FIN 311 29 01 2014 22 28 00 CHAPTER 5 THE TIME VALUE OF MONEY Time value of money refers to the fact that a dollar in hand today is worth more than a dollar promised at some time in the future because it earns interest will grow to over some period of time at some given interest rate Future value FV Refers to the amount of money an investment Compounding The process of leaving your money and any accumulated interest in an investment for more than one period reinvesting the interest therefore earning interest on interest interes compuesto ple Sim FV PV 1 r t PV FV 1 r t r FV PV 1 t 1 t ln FV PV ln 1 r doubling the interest rate more than doubles the future value interest The interest is not reinvested PRESENT VALUE is the reverse if future value Instead of compounding the money forward into the future we DISCOUNT it back to the present Discounted cash flow valuation DCF calculating the present value of a future cash flow to determine its worth today Discount rate rate used to calculate the PV of future cash flows Time value of money 4 methods 1 formula 2 Tables 3 Financial calculator 4 Spreadsheets Time value of money moving cash flows through time Opportunity cost for saving or borrowing Appropriate cost of interest Variables PV present value Cash flow that occurs today At T 0 investment ex discount rate T time period in chapter 5 The time we are valuing the cash flow in chapter 6 number of cash flows in the annuity FV future value Cash flow that occurs later than today At T n R Appropiate interest rate Different names reflecting the type of FIN 311 29 01 2014 22 28 00 CHAPTER 6 DISCOUNTED CASH FLOW EVALUATION Annuity a series of equal payments made at fixed intervals for a specified number of cash flows occur at the end of each period unless you are explicitly told otherwise Ordinary annuity a level stream of cash flows for a fixed periods of time occur at periods the end of the period with an ordinary annuity the cash flows occur at the end of each period Annuity due an annuity for which the cash flows occur at the beginning of the period lease se empieza a pagar desde el mes 1 Perpetuity an annuity in which the cash flows continue forever Consol a type of perpetuity Stated interest rate the interest rate expressed in terms of the interest payment made each period Also known as the quoted interest rate Effective annual rate EAR The interest rate expressed as if it were compounded once per year Annual percentage rate APR the interest rate charged per period multiplied by the number of periods per year A pure discount loan is the simplest form of loan the borrower receives money today and repays a single limp sum at some time in the future 3 types of annuities 1 ordinary cash flows occur at the end of each period used in all formulas 2 annuity due cash flows occur at the beginning of each period 3 deferred annuity the first cash flow occurs at some point in the future Deferred annuity ordinary annuity annuity due Example 8 we prefer vestal bank because it is compounded more frequently and therefore we make more money Annual percentage rate m the number of times interest is compounded each year APR return per period m Return per period Return per period APR m EAR 1 APR m m 1 Effective annual return property accounts for compounded interest effective periodic return 1 Effective Return m s 1 APR m Where m the of times interest is compounded each year S the of times payments are made in one year The blank in the effective if we want the effective monthly return EMR s 12 if we want effective quarterly return EQR s 4 if we want the effective annual return EAR s 1 suppose m s chapter 5 annual cash flows and interest is compounded annually M 1 and s 1 Effective return APR m example 9 on notebook return Future vaue of annuity FVA CF 1 r t 1 r Present value of annuity r 1 CF t r 1 r PVA t 1 a of PV perpetuity Interest can be compounded CF r c de cuanto son los pagos To find the PV of a perpetuity we use the equation monthly semiannually quarterly daily continuously the more frequently interest is compounded the higher the effective return annually annually Payments annuities can occur semiannually chapter 7 bonds quarterly monthly daily r effective return agree with units of t therefore t r must agree annual annual mensual mensual etc standard method for all TVM problems t define how payments occur Effective periodic return 1 Effective Return APR m m s 1 cuando se usa formula los exponents siempre van de cero a un numero menos del numero de pagos osea de 0 a n 1 for calculator we always use 5 keys PV FV PMT R I Y N formulas are derived 1 ordinary annuities 2 interest rates do not change 3 annuity same cash flow m s 1 EAR APR EXAM 1 chapter 1 5 6 Weds 2 12 8 15 9 30 Review session Sunday 2 9 2 00 4 00pm no discussion sessions on wed or thurs r appropriate interest rate t 1 the time a cash flows occurs fv chapter 5 2 Annuity how many cash flows in the annuity chapter 6 E R effective periodic return depends on the unit of T example payments occur quarterly t number of quarters R effective quarterly return Text assumes interest is compounded the same way payments occur For example if payments are monthly s 12 interest is also compounded monthly m 12 If m s then E R APR m TVM 1 define T how many payments occur 2 compute appropriate E R Annuity due Excel type 1 Calculator 2nd pmt 2nd enter 2nd Cpt always change back to original mode using Ordinary annuity is the value exactly 1 period prior to getting the first cash flow same keys Chapter Multiple choice Long problems 1 5 6 Qualitative 4 0 4 Quantitative 0 3 3 2 12 18 Conflict of interest agency cost explicit vs implicit Ordinary annuity value deferred annuity value FIN311 29 01 2014 22 28 00 next part of the semester topics the more efficient the market is the easier to value Valuation 1 characteristics of the financial security we are valuing Bond a bond is a contract between two parties one is the investor and the other is a expected cash flow cf1 cf2 cf3 risk of the cash flows r or i y appropriate return on the investment risk return tradeoff riskier returns earn a higher expective return 2 TVM techniques Lump sum annuities ordinary due deferred uneven cash flows growing annuities perpetuities growing perpetuities use appropriate technique which depends on how cash flows behave CHAPTER 7 INTEREST RATES AND BOND VALUATION company or a government agency Types of bonds government bonds corporate bonds foreign bonds …