# Time Value of Money Terms

An A to Z guide to the world of time value of money. Here is an explanation of many of the time value of money terms and jargon currently cropping up on a regular basis in everyday commerce and business conversation.

## Time Value of Money Terms in Alphabetical order

The glossary provides clear definitions to time value of money terms, abbreviations, and acronyms. Links with other terms make it easier for you to explore interesting topics further.

## A

### Annuity

An annuity is a series of equal periodic payments made at the end of each period. This type of annuity is also referred to as a regular or Ordinary Annuity.

### Annuity Due

An annuity due is a series of equal periodic payments made at the start of each period.

## B

### Banker’s Year

To make it easier to calculate interest, a banker’s year is based on twelve months of thirty days each resulting in a 360 day year.

## C

### Compounding

Compounding is the process of moving cash flows forward in time. Compounding converts a present value (PV) to a future value (FV).

### Compound Interest

Compound interest is interest calculated on the original lump sum plus the cumulative accrued interest at the start of the period.

### Cost of Equity

The cost of equity is the return the equity shareholders require from a business in return for providing equity capital.

The cost of equity is calculated using the dividend capitalization model.

```Cost of Equity = Dividend/Share price + Dividend growth rate
```

The dividend is the dividend per share for next year, and the share price is the market value of the share.

### Cost of Debt

The cost of debt is the effective rate a business pays on its current debt. As the cost of debt (interest expense) is allowable for tax, it is normal to use the after tax cost of debt in calculations.

The after tax cost of debt is given by the formula:

```After tax cost of debt = Cost of debt x (1 - tax rate)
```

### Coupon payments

The payments of interest that a bond issuer makes to a bondholder, usually specified as a coupon rate.

## D

### Deferred Annuity

A deferred annuity is one in which the periodic payments to the investor do not start when the investment is made, but start at some future date, normally on retirement. Investment in a deferred annuity is usually through a combination of an initial lump sum followed by periodic payments into the annuity fund.

### Discounting

Discounting is the process of moving cash flows back in time. Discounting converts a future value (FV) to a present value (PV).

### Discount Rate (i)

A discount rate is a periodic rate used to either compound a present value forward to a future value, or discount a future value backward to its present value.

## E

### e

The base of the natural logarithm (LN) ≈ 2.71828

### Effective Annual Rate (EAR)

If in a time value of money calculation compounding occurs m times a year, then the periodic discount rate (i) can be converted into an effective annual rate (EAR) using the formula below.

`EAR = (1 + i)m - 1`

For example, if the periodic discount rate is 2% (i) and the compounding period is quarterly, compounding occurs 4 times a year (m), and the effective annual rate is given as follows:

```EAR = (1 + i)m - 1
EAR = (1 + 2%)4 - 1
EAR = 8.24%
```

In this example, compounding annually at a discount rate of 8.24% is equivalent to compounding quarterly at 2%.

The effective annual rate allows comparisons to be made between discount rates with differing compounding periods.

## F

### Future Value (FV)

The future value of a lump sum received today is the value the lump sum would have in the future if it were compounded forward.

## G

### Growing Perpetuity

A growing perpetuity is a series of equal periodic payments that grow at a constant rate and continue forever.

## I

### Immediate Annuity

An immediate annuity is one which starts making periodic payments to the investor as soon as the investment is made. The periodic payments can be for a fixed period of time, referred to as period certain, of for the rest of a life (normally the investors or spouse). In addition payments can be fixed or variable depending on market performance.

### Interest

Interest is the cost paid by a borrower for the use of a lenders money.

### Internal Rate of Return (IRR)

The internal rate of return (IRR) is the discount rate which will give a net present value (NPV) of zero for a series of cash flows. If the cash flows result from an investment, it is the discount rate at which the investment breaks even.

## L

### LN

The natural logarithm, the logarithm to the base e.

## M

### MIRR

MIRR or modified internal rate of return is given by the formula

```MIRR  = (FV positive cash flows/-PV negative cash flows)(1/n) -1
```

MIRR assumes that all cash flows are reinvested at the cost of capital to the business unlike the IRR which assumes reinvestment at the projects IRR.

### Mortgage

A mortgage is an interest in a property that is transferred from a borrower (the mortgagor) to a lender (mortgagee) as security for a mortgage loan. If the borrower does not repay the loan then the lender can under certain circumstances take the property. The word mortgage itself literally means death pledge as the mortgage continues until either the loan is re-payed by the borrower or the property is subject to foreclosure and taken by the lender.

## N

### Number of Periods (n)

The number of periods (n) is one of the main variables used in time value of money calculations, and represents how many periods there are between the present value cash flow and the future value cash flow. Normally the present value is defined as being at the start of period 1 (time zero), and the future value is defined as the end of period n.

### Net Present Value (NPV)

The net present value (NPV) of a series of cash flows is found by calculating the present value of each cash flow and adding them together. The net present value indicates the magnitude of the cash flows.

## O

### Ordinary Annuity

An ordinary annuity is a series of regular payments made at the end of each period. An ordinary annuity is another name for an annuity.

## P

### Par Value of a Bond

This is the total amount a bond issuer will commit to pay back at the end of the bond maturity date. Sometimes referred to as the face value.

### Period

A period is a unit of time and can be of any length, but is typically monthly or yearly.

it is important point to remember that the discount rate (i) used in any calculations should be the rate for the same period.

### Perpetuity

A perpetuity is a series of equal periodic payments which continue forever. A perpetuity is a special case of an annuity.

### Present Value (PV)

The present value of a lump sum received in the future is the value it would have today if it were discounted back.

## R

### Rule of 72

The Rule of 72 states that if a lump sum is invested at a periodic discount rate (i), then the the number of periods (n) it takes to double the value of the investment is given by the formula:

`n = 72 / i`

Further information can be found at our Rule of 72 tutorial.

## S

### Simple Interest

Simple interest is interest calculated on the original lump sum amount.

### Structured Settlement Annuity

A structured settlement annuity (US) is an annuity used to pay out an award for legal settlements (personal injury, lottery winnings etc). The annuity is tax free and is used instead of paying out a lump sum award.

## T

### Time Value of Money

The time value of money is the concept that money today is not worth the same as money tomorrow due to the effect of discount rates.

## W

### WACC

WACC stands for the weighted average cost of capital.

A business uses both equity and debt as capital funding. The cost of capital is therefore a combination of the cost of equity and the cost of debt. Depending on how much of each type of capital is used the overall cost of capital will change.

The WACC is a method of weighting each type of capital used in proportion to the total capital of the business.

The weighted average cost of capital is given by the formula as follows:

```WACC = Cost of equity x E/(E+D) + Cost of debt x (1-tax rate) x D/(E+D)
```

Where E is the amount of equity and D is the amount of debt used by the business.