Time Value of Money Concepts - Flashcard set - Corporate Finance

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Present Value (PV)

The current value of a future amount of money or stream of cash flows given a specified rate of return. Formula:

PV = \frac{FV}{(1 + r)^n}

Future Value (FV)

The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. Formula:

FV = PV \times (1 + r)^n

Interest Rate (r)

The proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage of the loan outstanding. Formula: No general formula for a single value; it's a component in other formulas like PV and FV.

Compounding Frequency (n)

The number of times compounding occurs per period. More frequent compounding leads to a higher future value. Formula: Used in FV and PV formulas as an exponent.

Annuity

A series of equal payments made at regular intervals over a specified period. Formula:

PV_{\text{annuity}} = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)

Perpetuity

A type of annuity that lasts forever, i.e., infinite series of equal payments. Formula:

PV_{\text{perpetuity}} = \frac{PMT}{r}

Discount Rate

The rate used to discount future cash flows to their present value, often used in the context of bond valuation. Formula: It’s the interest rate (r) used in PV and FV formulas.

Net Present Value (NPV)

The difference between the present value of cash inflows and the present value of cash outflows over a period of time. Formula:

NPV = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0

Internal Rate of Return (IRR)

The discount rate that makes the net present value (NPV) of a project zero. Formula:

0 = \sum_{t=1}^{n} \frac{C_t}{(1 + IRR)^t} - C_0

Payback Period

The time it takes for the cash inflows from a capital investment project to equal the cash outflows, usually expressed in years. Formula: No simple formula since it's a time calculation.

Amortization

The process of spreading out a loan into a series of fixed payments over time. Formula:

PMT = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}

Effective Annual Rate (EAR)

The actual interest rate an investor earns or pays after accounting for compounding interest. Formula:

EAR = (1 + \frac{i}{n})^{n} - 1

Nominal Interest Rate

The interest rate before taking inflation into account. Formula: Not a specific formula, can be used to calculate EAR.

Inflation

The rate at which the general level of prices for goods and services is rising, and, subsequently, purchasing power is falling. Formula: Not a single formula, more a concept affecting the value of money.

Real Interest Rate

The rate of interest an investor expects to receive after allowing for inflation. Formula:

r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + \text{inflation rate}} - 1

Risk Premium

The return in excess of the risk-free rate of return that an investment is expected to yield. Formula:

\text{Risk Premium} = r_{\text{expected}} - r_{\text{risk-free}}

Time Preference

The tendency of people to prefer goods and services sooner rather than later. Formula: Implicit in the logic of PV and FV without a specific formula.

Future Value of an Annuity (FVA)

The future value of a stream of equal payments (annuity), assuming the payments are invested at a certain interest rate. Formula:

FVA = PMT \times \frac{(1 + r)^n - 1}{r}

Present Value of a Perpetuity

The value today of an infinite stream of future payments, where the payment amount is constant. Formula: Similar to a regular perpetuity PV formula:

PV_{\text{perpetuity}} = \frac{PMT}{r}

Discount Factor

A multiplier used to discount future cash flows to present value. Formula:

\text{Discount Factor} = \frac{1}{(1 + r)^n}

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