Chapter 5: Time Value of Money

Perpetuity

A steam of equal payments at fixed intervals expected to continue indefinitely

Loan Payment (Formula)

Actual PMT = PITI = Princ Int + Tax + Ins

Future Value (FV)

Amount to which a single or series of cashflows will grow to over a given period of time when compounded at a given rate

Effective Annual Rate (EFF% or EAR)

Annual Rate of Interest actually being Earned, as opposed to the Quoted Rate - Also called the "Equivalent" Rate

Annuity Due

Annuity whose payments occur at the beginning of each period

Ordinary (Deferred) Annuity

Annuity whose payments occur at the end of each period

Nominal Rate

Contracted Interest Rate - Also called "Quoted" or "Stated"

Cash Flow (CFt)

Designation of a Cashflow that is not part of an Annuity

Payment (PMT)

Designation of the equal Cashflows coming at regular intervals

Compounding Means Different Rates of Interest ______

Do not Equal Each Other

If PMT does not = C/Y, P/Y, then match i to ________

EAR

EAR Formula

EAR = ( 1 + iNom/m)^(m) EAR = ( 1 + periodic rate)^(m) - 1

Continuous Compounding (Formula)

FV = PV(e^in) Where e=2.7183 Or let M be an arbitrarily large number (10,000)

Types of TVM Problems

FV Single Sum PV Singl Sum FV of Annuity - Ordinary, Due PV of Annuity - Ordinary, Due Valuation of a Perpetuity Valuation of Uneven Cashflows Compounding more often than Annually Nominal v Effective Annual Rates Amortization Schedule

Future Value of an Annuity Due (Formula)

FVAdue = FVAordinary(1+i)

Interest Rate Formula

FVn = PV ( 1 + iNom/m)^(mn) FVn = PV (1 + periodic rate)^(mn)

Future Value (Formula)

FVn = PV(1 + i)^n

FVAn

Future Value of an Annuity over N periods

Amortized Loan

Loan that is repaid in Equal Payments over its life

Semiannual Compounding

Mathematical Process of determining the final Value of a Cashflow or series of Cashflow when Interest is added twice a year

Annual Compounding

Mathematical Process of determining the final Value of a final Cashflow or series of Cashflows when Interest is added once a year

Compounding

Mathematical process of determining the final value of a single or series of cashflows when compound interest is applied

TVM Solver Componenents

N: Number of Periods I/YR: Interest Rate Per Period PV: Present Value PMT: Payment FV: Future Value

Uneven Cashflows (Calculator) Solution

NPV (Net Present Value) NPV = (Required Return, CF concurrent w/ NPV, {CF1, CF2, ect},{#Frequencies CF1, CF2, ect})

Interest Rate must match __________________

Number of Periods

Present Value (Formula)

PV = (FVn)/(1+i)^N

Continuous Discounting (Formula)

PV = FV/(e^in) = FV(e^in) Where e=2.7183 Or let M be an arbitrarily large number (10,000)

Perpetuity (Formula)

PVt = PMT(t+1)/(k-g)

Payment Period or Compounding Period dictate Calculator?

Payment Period

Loan Amortization Schedule Spreadsheet

Period | Beg Bal | Pmt | Int PMT | Princ PMT | End Bal = X + Y [ (i/m)(beg bal) ]

Annual Percentage Rate (APR)

Periodic Rate Times the Number of Periods per Year

PVAn

Present Value of an Annuity over N Periods

Discounting

Process of finding the present value of cash flow or a series of cashflows - Reverse of Compounding

Opportunity Cost

Rate of Return an investor could earn on an alternative investment of similar risk

Annuity

Series of Equal Payments at fixed Intervals for a specified number of periods

Uneven (Nonconstant) Cash Flows

Series of cash flows where the amount varies from one period to the next

Ways to Solve Cashflow Problems

Step By Step Approach - Doing each calculation individually on a timeline Formula Approach - Applying an algebraic formula to determine the change Financial Calculator Approach - Using the TVM Solver Program on a calculator Spreadsheets - Using computer programs like Excel

Amortization Schedule

Table showing precisely how a loan will be Repaid, breaking down the payments and showing what proportion pays interest (debt servicing costs) and goes towards paying down the principal

Present Value (PV)

Value today of a future single or series of cashflows

Time Line

Visual tool in managing future and present value scenarios

Begin Mode

When Calculator is set to recognize an Annuity in which Payments are made at the Beginning of a Period (Annuity Due)

End Mode

When Calculator is set to recognize an Annuity in which Payments are made at the End of a Period (Ordinary Annuity)

Compound Interest

When interest is calculated and includes prior Interest earned

Single Interest

When interest is calculated on the Principal alone