Single Cashflow

1. Present Value (PV) * the value on a given date of a payment or series of payments made at other times (past or future) * Discounting from the future * Value at t=0 on a given time line (“t” is the period, ranging from 0 to n where “n” being the last period). * Net Present Value (NPV): PV after deducting all the costs

2. Future Value (FV) * The amount to which a specific sum and /or series of payments will grow on a given date in the future * Compounding (interests upon interests) * Value at t>0 on a given time line

Single Cashflow: Formulas

FV = PV(1 + i)t

PV = FV / (1+i)t i = (FV / PV)1/t – 1

Effective Interest Rate * Effective (Annual) Interest Rate (EIR) * The interest rate expressed as if it were compounded once a year. * Used to compare two alternative investments with different compounding periods * Does not include any fees incurred as part of the loan package * Nominal or Quoted Annual Interest Rate (NIR) * (periodic rate) x (number of periods per year) * The rate normally quoted in the loan agreement * All-in Rate * NIR that includes all the fees incurred as part of the loan package

Formulas: Uneven Cashflow

Even Cashflow * Annuity – series of equal payments (“PMT”) that occur at regular intervals for a period of time (“t”). * Payment is normally made at the end of the period. For payment occurs at the beginning of the period, it is Annuity Due.

Perpetuity – infinite series of equal payments

Formula: Annuities

Formula: Perpetuities

When n → ∞, PV (Perpetuity) =