Business Finance - Time Value of Money Part 2: Multiple Cash Flows

Vocabulary flashcards covering uneven cash flows, annuities, perpetuities, loan amortization, interest rate perspectives, and effective annual rates.

Uneven cash flows

A payment stream consisting of varying cash flow amounts occurring across different time periods, whose total future value or present value is computed by evaluating each cash flow as an individual lump sum and summing the results.

Annuity

A series of equal cash flows occurring at regular time intervals over a specified period.

Future Value of Annuity (FVA)

The total accumulated value of a series of equal periodic payments $C$ at a future time, calculated using the formula $FVA = C \times \frac{(1+r)^t - 1}{r}$.

Present Value of Annuity (PVA)

The current lump-sum value of a stream of equal periodic cash flows $C$, calculated using the formula $PVA = C \times \frac{1 - [1 / (1+r)^t]}{r}$.

Perpetuity

An annuity that continues indefinitely without an end date, where the number of periods $t \rightarrow \text{infinity}$.

Present Value of Perpetuity (PVP)

The present value of an infinite stream of equal periodic cash flows $C$, calculated using the formula $PVP = \frac{C}{r}$.

Discount loan

A loan payment method where the borrower repays the principal and all accrued interest together in a single lump-sum payment at maturity.

Interest-only loan

A loan payment method where the borrower makes regular payments covering only interest during the loan period and pays off the entire principal at maturity.

Amortized loan

A loan payment method requiring equal periodic payments, where each payment covers the interest expense for that period and reduces the remaining principal balance.

Amortization schedule

A tabular schedule detailing the allocation of each loan payment to interest expense and principal reduction, along with the beginning and ending loan balances for each period.

Annual Percentage Rate (APR)

The annual interest rate quoted by banks and financial institutions for loans or investments.

Periodic interest rate

The interest rate charged or earned during each individual compounding period, defined as $r = \frac{APR}{m}$, where $m$ is the compounding frequency per year.

Compounding periods per year ($m$)

The frequency with which interest is applied within a year, such as $m = 1$ for annual, $m = 4$ for quarterly, $m = 12$ for monthly, or $m = 365$ for daily compounding.

Effective Annual Rate (EAR)

The true rate of return earned by a lender or the actual annual interest rate paid by a borrower accounting for compounding, calculated as EAR = \begin{pmatrix} 1 + \frac{APR}{m} \begin{pmatrix}^{(m)} - 1.

Interest rate (Lender's perspective)

The financial reward earned by a lender for postponing immediate spending.

Interest rate (Borrower's perspective)

The financial penalty paid by a borrower for spending money prior to earning it.