Time Value of Money Concepts - Flashcard set - Corporate Finance

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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

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.

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)

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

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

Nominal Interest Rate

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

Discount Factor

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

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

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.

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

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}

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}

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.

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

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.

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}}

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}

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.

Perpetuity

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

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

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}

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