswana) bond or T-bill 55 56 08/09/2024 29 3.Default risk (DRP) •The probability of a borrower being unable to service his/her debt obligations, i.e. paying principal and interest at agreed intervals •Default risk is largely influenced by the borrower’s history in debt servicing, hence rating agencies become important. Debt securities of companies rated highly carry low DRP •Central Bank debt securities carry the lowest (near zero) DRP while lowly rated companies carry the highest DRP •Effectively govt security is regarded as carrying no default risk 57 4.Liquidity Premium(LP) •Securities with weak secondary market tie-up the funds of an investor •The liquidity premium is levied depending on the marketability or liquidity of the security • Liquidity is measured by the extent to which a security is easily marketable and saleable at reasonable price on short notice in the secondary markets •This is usually influenced by the depth and breath of the security plus the features of that security such as restrictive covenants 57 58 08/09/2024 30 5. Maturity Premium(MRP) • Investing in long-term securities carries a risk that is associated with unanticipated adverse economic events that may occur with the passage of time i.e. economic/political/environmental/social events that may occur with the passage of time •The rate is to shield the investor’s returns on long-term securities from the possibility of being disadvantaged from the prospects of some unanticipated occurrence happening with the passage of time. This is also included in Central Bank long-term securities •The maturity risk premium is charged for risking capital losses due to the passage of time as a result of unexpected changes in interest rates, •Generally, the longer to maturity for a security the higher will be the maturity risk premium 59 Structure of Interest Rates- RECAP •K = Nominal or Quoted Interest rate – Reward for lending one’s funds i. K = K* - Real risk-free rate - True/Pure Compensation ▪Would be enough in a world without inflation and any other risk of loss ▪Doesn’t exist in the real world ii. K = K* + IP = Compensation for inflation → Krf - Nominal risk-free ▪Bt absolutely no other risk exposure – No company can offer that. Only Govt short-term bonds → T-Bills – come close to that iii. k = krf + DRP includes the possibility of Default ▪The possibility of default exists for all Businesses even the Blue-chip Firms iv. k = krf + DRP + LP includes a measure of liquidity ▪Marketability depends on the breadth and depth of the secondary market for the concerned security ▪It also depend on some features or conditions imposed on each security 59 60 08/09/2024 31 •k = krf + DRP + LP + MRP – finally add Maturity risk premium which is a collective name for all risks or potential calamities that can befall the investment in the interim ▪The longer the investment period the higher such risk even for govt bonds ▪Could be economic/political/social/environmental and even technological ▪Examples of Economic Calamities are Stock Market Crushes and Financial Crisis ▪Examples of Political risk are the ideological difference between Russia and Ukraine that affected many markets and industries including Confectioneries and the Energy sector ▪Examples of Social Unrest is the toppling of Sri Lanka Govt recently through Protest. •There are other examples of Social unrest in Bolivia Iraq, Sudan even Canada where the transport routes where brought to a grinding halt which affected many Business •Environmental impact can be found from the move from Coal to cleaner sources of energy. This affect coal based Business massively •Technological impact could be a Trade/Credit Union whose members were mostly concrete mixtures and Labourers being replaced by concrete mixers and other Industrial machinery. Washing Machines and Dish washers being replacing Maid Requirements etc •Artificial Intelligence and Robotics are also affecting quite a number of workplaces 61 62 08/09/2024 32 Exercise 1 63 •Gibbs, a UB graduate aged 21, has just been employed and is looking forward to moving out of his parents’ house to establish himself. Mr Oldie, on the other hand has served the government for 18 years and is starting to think of a retirement package. Based on the concept of time preferences for consumption, explain why these two individuals would potentially demand different interest rates (returns). Who would demand a higher interest rate (return) as a motivation to invest? •Answer: •Gibbs will demand a higher interest rate than Oldie in the context of the time preference for consumption because most of his income by necessity has to go towards current consumption in covering his basic necessities which includes rent and other amnesties such as grocery. •He therefore has to be incentivized by a higher margin to give up consumption •His propensity for current consumption can be measured by his � �𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 � �𝑜𝑡𝑎𝑙 𝐼𝑛𝑐𝑜𝑚𝑒 which surely exceeds that of Oldie’s 63 64 08/09/2024 33 II.Distinguish between ‘real’ and ‘nominal’ risk-free rates. •Answer: •The ‘nominal’ rate indicates that the rate includes inflation and ‘real’ indicates that the rate is net of inflation •Therefore Nominal Risk-free Rate(krf )is equal to Real Risk free(k*)plus Inflation Premium(IP) •krf = k* + IP •Real Risk-free is equals to k* . If given krf then: •k* = krf - IP III.There is a 5-year security to be offered next-year. You are informed that the current rate of inflation is 3.5% and is to be as follows in the next 5 years: 5.0%, 5.6%, 4.9%, 7.0% and 7.2%. You are required to compute the Inflation Premium for the security. •Answer: •The inflation rates that are relevant are those of the period of investment. In this case the investment occurs over the next 5 years we therefore take year 1, 2, 3, 4 and 5 65 66 08/09/2024 34 •Note that we exclude the current year’s inflation of 3.5% as it has already occurred •The answer is therefore is the average of those 5 years which is •IP = 5+5.6+4.9+7+7.2 5 =29.7 5 = 5.9% iv.Information drawn from the Central Statistics Office predicts inflation for the next 6 years as follows; 4.4%, 5.3%, 3.5%, 4.0%, 3.7% and 4.8%. The following data is available with regard to a company’s 6-year security: Real Risk-free rate 3.75% Default Risk Premium 1.25% Liquidity Premium 2.20% Maturity Risk Premium 1.45% You are required to compute the Nominal Risk-Free Rate and the Nominal Interest Rates for the company’s security. 67 68 08/09/2024 35 iv.Information drawn from the Central Statistics Office predicts inflation for the next 6 years as follows; 4.4%, 5.3%, 3.5%, 4.0%, 3.7% and 4.8%. The following data is available with regard to a company’s 6-year security: Real Risk-free rate 3.75% Default Risk Premium 1.25% Liquidity Premium 2.20% Maturity Risk Premium 1.45% You are required to compute the Nominal Risk-Free and the Nominal Interest Rates for the company’s security. •Answer: •Nominal Risk-free rate (krf ) = k* + IP • Inflation Premium(IP) = (4.4+5.3+3.5+4+3.7+4.8) 6 = 25.7 6 • = 4.3% •Nominal Risk-free rate (krf ) = k* + IP • = 3.75 + 4.3 • = 8.05% •K = krf + DRP + LP + MRP • = 8.05 + 1.25 + 2.20 + 1.45 • = 12.95% 69 70 08/09/2024 36 Exercise 5 The following data has been compiled for a security with 4 years to maturity: Nominal Risk-free rate of return 7.5% Default Risk Premium 1.75% Liquidity Premium 2.25% Maturity Risk Premium 2% The current rate of inflation is 4.75%, and that expected for the next 5 years is 4.0%, 4.2%, 4.6%, 5.0% and 5.75%. Time Value of Money •Money has time value •This means that the same amount at different time periods commands different weights in value •One Pula received today has more value than the same one Pula to be received in future •This can be considered from a number of perspectives: 1. First the amount received today can purchase more goods today than in future. •This means that if you postpone consumption today you have to be compensated by an extra amount to enable you to buy the same amount or basket of goods tomorrow 73 74 08/09/2024 38 2. On the other hand today’s value is certain whilst the amount expected in future has some degree of uncertainty •Thus the saying ‘ a bird in hand is worth more than two in the bush’. •This makes today’s same amount more valuable •From yet another dimension if you get your one pula earlier you can invest it and earn more money rather than be given the one Pula at the end of the period. •This makes one Pula earned today potentially worth more than one Pula in future •This concept of the time value of money is used to price payments from different time periods in financial management 75 Price of Money •Money like any commodity/product has a price and this price is called interest. •Interest is the compensation for loss of value or purchasing power of the future amount •This interest should atleast be just enough to compensate for loss in purchasing power •There is therefore a need to compare Today’s values with Future values 76 75 76 08/09/2024 39 PRESENT VALUES vs FUTURE VALUE •The same amount of Pulas/money occurring at different time periods have different values •These amounts have to be translated into the same time value in order to be compared •One can translate these amounts into either FUTURE VALUE or PRESENT VALUE •Risk- The present value is certain and has no risk whilst the future value is uncertain and therefore carries a certain amount of risk •In order to compare these two you use either present value(PV) or Future value(FV) computations 77 Future & Present Values •Future value (FV) is how much your money today (Present Value) will be worth in the future after growing it by a certain interest rate. •The process of going to future values from the present is called compounding. •Present value (PV) is how much your future amount (FV) is worth in today’s terms i.e assuming you were to use it now. •The process of moving from future values (FV) back to present values(PV) is called discounting. 78 77 78 08/09/2024 40 •Today’s values can be compounded (grown) to future values. •On the other hand Future Values that can be discounted (reduced) to today’s values: •Example •There are four procedures that can be used to solve time value problems.–Timelines (step-by-step approach)–Formula approach–Financial calculators &–Spread sheets–Financial tables–Statistical softwares e.g STATA, EVIEWS, SPSS ETC 85 •The future value could be for a lumpsum over a specific time period •E.g In the previous exercise a lumpsum of P40 was allowed to grow over a period of time •In certain instances, it will be a series of amounts being deposited at intervals over a certain period of time •Example, one could put P500 every month in a bank savings account •A series of payments or deposits is referred to as a cashflow or a cashflow stream •In this case each deposit will be earning interest 86 85 86 08/09/2024 44 Using Timeline to determine FVs •Lumpsum •A timeline help you to visualise what is happening in a particular problem. Refer to the illustration below. 87 1 0 3 2 PV = P200 Periods 6% Cash FV = ? •Using a timeline is a step-by-step approach in which FV & PV can be obtained depending on what information you have been given. •In the timeline illustration above we are given time periods (3 years), interest rate (6%), PV(200) and we are required to calculate FV in period 3. •To get the FV for period three you have to get the FV for period 1 and 2 first. •Basically you multiply the initial amount at each period with (1+ i) to get the FV for the next period until you get to the last FV. See the figure below. 87 88 Understanding Interest tables–In the last example where we used the Formula FVn=PV(1+i)n–The (1+i)n is called the FV interest factor (FVIF). The factor that multiplies the PVn to get the FVn. •The FVIF can be obtained from interest tables and used directly to calculate the FV given the PV, i and n. •From the interest table the FVIF is represented as FVIFi,n and is a rounded off figure. •From our example we look for FVIF6%,3 91 •FVIF6%,3 = 1.194 •FV3 = FVIF6%,3 •FV3 = 200(1.194) • = P238.80 •Formula gave P238.84 •The difference is due to rounding off errors 91 92 08/09/2024 47 •Note that you don’t divide by the PVIF but rather you multiply by the factor. Whenever you use the interest table you will always multiply by the interest factor whether it’s a FV or PV interest factor. PVIF explained •PV = 𝐹𝑉 (1+1)𝑛 • = FV x 1 (1+𝑖)𝑛 • PV = FV x PVIF Finding the interest rate(i) and and the period of investment (n) • FVn = PV(1+i)n •Once you have the PV or FV formula, given the value of any of the three variables you can always determine the value of the remaining variable from the formula. •E.g from our previous example assume in a FV calculation you know both your FV, PV and (n) to be P238.20, P200 and 3 years respectively, 108 107 108 08/09/2024 55 Annuities 115 Introduction •An Annuity is a series of equal instalments or amounts made at agreed time intervals for a specified time period. •There are two types of Annuities •Ordinary (deferred) annuity – whereby payments are made at the end of each period, e.g. loans, mortgages, Salaries, Dividends, Interest on debt etc •Annuity due (in advance) – where payments are made at the beginning of each period, e.g. rentals, medical aid, Insurance etc. 116 115 116 08/09/2024 59 FV of an Ordinary Annuity •Note that the PV of Annuity due > PV of Ordinary annuity. This is because with Annuity due, each PMT is discounted back one less year. PERPETUITIES •A perpetuity is actually an annuity but with an extended life into the future •They pay equal instalments forever, for eternity •Preferred stock dividend is an example of a perpetuity. •Other examples were the UK and US Govt Bond called Consols issued in 1751 and 1877 Respectively SEMI-ANNUAL AND OTHER COMPOUNDING PERIODS •Different securities yield returns at different intervals in a year •Bonds may be compounded semi-annually. •Bank loans may be monthly compounded. •Whilst dividends are usually compounded quarterly. •In the event of multiple periodic payments in a year also ca Conclusion •We conclude that A.The more the compounding periods in a year the greater the FV of the investment at the end of the period, and B.By extension, the higher the Total interest or return paid by the investment •This is basically a measure of effective annual rate 154 153 154 08/09/2024 78 Effective annual rate (EFF%) •Different types of investments and loans use different compounding periods (eg loans compound monthly; bonds compound semi-annually - pay Coupons twice a year); while company shares usually pay dividends quarterly). •Different compounding periods will yield different FVs & PVs for the same amount of investment even though the annual percentage rate ( APR) also called Nominal Interest rate (INOM) is the same 155 •Therefore, to compare the effect of different compounding periods each year, a common base called Effective Annual rate (EAR) or Equivalent Annual Rate (EAR) has to be determined. 155 156 08/09/2024 79 EAR •Given the Nominal Rate (iNOM) and the number of compounding periods per year, we can find the effective annual rate (EFF/EAR%). Where: •iNOM = nominal rate expressed as a decimal •M = number of compounding periods per year 157 Effective or Equivalent rate •Periodic compounding or compounding more than once in a year has been proven to provide a progressively higher return than annual compounding 158 Compounding Periodic Rate(FV) Annually 0.16 P 42,006.83 Semi-Annually 0.08 P43,178.50 Quarterly 0.04 P43,822.46 Daily 0.0004 P44,503.02 157 158 08/09/2024 80 •This means that the actual return in each instance is higher. This is referred to as the Effective Annual Rate(EAR) or Equivalent Annual Rate(EAR) EXAMPLE •Assume you have two equally risky investment options, Investment A pays 20% compounded semi-annually and Investment B pays 20.6% compounded annually. Which investment will you choose? Solution •First convert 20% semi-annual to an effective annual rate (EFF%) 160 159 160 08/09/2024 81 •Therefore we choose investment A since the 21% expected interest in annual terms for Investment A is greater than 20.6% expected for investment B. Amortisation 162 Application of Time Value of Money Concepts 161 162 08/09/2024 82 Amortised Loans •Some loans are paid off in equal instalments over time •Examples include Mortgages and automobile loans •These kind of loans are called amortised loans •The borrower often want to know the amount of the loan that remains and the interest they owe at any point in time. •To determine these details you have to create what is called a loan amortisation schedule. •Lets take an example: 163 Example •Assume a homeowner borrows P100,000 as a mortgage loan and the loan is to be repaid in five equal instalments at the end of each of the next 5 years. The loan has an annual interest rate of 6%. •Required: (a)Construct the loan amortisation schedule. (b)What is the Total interest Paid on the loan? (c)How much will be owed on the loan at the beginning and end of 5th year? 164 163 164 08/09/2024 83 Solution 1.First, we need to calculate the PMT to be paid by the borrower each year. PMTs should be such that the sum of their PVs is equals the original loan amount. i. To determine PMT: • PVOA = PMTxPVIFOA(6%,5) • PVIFOA(6%,5) = ??? • = 4.2124 • PVOA = PMTxPVIFOA(6%,5) • 165 • •100 000 = PMT(4.2124) •Solve for PMT: •PMT = 100 000 4.2124 = ??? • = P23,739.44 •You can use the formula to solve for PMT 165 166 08/09/2024 84 •Notice that this PMTs are equal and constant over time for 5 years. •This represents an annuity; it is an ordinary annuity since PMTs are made at end of each year. •Remember when using Financial tables: •PVOA = PMT*PVIFOA(i,n) 2.Next construct the payment table as shown below: Loan Amortisation Schedule 168 Amount BorrowedBWP 100 000.00 Maturity 5 years Rate 6% PMT BWP -23 739.44 YEAR BEGINNIN AMOUNT PAYMENT INTEREST PRINCIPAL REPAYMENT ENDING BALANCE 1 100 000.00 23 739.44 6 000.00 17 739.44 82 260.56 2 82 260.56 23 739.44 4 935.63 18 803.81 63 456.75 3 63 456.75 23 739.44 3 807.41 19 932.03 43 524.72 4 43 524.72 23 739.44 2 611.48 21 127.96 22 396.76 5 22 396.76 23 739.44 1 343.81 22 395.63 1.13 167 168 08/09/2024 85 YEAR BEGINNIN AMOUNT PAYMENT INTEREST PRINCIPAL REPAYMENT ENDING BALANCE (1) (2) (3) (2) X (i) = (4) (3)-(4) = (5) (2)-(5) = 6 1 100 000.00 23 739.44 6 000.00 17 739.44 82 260.56 2 82 260.56 23 739.44 4 935.63 18 803.81 63 456.75 3 63 456.75 23 739.44 3 807.41 19 932.03 43 524.72 4 43 524.72 23 739.44 2 611.48 21 127.96 22 396.76 5 22 396.76 23 740.57 1 343.81 22 396.76 0.00 Total -----118 698.3318,698.33 100 000---- Solution Conti (a)Payment Schedule is given above (b)Total interest paid = P18,698.33 (c)Beginning of year 5, P22396.76 will be owed (d)End of year 5, nothing (P0.00) owed, as the loan is fully amortised.