FIN 200 Notes PDF

07/10/2024 FIN 200: Business Finance 1 FIN 200 GROUPS 2024 Lecturer Office Tel GROUP Mr L. Bakwenabatsile 245/234 355 5679 1 Mr P.S. Pelaelo 245/212 355 5538 2...

07/10/2024 FIN 200: Business Finance 1 FIN 200 GROUPS 2024 Lecturer Office Tel GROUP Mr L. Bakwenabatsile 245/234 355 5679 1 Mr P.S. Pelaelo 245/212 355 5538 2 Dr G.N Jatty 245/209 355 2142 3 2 1  07/10/2024 Lecture Timetable: FIN 200/Lec/01 Tuesday,Thursday 10:00 AM 12:00 PM BLDG 240 ROOM 011 Jatty Monday,Wednesday, FIN 200/Lec/02 Friday 12:00 PM 1:00 PM BLDG 240 ROOM 011 Pelaelo FIN 200/Lec/03 Tuesday,Thursday 8:00 AM 10:00 AM BLDG 240 ROOM 011 Bakwenabatsile FIN 200/TUT/01 Monday 5:00 PM 6:00 PM BLDG 248 ROOM 011 Tutor 1 FIN 200/TUT/02 Tuesday 2:00 PM 3:00 PM BLDG 245 ROOM 135 Tutor 2 FIN 200/TUT/03 Wednesday 5:00 PM 6:00 PM BLDG 248 ROOM 011 Tutor 3 FIN 200/TUT/04 Thursday 5:00 PM 6:00 PM BLDG 245 ROOM 042 Tutor 4 3 Tutorials Monday 5-6PM 248/11 Tuesday 2-3PM 245/135 Wednesday 5-6PM 248/11 Thursday 5-6PM 245/42 4 2  07/10/2024 FIN 200 Statutory Supplementary Instructions Schedule 2024 Two Sessions Venues and Time Slots to be announced 5 Business Finance - Introduction Business Finance is a Finance Course It deals with the flow of funds in a Business Organisation i.e in for-profit Entities Business Finance is part of a subject called Finance Finance as a subject of study refers to the scientific management of funds in Entities The simple means the use of money in a smart and wise way manner Finance is quite a wide subject 6 3  07/10/2024 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 7 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 8 4  07/10/2024 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 9 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 10 5  07/10/2024 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 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 12 6  07/10/2024 At times one doesn’t look only at the cost of raising these funds but rather consider the convenience in terms of matching repayment income to the instalments to be paid. In some cases, supplementary features of the financing process will have the upper hand such as less stringent conditions of the funds being raised 13 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. 14 7  07/10/2024 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 15 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 16 8  07/10/2024 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 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) 18 Corporate Governance and Business Ethics 18 9  07/10/2024 Capital Formation…Fundamental Model 19 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, 20 processes and procedures) 20 10  07/10/2024 ▪ 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 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 22 11  07/10/2024 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 23 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 24 12  07/10/2024 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 25 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 26 13  07/10/2024 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 27 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 28 14  07/10/2024 Direct Transfer BUSINESS SAVERS Securities (Shares & Bonds) SAVINGS (INVESTORS) DEFICIT SAVINGS UNITS (SDU) Capital (Pula) SURPLUS UNITS(SSU) 29 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 30 15  07/10/2024 II. Direct Transfer Through Investment Banks or brokers 31 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 32 16  07/10/2024 Indirect Capital Transfer 33 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 34 17  07/10/2024 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. 35 36 36 18  07/10/2024 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 companies37 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 and38make finance readily available to small savers overlooked by commercial banks, e.g. BSB 38 19  07/10/2024 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 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 40 20  07/10/2024 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 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 42 21  07/10/2024 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 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 44 22  07/10/2024 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 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 46 23  07/10/2024 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 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 cost48of capital 48 24  07/10/2024 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 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 50 25  07/10/2024 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 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 52 26  07/10/2024 –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 53 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 54 27  07/10/2024 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 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 56 28  07/10/2024 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 carrying57 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 58 29  07/10/2024 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 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 60 30  07/10/2024 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. 61 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 62 31  07/10/2024 Exercise 1 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? 63 63 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 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 which surely exceeds that of Oldie’s 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑐𝑜𝑚𝑒 64 32  07/10/2024 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 65 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 66 33  07/10/2024 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 5+5.6+4.9+7+7.2 29.7 IP = = = 5.9% 5 5 67 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. 68 34  07/10/2024 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. 69 Answer: Nominal Risk-free rate (krf ) = k* + IP (4.4+5.3+3.5+4+3.7+4.8) 25.7 Inflation Premium(IP) = = 6 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% 70 35  07/10/2024 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%. i) Calculate the security’s inflation premium. ii) Calculate the security’s interest rate level. iii) What is the difference in interest rates between a short-term and long-term government security. iv) What is the real risk-free rate of return in this economy 71 71 (4.0+4.2+4.6+5.0) 17.8 i. IP = = 4 4 = 4.45% i. K = krf + DRP + LP + MRP = 7.5 + 1.75 + 2.25 + 2 = 13.5% 72 36  07/10/2024 iii. The main difference given that the two sets of security would be given by the same entity therefore accounting for the same financial strength and same market depth would be Maturity risk which relates to difference in investment horizon or investment period. We know that: krf = k* + IP then k* = krf - IP = 7.5 - 4.45 = 3.05% 73 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 74 37  07/10/2024 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 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 76 38  07/10/2024 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 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 78 values(PV) is called discounting. 78 39  07/10/2024 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 Suppose P40 can be able to buy a bag of oranges today but a person would need P46 to buy a bag of orange in a year’s time. 79 79 Observations: This means that P40 is the Present Value(PV) P46 is the Future Value(FV) 46 Interest Factor(1+i) = = 1.15 40 𝐹𝑉 Interest factor of a single amount(1+i)= 𝑃𝑉 80 40  07/10/2024 𝐹𝑉 If (1+i) = 𝑃𝑉 You can solve for FV-Future Value 𝐹𝑉 (1+i)x PV = x PV 𝑃𝑉 𝐹𝑉 (1+i)x PV = x PV 𝑃𝑉 PV x (1+i) = FV FV = PV(1+i) FV = 40 x 1.15 81 81 FV = P46.00 In the above example the sum of P40 is regarded as a lumpsum amount in this transaction as only a single amount is made as payment. This lumpsum amount is then allowed to grow over a period of time. In this case over a period of 12 months or 1 year Assuming constant growth of 15% the sum will grow as follows: 82 41  07/10/2024 Year 0 40 Year 1 40(1.15) = P46 Year 2 46(1.15) = P52.90 Year 3 52.90(1.15) = P60.84 ________________________________________ Also recognized the following: Year 0 = 40 Year 1 = 40(1.15) = P46 Year 2 = 40(1.15)(1.15) = P52.90 83 83 = 40(1.15)2 = P52.90 Year 3 = 40(1.15)(1.15)(1.15) = P60.84 = 40(1.15)3 = P60.84 ____________________________________ PV = P40 FVs = P46, P52.90, P60.84 etc Interest Factor(1+i ) = 1.15 = FVIF(Future Value Interest Factor) Therefore FVn = PV(FVIF)n FVn = PV(1+i )n 84 84 42  07/10/2024 Determining FVs & PVs 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, 85 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 86 43  07/10/2024 Using Timeline to determine FVs Lumpsum A timeline help you to visualise what is happening in a particular problem. Refer to the illustration below. Periods 0 1 2 3 6% Cash PV = P200 FV = ? 87 87 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. 88 44  07/10/2024 Timeline Approach 0 1 2 3 Periods 6% (1+i) P212.00 P238.20 Cash P200.00 P224.72 To get FV for Period 1-3 you compute: FV1 = P200(1+0.06) = P212.00 FV2 = P212(1+0.06) = P224.72 FV3 = P224.72(1+0.06) = P238.20 Therefore, the required FV3 = P238.20 89 89 Yearly interest earned is as follows: Year FVt Interest(i) 1 212.00 12.00 2 224.72 12.72 3 238.20 13.48 Total Interest 38.20 Interest earned each period increases because the beginning balance is higher each successive year. Total interest earned (P38.20) is reflected in the final balance (P238.20). 90 90 45  07/10/2024 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 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 92 46  07/10/2024 Understanding financial tables In the previous example of a bag of Oranges where PV was P40 and the FV1= P46, the interest factor (1 + 𝑖)𝑛 were as follows: Year 1 = (1.15) = (1+i)1 Year 2 = (1.15)(1.15) = (1.15)2 = (1+i)2 Year 3 = (1.15)(1.15)(1.15) = (1.15)3 = (1+i)3 __________________________________________________ 93 Future Value Interest Factors (FVIF) each year Year 1 = (1.15)1 = 1.15 Year 2 = (1.15)2 = 1.323 Year 3 = (1.15)3 = 1.521 ____________________________________________________________________________ Using the financial tables at 15% Column and Rows n = 1, 2 and 3 you get the same values of 1.150, 1.323 and 1.521 This implies that Financial tables are worked out from the basic compounding Process 94 47  07/10/2024 Discounting to Present Values We now know that FVn = PV(1+i)n = Compounding To discount to the PV you simply do the reverse of finding FV. From the previous equation: FVn=PV(1+i)n solve for PV. FV = PV(1+i)n 𝐹𝑉 𝑃𝑉(1+𝑖)𝑛 = (1+𝑖)𝑛 (1+𝑖)𝑛 95 95 𝐹𝑉 𝑃𝑉(1+𝑖)𝑛 = (1+𝑖)𝑛 (1+𝑖)𝑛 𝐹𝑉 Therefore = PV (1+𝑖)𝑛 𝐹𝑉 Rewritten; PV = (1+𝑖)𝑛 96 48  07/10/2024 𝐹𝑉 This is the PV formula: PV = (1+1)𝑛 All the four methods discussed earlier (step-by-step approach, formula, Financial calculator and spread sheets can be used to solve PV problems. Example A security promises to pay P238.20 at the end of 3 years. How much is it worth today. Use the formula approach to solve for the PV or fair price of this security using a discount rate of 6%. 97 97 Formula Approach 𝐹𝑉 PV = (1+𝑖)𝑛 Pv = ? FV = 238.20 n = 98 98 49  07/10/2024 3 i = 6% or 0.06 𝐹𝑉 Therefore PV = (1+𝑖)𝑛 99 99 238.20 = (1.06)3 = 199.997 = P200 100 50  07/10/2024 1. Step-by-step approach To get the PV for period zero(now) you have to get the PV for period 2 and 1 first. Basically you divide the amount at the end of each period by (1+ i) to get the PV for the previous period. See the figure below. 101 101 0 1 2 3 Periods (1+i) 6% Cash P200.00 P212.00 P224.72 P238.20 For example to get PV for Period 2-0 you compute: 102 102 51  07/10/2024 PVn-1= FVn /(1+i) PV2= P238.20/(1+0.06) = P224.72 PV1= P1224.72/(1+0.06) = P212.00 PV0 = P212.00/(1+0.06) = P200.00 Therefore the required PV0 = P200 and we have successfully discounted FV3 to the present (PV0). 103 Using Interest Table PVIF(6%,3) = ? = 0.840 PV = FVxPVIF PV = FV(1+i)-n PV = 238.20 x 0.840 104 104 52  07/10/2024 PV = P200 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. 105 PVIF explained 𝐹𝑉 PV = (1+1)𝑛 1 = FV x (1+𝑖)𝑛 106 106 53  07/10/2024 1 = FV x 𝐹𝑉𝐼𝐹 1 PVIF = 𝐹𝑉𝐼𝐹 PV = FV x PVIF 107 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, 108 108 54  07/10/2024 Calculate (i) FV3 = PV(1+i)3 238.20 = 200(1+i)3 109 Calculating “i” – the Interest rate Solve for i FV3 = PV(1+i)3 238.20 = 200(1+i)3 238.20 = (1+i)3 200 1.191 = (1+i)3 3√(1.191) = 3√(1+i)3 110 110 55  07/10/2024 1.06 = 1+i 1+i = 1.06 1+i - 1 = 1.06 -1 i +0 = 1.06 -1 i = 0.06 Therefore i = 0.06 = 6% 111 Calculating “n” – the period of investment Now, assume that you are given all values except (n) from the previous example, thus FV3 = PV(1+i)3 238.20 = 200(1.06)n Calculate (n), the number of years or Maturity of the Investment. 112 112 56  07/10/2024 Solution 238.20 = 200(1.06)n 238.20 = (1.06)n 200 1.191 = 1.06n Ln1.191 = (n)Ln1.06 0.1748 = (n)Ln1.06 0.1748 = (n)0.0583 113 113 0.1748 = n 0.0583 n = 2.998 Therefore, the period or maturity of this investment is 3 years 114 57  07/10/2024 Annuities 115 115 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. 116 116 58  07/10/2024 FV of an Ordinary Annuity Example 1 Assume that instead of 1 lump sum payment of P200, you actually deposit P200 at the end of each year for 3 years in your savings account. How much money will you have in your account at the end of 3 years, if you earn 6% interest per year. 117 117 Solution 1. Formula approach {(1+i)n −1} FVA n = PMT[ ] i {FVIFn −1} FVA n = PMT[ ] i {(1+0.06)3−1} FVOA 3 = 200x [ ] 0.06 {(1.191016)−1} FVOA 3 = 200x [ ] 0.06 118 118 59  07/10/2024 {1.191016−1} FVOA 3 = 200x [ ] 0.06 (0.191016) FVOA 3 = 200x [ 0.06 ] (0.191016) FVOA 3 = 200x [ 0.06 ] FVOA 3 = 200x 3.1836 FVOA 3 = P636.72 119 Using Financial tables FVAn = PMT(FVIFA)(i,n) FVOA = PMT*FVIFOA(6%,3) Note sometimes we use * as the multiplication sign Find the FVIFOA(6%,3) from the table FVIFOA(6%,3) = 3.1834 Apply to FVOA = 200(3.1834) = P 636.68 Note that we are able to get the FVIFA(6%,3) of 3.1834 directly from the table which is a bit quicker. 120 60  07/10/2024 FV of an Annuity Due Example 2 Assume the P200 in the previous example is deposited at the at the beginning of each period(annuity due) for three years. 1. Formula Approach FVAdue = FVA(1+i) FVAD = FVOA x(1+i) FVAD = 636.68*(1.06) = P674.88 121 121 2. Using Financial tables FVAdue = PMTxFVIFAdue(6%,3) FVAD = PMT*FVIFAD(6%,3) Find FVIFAdue(6%,3) = ? = 3.37462 122 122 61  07/10/2024 FVAD = 200(3.37462) = P674.92 Note that FVAD > FVOA, thus 674.92 > 636.68. This is because each payment occur one period earlier in the case of an annuity due, hence all of the payments earn interest for one additional period. 123 PV of an Ordinary Annuity Example 1 Assume that the series of P200 is actually deposit at the end of each year for 3 years in your savings account. How much is your account worth in today’s terms if it earns 6% interest per year. 1. Formula Approach 1 1−{ (1+i)n } PVA n = PMT [ 𝑖 ] 124 124 62  07/10/2024 1−(1+𝑖)−𝑛 PVOA n = PMT[ ] 𝑖 PVOA n = PMT [1−{ 𝑃𝑉𝐼𝐹𝑖 𝑛 , }] 𝑖 Solution PVOA n = PMT [1−{ 𝑃𝑉𝐼𝐹 𝑖𝑛 , }] 𝑖 125 1−{ 0.840} PVOA n = 200[ ] 0.06 1− 0.840 PVOA n = 200[ ] 0.06 0.16 PVOA n = 200[ ] 0.06 126 63  07/10/2024 PVOA n = [ 200 2.667 ] PVOA n = P534.40 127 You can also follow the formula by plugging in the relevant values 1 1−{ (1+i)n } PVOA n = PMT [ 𝑖 ] 1 1−{ (1+0.06)3 } PVA n = 200 [ 0.06 ] BODMAS – BRACKETS, ORDERS, DIVISION, MULIPLICATION,ADDITION AND SUBSTRACTION 128 128 64  07/10/2024 1 1−{ (1.06)3 } PVA n = 200[ 0.06 ] 1 1−{ } PVA n = 200[ 1.191016 ] 0.06 1−0.8396 PVA n = 200[ ] 0.06 129 PVOA n = 200[ ]0.1604 0.06 PVOA n = 200[2.673] PVOA = P534.60 difference due to rounding off 130 130 65  07/10/2024 2. Using Financial tables PVOA = PMT*PVIFOA(6%,3) Find the PVIFOA(6%,3 from the table = ?? PVIFOA(6%,3 = 2.673 PVOA = 200(2.673) = ? = P534.60 131 131 PV of an Annuity Due(PVAD) PVAD = PVOA*(1+i) PVAD = 534.60* 1.06 = ? = P566.68 Using Financial table: PVAD = PMT*PVIFAD(6%,3) Find PVIFAD(6%,3) = ? PVIFAD(6%,3) = 2.83339 PVAD = 200*2.83339 = P566.68 132 66  07/10/2024 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. 133 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 Perpetuities can be valued using the following formula: 𝑃𝑀𝑇 PV of a perpetuity = 𝑖 134 134 67  07/10/2024 Example Example: Assume a preference stock dividend of P2.50 per annum indefinitely. What is the PV of the perpetual dividends assuming a discount rate of 10%? Solution 𝑃𝑀𝑇 PV of a perpetuity = 𝑖 2.50 PV = 0.10 PV = P25 135 135 Example Example: Assume Preference Shares that pays dividend of P2.50 per annum indefinitely. What is the PV of the perpetual dividends assuming a discount rate of 10%? Solution 𝑃𝑀𝑇 PV of a perpetuity = 𝑖 2.50 PV = 0.10 PV = P25 136 136 68  07/10/2024 Uneven Cash Flows So far, our discussion has been based on constant (even) cash flows (CF) in the form of annuity payments. However, some situations may by nature require the use of non-constant (uneven) cash flows. For e.g common stock dividend & Cash Flow from capital projects are usually uneven and increase over time. Uneven cash flows are of two classes: 137 137 1. Constant plus a lumpsum In stream 1 the Cashflow(CFs) stream consists of annuity PMT + Additional final lump sum PMT ( e.g Bonds) 0 1 2 3 Periods i=6% Cash Flows P200.00 P200.00 P200.00 P0.00 P1000.00 P1200.00 138 138 69  07/10/2024 2. Irregular Stream In this instance the payouts are uneven or irregular streams (e.g Stocks & Capital Investments) Periods 0 1 2 3 i=6% Cash Flows P100.00 P300.00 P250.00 P0.00 139 Finding PV of Uneven Cash Flows In stream 1 consisting of Annuity PMT + Lump Sum (Bonds) 0 1 2 3 Periods i=6% Cash Flows P200.00 P200.00 P200.00 P0.00 P1000.00 P1200.00 140 140 70  07/10/2024 Solutions Calculate the PV for Stream 1 above. PV = Annuity + Lumpsum PV = PMT(PVIFOA6%,3) + Principal(PVIF6%,3) PV = 200(????) + 1000(???) PV = 200(2.673) + 1000(0.840) PV = 534.60 + 840 = P1,374.60 You can also USE A FORMULA for (PVOA +141PV) 141 2. PV of Irregular Cashflow Stream (Shares & Capital Investments) Periods 0 1 2 3 i=6% Cash Flows P100.00 P300.00 P250.00 P0.00 142 71  07/10/2024 PV of Stream 2 𝑃𝑀𝑇 𝑃𝑀𝑇 𝑃𝑀𝑇 PVn = + + (1+𝑖)𝑛−2 (1+𝑖)𝑛−1 (1+𝑖)𝑛−0 PV0 = 100/(1+0.06)1 + 300/(1+0.06)2 + 250/(1+0.06)3 PV0 = 94.34 + 267.00 + 209.90 = P571.54 143 FV of Uneven Cash Flows Calculate the FV for Stream 1 above. FV = PMT(FVIFOA(6%,3) ) + Principal FV = 200(3.1836) + 1000 FV = 636.72 + 1000 = P1,636.72 You can also use the formula to find (FVOA + Principal) 144 144 72  07/10/2024 Calculate the FV for Stream 2 FVn= PMT(1+i)n-1 + PMT(1+i) n-2 +….PMT(1+i) n-n FV3 = 100(1+0.06)2 + 300(1+0.06)1 + 250(1+0.06)0 FV3 = 112.36 +318.00 + 250 = P680.36 145 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 called periodic compounding the following two adjustments applies for any security or146loan 146 73  07/10/2024 1. Annual interest rate(i) Annual interest must be converted to a periodic rate. Stated annual rate Periodic rate(r) = number of payments per year E.g 6% annual rate becomes: 6% = 3% semi-annual 2 6% = 1.5% Quarterly 4 6% = 0.5% Monthly 147 12 147 2. Investment Period/ [Maturity of the investment] - (n) The annual periods or number of years must be converted to the correct number of periods. No. periods(n) = No. years X compounding periods per year Example: 3 years becomes : 3 x 2= 6 periods; Semi-annually 3 x 4= 12 periods; Quarterly 3 x 12 = 36 periods; Monthly 148 148 74  07/10/2024 Example P20 000 is deposited into a savings account paying 16% interest for 5 years. Compute the FV of the investment assuming the interest is compounded: i. Annually ii. Semi-annually iii.Quarterly iv.Daily (365 days in a year) 149 149 Solution i) Annually: FVn = PV(1 + i)n FV5 = 20 000(1.16)5 = 20 000(2.10034) = P 42,006.83 ii) Semi - Annually FVn = PV(1 + i)n 150 150 75  07/10/2024 0.16 1. Periodic Rate(i) = 2 = 0.08 2. No. Periods(n) = 5 x 2 = 10 FVn = PV(1 + i)n FV10 = 20 000(1.08)10 = P43,178.50 151 3)Quarterly FVn = PV(1 + i)n 0.16 Periodic Rate = = 0.04 4 No. Periods (n) = 5 x 4 = 20 FV = 20 000 (1.04)20 = P43,822.46 152 152 76  07/10/2024 iv) Daily FVn = PV(1 + i)n 0.16 Periodic Rate = = 0.0004 365 No. Periods (n) = 5 x 365 = 1,825 FV = 20 000(1.0004)1825 = 20 000 (2.2251) = P44,503.02 153 153 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 154 154 77  07/10/2024 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 155 155 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. 156 78  07/10/2024 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 157 per year 157 Effective or Equivalent rate 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 Periodic compounding or compounding more than once in a year has been proven to provide a progressively higher return than annual compounding 158 158 79  07/10/2024 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) 159 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%) 160 160 80  07/10/2024 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. 161 Application of Time Value of Money Concepts Amortisation 162 162 81  07/10/2024 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: 163 163 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? 164 164 82  07/10/2024 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) 165 165 100 000 = PMT(4.2124) Solve for PMT: 100 000 PMT = = ??? 4.2124 = P23,739.44 You can use the formula to solve for PMT 166 83  07/10/2024 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: 167 Loan Amortisation Schedule Amount BorrowedBWP 100 000.00 Maturity 5 years Rate 6% PMT BWP -23 739.44 BEGINNIN PRINCIPAL ENDING YEAR AMOUNT PAYMENT INTEREST REPAYMENT 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 1.13 168 168 84  07/10/2024 PRINCIPAL ENDING YEAR BEGINNIN AMOUNT PAYMENT INTEREST REPAYMENT 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 ----- 118 698.33 18,698.33 100 000 ----- 169 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. 170 170 85  07/10/2024 TIME VALUE OF MONEY (TVM) CONCLUSION WHAT IS FINANCE It is a scientific/methodological/systematic or structured approach to managing large sums of money. The primary objective being to maximize the wealth of the owner. In business this requires that the share price of the company be maximized This is achieved through either; 171 171 Maximising the return/profitability of an organisation or Minimising its costs It involves making decisions about the best alternative options Such decisions are premised/based upon three fundamental principles of TYM, viz; 172 86  07/10/2024 Fundamental Principles of TVM 1. MORE VALUE IS PREFERABLE OVER LESS P100 now vs P70 now 2. THE SOONER CASH IS RECEIVED THE MORE VALUABLE IT IS ♦Prefer to receive cash now than at end of year, because; ♦You can buy more with it before prices of goods increase ♦ You can reinvest it and, earn interest for the rest of the year. 173 173 ♦Or the person/(organisation) that had promised you the money may become bankrupt or cease to exist 3. LESS RISKY ASSETS ARE MORE VALUABLE. THESE ARE Shares vs Bonds vs Money Market Instruments vs Cash 174 87  07/10/2024 Additional Principles of Finance 4. Higher returns are expected for taking on more risk 5. Financial Markets are fairly efficient in pricing Securities – EMH: Weak, Semi-strong and strong form Example of EMH Suppose a security of a company is selling for P1000 and promises to pay 10% interest. This means that the interest amount is 1000 x 0.10 = P100 175 175 100 The rate of return is = 0.10 or 10% 1000 The above is the current or going market rate of the bond If the price of the bond falls in the next year due to unfavorable market conditions say to P800, what will be the new rate of return? 176 88  07/10/2024 100 It will be = 0.125 or 12.5% 800 This is a clear indication that whenever the risk of a security increases due to unfavorable conditions, its price will fall which results in a rise in its going market rate 177 The higher market rate is a reflection of an increase in risk 4. Investing in different kinds of securities spread the risk through a process known as diversification This simply means avoid putting your eggs in one basket 178 89  07/10/2024 4. The primary objective in finance is always to maximise shareholders wealth by maximising profit or share price But Managers and Shareholders’ objectives may differ creating an agency problem 179 TVM CONCLUSION (CONT) TVM CONCEPT - when making decisions you have got to compare “like with like” - thus you must restate/translate all the cashflows that you are comparing to a single reference point in time; either “t=0” (present value) or “t=n” (future value) - to achieve this, we use the time value of money concepts 180 180 90  07/10/2024 TVM CONCLUSION (CONT) This TVM Concept is used to move the value of money across time to bring it to a single reference point/date, viz; 1. MOVING A LUMPSUM PAYMENT BACK (PV via discounting) OR FORWARD (FV via compounding) 2.MOVING THE VALUE OF A SERIES OF EQUAL CASHFLOWS RECEIVED OVER A SPECIFIED PERIOD, TO A REFERENCE DATE -DISCOUNTING (PV) vs COMPOUNDING (FV) - FOR ORDINARY ANNUITY VS ANNUITY DUE 3. FINDING THE VALUE OF AN UNENDING/PERPERTUAL, CONSTANT-VALUE, SERIES OF PAYMENTS -PV of a PERPETUITY -WHERE “n=infinity” 181 181 TVM CONCLUSION (CONT) 4. FINDING THE FUTURE/PRESENT VALUES OF AN UNEVEN STREAM OF CASHFLOWS/PAYMENTS -Getting the Summation of the Present Values of Each one of the Cashflows -(you might sometimes identify annuities within the series; which can make your calculations/work a lot more easier) 182 182 91  07/10/2024 TVM CONCLUSION (CONT) 4 METHODS OF SOLVING TVM PROBLEMS –1. CASHFLOW TIMELINE METHOD –2. EQUATION (FORMULA) METHOD –3. FINANCIAL TABLES –4. USING TECHNONOLGY – financial calculator and spreadsheet 183 183 TVM CONCLUSION (CONT) -TVM is also used to quantify the true expected cost/return of a loan/investment, at t=0, regardless of how many times interest is compounded per year. - APR (simple/nominal rate) vs Effective Annual Rate - APR vs EAR -LOAN ARMORTISATION SCHEDULE -a schedule of a series of equal loan repayments, broken down into the principal and interest repayment components - (the longer the repayment period the more interest the borrower pays to the bank in money terms) 184 184 92  07/10/2024 The Basics of Capital Budgeting 185 Capital Budgeting A capital budget is a plan for resources required to acquire and operate Capital Assets Simple put, it is a list of all the Projects and long-term Assets that a company will need to acquire over a certain period of time Capital Assets basically refers to those assets that are used to produce other assets and benefits including investments in other companies 186 93  07/10/2024 This is in contrast to consumables such as office supplies like as pen, pencils, envelopes, paper etc that are exhausted in during the period of operations The plan or budget will depend on the objective of the company, the resources it has and the strategies in place. Therefore Capital budgeting is a plan to select certain projects and capital assets in line with the aims and capabilities of each company It is intended to grow the business and sustain it 187 Types of Capital budget Items Replacement Projects The replacement projects help to maintain normal operation. They may be projects to repair, replace, or rehabilitate existing buildings, machinery, and equipment. The projects aim to maintain current operating levels. Examples are a manufacturer replacing their production machine with a new one or a transportation company replaces its operating vehicle with a new one. This is general a routine review and replacement but some can be more complex if they are high tech items 188 94  07/10/2024 Expansion projects The expansion project aims to increase the business size. For example, a company builds a new factory. This contributes to increasing the production capacity Other examples are building warehouses in multiple areas, Building a new hotel in a strategic location etc Expansion projects are more complex and expensive than replacement projects. A more detailed analytical review is usually required. 189 New product line and services projects Projects to develop new products and services are highly uncertain Requires a detailed Research and development Example is Engen venturing into Quick shops and property market Walmart taking over the food processor Proctor and Gamble and 3M’s manufacture of over 600 000 products including protective equipment 190 95  07/10/2024 Regulatory, safety, and environmental projects Companies sometimes launch new projects to meet government regulations or environmental requirements. The project may not contribute to revenue. Instead, it may provide other benefits, such as avoiding penalties and compromising reputation At other times these are projects undertaken to allow the company to undertake other income-generating projects undertaken by the company. Such example will be a company with a filling station which attracts strict regulation running voluntary firefighting crash courses may be an added advantage 191 Additional notes - REcap New investments such as a new subsidiary or division to a company Moving into a new sector or Industry such as an Aviation Company adding the hospitality or Hotels Industry Even buying or hiring or maintain (old) machinery and equipment or upgrading an entire software program A firm’s growth and its ability to remain competitive depend on a constant flow of ideas for new products, new ways to make existing products better, ways to produce output at a lower cost and even venturing out into other sectors. Procedures must be established for evaluating the worth of such projects. 192 96  07/10/2024 What is Capital Budgeting? The process of planning and evaluating expenditures on assets whose cash flows are expected to extend beyond one year –Analysis of potential additions to fixed assets –Long-term decisions which involve large expenditures –Analysis of replacement of existing equipment or processes –Very important to the firm’s future 193 Project Classifications 1. Replacement Decisions: whether to purchase capital assets to take the place of existing assets to maintain or improve/upgrade existing operations 2. Expansion Decisions: whether to purchase capital assets and add them to existing assets to increase existing operations (grow the firm) 3. New Product Line or Services – Here the company will be expanding into new markets using the strength of its brand and experience of running an enterprise 4. Safety, Health and Environmental Projects (SHE) – These are compliance projects meant to meet safety, non pollution or health protocols. 194 97  07/10/2024 Other classification of Projects 4. Independent Projects: Projects whose cash flows are not affected by decisions made about other projects There is no competition between these projects 5. Mutually Exclusive Projects: A set of projects where the acceptance of one project means the others cannot be accepted Here there is competition for only one place 195 Normal and non-normal cash flow streams The cash flow of projects under the capital budgeting process falls under two categories: Conventional cash flow stream – Cost (negative CF) followed by a series of positive cash inflows. One change of signs. 0 1 2 3 Project x CFt -100 10 60 80 196 98  07/10/2024 Unconventional cash flow stream – Two or more changes of signs. Most common: Cost (negative CF), followed by a string of positive CFs, and finally cost to close project. Nuclear power plant, strip mine, etc. 0 1 2 3 Project x CFt -100 30 80 -10 197 Steps in capital budgeting 1. Estimate the cash flows expected from the project. 2. Evaluate the riskiness of cash flows. 3. Determine the appropriate cost of capital 4. Compute the present value of the expected cash flows to obtain an estimate of the asset’s value to the firm. 5. Compare the present value of the future expected cash flows with the initial investment. 198 99  07/10/2024 Capital Budgeting Criteria We are going to consider 5 different methods of Capital Budgeting: 1. Regular Payback Period 2. Discounted Payback Period 3. Net Present Value (NPV) 4. Internal Rate of Return (IRR) 5. Modified Internal Rate of Return (MIRR) 199 Regular Payback Period The length of time it takes to recover the original cost of an investment f