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Attention!. In Even weeks lecture starts earlier!!! At 16.00 – 18.00 in room EF. 13-15 In odd weeks at 18.10 -19.40 Midterm exam: 26. October 2010. Topic: present value calculations. Investment decisions and time value of money. „ Res tantum valet quantum vendi protest”

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**Attention!**• In Even weeks lecture starts earlier!!! • At 16.00 – 18.00 in room EF. 13-15 • In odd weeks at 18.10 -19.40 • Midterm exam: 26. October 2010. • Topic: present value calculations**Investment decisions and time value of money**„Res tantum valet quantum vendi protest” A thing is worth only what someone else will pay for it. (unknown)**Learning goals**• Discuss the role of time value in finance • Understand the concepts of future and present value • Find the future and present value of ordinary annuity • Find the present value of a perpetuity**Materials to learn from**• Lawrence J. Gitman: Principles of Managerial Finance, Addison - Wesley 10th Edition – see sharepoint: CH4 + web • http://wps.aw.com/aw_gitman_pmf_11 • Brealey and Myers: Principles of corporate Finance, West Publishing Company www.mhhe.com/business/finance Lecture material**Basic principles of finance**• Time value of money- a dollar today worth more than a dollar tomorrow • A safe dollar is worth more than a risky one**Basic idea and theories**• Theory of Present Value • Castle-in-the –air Theory**Castle-in-the-air Theory**• Baloon theory by Lord Keynes (1936) • Investor psychology • Follow others • Succesful investor: identify timepoint of building castle in the air, and buy before that point • „Tronics prosperity”**Theory of Present Value**• Theory by John B. Williams • Based on : dividends and assumes long-term decisions • Compares actual value and real value**Basics**• Yield • Rate of return • Rate of interest • Income • Maturity • Nominal/ par/face value-the principal • Future and present value • Simple interest • Compound interest**Concept of time value of money postulate**All operations with money must be compared between alternatives to find the best result. Interest rate is a simple but prominent equivalent of any change of time value of money.**Rate of return rule**• We accept investments that offer rates of return in excess of their opportunity cost of capital • Cost of capital invested: the return forgone by NOT INVESTING in other securities**Future value and present value**Changing in time value of money gets future and present nomination Getting from present value to future value is called compounding. Getting from future value to present value is called discounting.**PV and FV**• PV – cash in hand today • FV – cash received at given future date • Time line – can be used to depict the cash flows in time**Simple interest**• Presentvalue = discountfuturevalueby an appropriate interest rate • Interest rate – opportunitycost of capital • principal – amount of moneyonwhich interest is paid • Upto 1 year • PV= FV / (1+ r) • FV = PV ( 1+ r)**Where to use simple interest**• Money market instruments • Treasury bills (T-bill) • Local authority/ public utility bills • Certificate of deposit (CD) • Commercial paper (CP) • Bill of exchange • Bankers` acceptance (BA)**Money market**• Short term instruments • Pure discount securities • Contracts up to 1 year • Huge volume and vigorous competition • No physical place • Essentially for professionals ( banks,institutional investors,brokerage firms,companies) • Liquidity ( fine spreads based on interest rate of lending and borrowing) • Creditworthiness**Money market securities**• T-bills • Domestic instruments issued by governments to raise short term finance balancing cashflow • Non-interest bearing and interest-bearing, sold at discount in auction • Negotiable • Generally 13,26,52 weeks • Certificate of deposit - CD • Usually issued by banks, is simple the evidence of time deposit • Negotiable not as time deposit • Sold at discount or pay coupon • Interest payed at maturity • 30 days to 3 month or could be longer**Money market securities 2**• Commercial paper- CP • Issued by large, safe and well-known companies bypassing banks to achieve lower borrowing rates (sometimes below the bank’sprime rate) • Very short term (max 270 days, most 60days or less) • Issued at discount • Unsecured security**Money market securities 3**• Trade bill, bills of exchange, bankers’acceptance • Used by companies for trade purposes • The seller draws up a bill to the buyer to pay and asks to sign it • Could be sold at a discount to the bank • Bank’s signature is a guaranty ( eligible bills in UK the Bank of England is the guarantor)**HELP!!!**• Computational tools for finding PV and FV: • Financial tables • Financial Calculators • Computers and spreadsheets**FV**• FV = PV ( 1+ r)t • r = interest rate • PV = recent cashflow • FV = future cashflow • t = time period • FVIF= (1 + r)t • FV = PV ( FVIF) • PV = $100 • r = 10% • FV = ? • t = 1 year • t = 3 years • FV = 100 (1 + 0.10) = 110 • FV = 100 (1.10)3 = 133.**Future value and present value**(1 + r)ⁿ is a future value factor (FVF) To simplify calculations of FV use table of FVF.**Nominal and Effective Annual Rate of Interest (EAR)**• EAR = (1+ r/t )t - 1 • EAR …?…. with increasing compounding frequency**Compound Interest 1**• Invetments for more than 1 year • Contracts in the capital markets**Capital market**• Instruments • Bonds • Government bonds • Local authority papers • Mortgage or other assets backed bonds • Corporate • Foreign • Junk • Shares • Preferred • Normal • Innovations • Convertibles • Variables • Investment notes**Present Value**• PV = $125 • FV = $132 • r = ? • PV = FV / DF • DF = discount factor • DF = 1 / 1 + r • DF = PV / FV • DF = 125: 132 = 0.899**2. Future value and present value**Table of present value factor**Compound Interest 3**• DF8 = 0.285 • FV8 =CF8 = $ 596 • PV = ? • PV = FV (DF) = 596 X 0.285 = $170**Valuing more assets**• We have plenty of investments: • PV = PV1 + PV2 + PV3 + ….+ PVn**Basic patterns of cash flow**• Single amount : a lump sum amount • Annuity : A level periodic stream –fixed amount for fixed period of time • Mixed stream: stream of CF that reflects no particular pattern • Perpetuity: fixed amount of payments forever**Annuities**• Asset that pays a fixed sum each year over a specified period of time • Outflows or inflows • Expl: house mortgage, Installment credit, bond • Types: • annuity due ( CF at the begining) • Ordinary annuity ( CF at the end of each period)**Annuities 2**• End of year CF • 1 100 • 2 100 • 3 100 • 4 100 • 5 100**Annuities 3**The model of annuities present value calculation is: PVa = cf / (1 + r)¹ + cf / (1 + r)² + cf / (1+ r)³ + … + cf / (1+ r)ⁿ-1; Matematical expression: PVIFAr, t = 1 / r X ( 1 - 1/ (1 + r)t Pva = CF X PVIFA**CalculatingThe Future Value of an Annuity**• Fred wishes to determine how much money he will have at the end of 5 years, if he puts $1000 at the end of each year. • The saving account pays 7% interest per annum**Future and present value of stream of cash flow**Table of future value factor of annuity**CalculatingThe Future Value of an Annuity**• CF = $1000 • t = 5 years r = 7% FVa = CF X FVIFA FVa = CF X ∑ (1 + r )t-1 • Years amount PV • 1. 1000 1311 • 2. 1000 1225 • 3 1000 1145 • 4. 1000 1070 • 5. 1000 1000 ? 5000 5751

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