Future Value (FV)the amount an investment is worth after one or more periods FV = PV * ( 1 + i )^nAn $105 payment your bank credits to your account one year from the original investment at 5% annual interest is an example of?Future ValueSingle Period Future ValueTo compute the future value of a sum of money one year from today, you simply add the interest earned to today's cash flow Interest is earned on principalCompoundingthe process of adding interest earned every period on both the original investment and the reinvested earning.Present Valuethe amount of money you would need to deposit now in order to have a desired amount in the future EX: If the bank will pay you $105 in one year and interest rates are 5 percent, how much would you be willing to deposit now, to receive that payment in one yearFuture Value = ____________________ Present Value = _____________________Compounding DiscountingPresent Value EquationPV = FV/(1+i)^nDiscountingThe process of finding present value by reducing future values using the discount - significantly decreases the value of a future amount to the presentDiscounting over Multiple PeriodsDiscounting over multiple periods is simply the reverse of compounding over multiple periodsDiscounting with Multiple RatesA future cash flow can be discounted at different interest rates for period PV = FV / ( 1 + i per 1) * ( 1 + i per 2) * ( 1 + i per 3)Using Present Values and Future ValuesManagers find it useful to move cash flows to different points in time as they analyze investment projects, debt management, and cash flowsUse the Present Value equation to move cash flows to an _________ point in timeearlierUse the Future Value equation to move cash flows to a _________ point in timelaterRule of 72A mathematical method that can be used to show approximately how many years it will take to double your money in an investment simply by dividing 72 by the rate of interest. 72 / interest rate (not as a decimal) = # of yrsWhat to remember when doing rule of 72 calculations when finding how many years it will take to double an investment?DO NOT ENTER THE INTEREST RATE AS A DECIMAL!!Information needed for Solving for Time- starting cash flow - interest rate - future cash flow (or the amt you will need) Complex Calculation - USE CALCULATOR!Solving for time example: When interest rates are 9%, how long will it take $5,000 to double?N I/Y PV PMT FV --> CPT --> N = 8.04 years ? 9 -5000 0 10,000 Remember to enter present value as a NEGATIVE number!When working with present value, the number is going to come back ____________lowerWhen working with future value, the number is going to come back ____________higherWhen working with questions, PAY ATTENTION to what _______ you are starting and ending at !!!!!yearFuture Value of Multiple Cash FlowsThe future value of each contribution can be added together to determine worth at some future point in time Use a time line!Future Value -- Level Cash Flows Define an annuityAn annuity is a stream of level and frequent cash flows paid at the END of each time period - often referred to as an ORDINARY annuity - FVA = PMT * [ (1+i)^N - 1) / i ]Future Value -- Multiple AnnuitiesTo solve for multiple annuities, compute FV for each separately and add them togetherFuture Value -- Multiple Annuities Example Invest $100 at end of year 1 - 3 at 8% Invest $150 at end of years 4 - 5 at *%Time Line Example period 0 1 2 3 4 5 Cash Fl 0 -100 -100 -100 -100 -100 - 50 - 50 Same as FV of level cash flows calculationPresent Value -- Level Cash FlowsMost loans are set up so that the amount borrowed (the present value) is repaid through level payments made every period (the annuity) Each cash flow is the same, and the borrower pays the cash flow every periodFuture Value of an Annuity EquationFVA = Payment * Annuity CompoundingPresent Value of an Annuity EquationPVA = Payment * Annuity DiscountingPresent Value Annuity Example $ 100 payments are made at the END OF EACH YEAR for 5 years (End of each year means it is an ORDINARY ANNUITY) Interest rates are 8% per yearN I/Y PV PMT FV 5 8 ? 100 0 = -399.2710 Means if you borrow $399.27, then you must pay $100 each year to pay it all off!Present Value -- Multiple AnnuitiesWe can combine annuities to solve some present value problems with changing cash flows Find PVA for each annuity and add them togetherWhen using present value, getting the money _______ makes you more moneyupfrontPerpetuityAn annuity with cash flows that continue forever Preferred stocks are an example of perpetuities (fixed set dividend), scholarships tooAnnuities have a ______ period of time, and perpetuities ________________a set period of time go on foreverThe value of an investment is the _______________ value of all future annuity paymentspresentCannot calculate the ______________ value with perpetuities because they go on forever, so the __________________ value is infinite for perpetuitiesfuturePresent value of a perpetuityPayment / Interest RatePerpetuity Example: $2,000 scholarship, interest rate 10%, what is the present value in 5 years?$2,000 / 0.10 = $20,000Rearrange Present Value of a Perpetuity equation to get other factorsPV = Payment / i i = Payment / PV Payment = PV * iOrdinary Annuity Annuity DueOrdinary Annuity - cash flows occur at the END of every period Annuity Due - Cash flows occur at the BEGINNING of every periodFive annuity-due cash flows are essentially the same as a __________ today and a ___________________ ordinary annuitypayment today and a 4 year ordinary annuityPayments for annuity dues occur one period sooner than ordinary annuity -- which earns an extra?Period of interest it will have a higher future value than the future value of an ordinary annuity and a higher present value than the present value of an ordinary annuityMust do what in calculator when working with annuity due?Switch PMT settings to BGNFuture Value of an Annuity DueThe future value of an annuity due will simply be the future value of the ordinary annuity multiplied by (1 + i) GOING TO HAVE A GREATER VALUE THAN AN ORDINARY ANNUITY!!!!!!!!!!!Present Value of an Annuity DueThe present value of the annuity due is simply the present value of the ordinary annuity multiplied by (1 + i)Compounding FrequencyUsed in situations that do not use yearly time periods - semiannual bond payments, quarterly stock dividends, consumer loans (monthly payments)The more often you compound, the _______________ the amount will behigherAPR (Annual Percentage Rate)The interest rate per period times the number of periods in a yearEAR (Effective Annual Rate)The annual rate of interest actually paid or earned, reflecting the impact of compounding frequency. Also called the true annual return. A more accurate measurement of what you will actually pay EAR = ( 1 + APR / m ) ^m - 1When computing EARs, switching from semi-annual to quarterly makes the number?larger! More time periods means a larger number will be returnedAPR and EAR in the calculatorBorrow $100 today, 12% interest rate APR: loan compounds annually, you pay 12% EAR: loan compounds monthly, you pay 12.68% ICON over number 2 on the calculator, should say NOM = 0.0, type 12 hit enter, up arrow, type in compounding periods, enter, arrow up, compute to find EAR NOM = APRWant to buy a new car for $40,000 Pay it all off within 5 years 9.99 Interest Rate How do we find our payment?Enter it into calculator!! N I/Y PV PMT FV 60 9.99 40,000 ? 0 We get 60 from taking 5 years times 12 to get 60 months... Make sure P/Y in the calculator is set to 12!!! Hit 2nd I/Y set P/Y for 12, hit clear twiceThe difference between a 30 year loan and a 15 year loan...The 15 year loan will have a higher monthly payment, but far less interest that you will have to pay!!Amortized Loancharacterized by a borrower paying both interest and principal over time Payment = Present Value * AmortizationFinancial MarketsThe arenas through which funds flowTwo Major Market DimensionsPrimary vs Secondary Markets Money vs Capital MarketsPrimary MarketsMarkets in which corporations raise funds though new issues of securities Corporations sell the new financial instrument issues to initial fund suppliers (households) in exchange for the funds that the issuer requiresWhy do companies go public? I.E. issue stockThey do this to raise large amounts of money to put into new projects and to grow their businessIPOInitial public offering, a corporation's first offer to sell shares to the publicSecondary MarketsMarkets that trade financial instruments once they are issued NYSE (New York Stock Exchange) NASDAQ (Online, technology based exchange) Centralized marketplace -- makes it very easy to make transaction, easy to buy and sellBenefit of Secondary MarketsProvides liquidity and diversification benefits for investors, easy to get in and out of Diversification-- can have a variety of assets Security Valuation information for issuers-- provides info based on price changes, new info comes out stock prices change accordingly, shows which stocks have future growth prospects.When companies go public, do they issue all of the stock they are authorized to?NO. They only issue a fraction of how much stock they are authorized to, if the stock price grows substantially, they can issue more stock in the future to make even more money.Money MarketsTrade debt securities or instruments with maturities of less than one year (short-term liquidity issues, paying short-term day to day acquisitions)Capital MarketsTrade debt and equity instruments with maturities greater than one year (stocks, debt, long-term capital acquisition for the firm to grow)Stocks have no specified _______________, theoretically stocks can remain outstanding for ______________maturity can remain outstanding foreverForeign Exchange Marketstrade currencies for immediate (spot) or some future stated deliveryForeign Exchange RiskArises from the unknown value at which foreign currency cash flows can be converted into U.S. dollarsDerivative Secuirtyformalizes an agreement between two parties to exchange a standard quantity of an asset at a predetermined price on a specified date in the future Heavily involved with agricultural commodities, locking in a price for the crops they anticipate having, having future price certainty protecting against the downside potential but loosing out on the upsideDerivative MarketsHighly leveraged financial securities linked to underlying security Potentially high risk Used for hedging (person looking to reduce their risk and transfer it to somebody else willing to take it on) and speculatingFinancial Institutionsperform the essential function of channeling funds from those with surplus funds to those with a shortage of funds - Banks, Thrifts, Insurance Companies, Mutual FundsUnique Economic Functions Performed by FI'sMonitoring Costs - FIs act as delegated monitors, economic agents appointed to act on behalf of smaller investors in collecting information and investing funds on their behalf Liquidity and Price Risk - FIs act as asset transformers by purchasing the financial claims that fund users issue and then financing the purchase by selling secondary securities to household investorsInterest Rates Nominal Interest RatesNominal Interest Rates are observed in financial markets and most often quoted by financial news servicesLoanable Funds Theoryviews equilibrium interest rates in financial markets as a result of the supply of and demand for loanable funds Greater demand you have for funds, or the less funds available, the higher the rates are going to be Interest rate going to be affected by the interaction of supply and demandSpecific factors that affect differences in interest ratesInflation (Interest rates are always going to be higher than inflation rates) Real risk-free rate (portion that investors will demand to make sure they are not losing buying power) Default Risk Liquidity Risk Special provisions regarding the use of funds raised by a particular security issue The security's term to maturity, how long before the instrument maturesInflationThe continual increase in the price level of a standardized basket of goods and services Measured using the CPI and PPI When the price for producers supply needed to make products goes up by more than 10%, than it is passed onto customersReal Risk Free Rateis the rate that a risk free security would pay if no inflation were expected over its holding periodThe Fisher EffectThe relationship among real risk free rates (RFR) expected inflation (IP) and nominal risk free rates (i)Default Riskthe risk that a security issuer will default on that security by being late on or missing an interest or principal payment Investors demand higher interest with a higher default risk_______________________ bills are generally considered to be free of default riskU.S. Treasury Bills (T-Bills)Liquidity RiskThe risk that a security cannot be sold at a fair-market price with low transaction costs on short noticeInterest Rate on a Security reflects its relative ___________Liquidity Highly liquid assets carry the lowest interest rates (assuming all other characteristics remain the same) If a security is illiquid, investors add a liquidity risk premium (LRP) to the interest rateA security's Issuing party may attach special provisions or covenants to the security issued, and these provisions affect the __________ ______Interest Rate Examples: covenants impacting taxability, convertibility, callabilityThe term structure of interest rates, or the yield curve isa comparison of market yields on securities, assuming all characteristics except maturity are equalLonger term debt has a _____________ yield of interest than short term debthigherThree Yield-Curve Theories Unbaised ExpectationsAt any given point in time, the yield curve reflects the market's current expectations of future short-term ratesThree Yield-Curve Theories Liquidity PremiumInvestors will hold long-term maturities only if these securities with longer term maturities are offered at a premium to compensate for future uncertainty in the security's valueThree Yield-Curve Theories Market SegmentationIndividual investors and FIs have specific maturity preferences, and convincing them to hold securities with maturities other than their most preferred requires a higher interest rateForecasting Interest RatesAs interest rates rise, the value of investment portfolios of individual corporations will fall, resulting in a loss of wealth We can use the unbiased expectations theory to forecast (short-term) interest rates in the future (i.e. forward one-year interest rates)We can use the ___________ ________________ _________ to forecast (short-term) interest rates in the future (i.e., forward one-year interest rates)unbiased expectations theory

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