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