Principles of Banking and Finance: 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 timeline (“t” is the period, ranging from 0 to n where “n” is the last period).
Net Present Value (NPV): PV after deducting all the costs
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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 timeline. Single Cashflow:
Formulas FV = PV(1 + i)t PV = FV / (1+i)t i = (FV / PV)1/t – 1 .
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 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) = PMT/i.
Remember. This is just a sample.
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