Chapter 5 Time Value of Money Concepts Intermediate Accounting 1

If the inflation rate were higher than 6%, then the

$106 you would have in the savings account actually would be worth less than the $100 you had a year earlier.

In present value problems involving annuities, there are four variables:

(1) present value of an ordinary annuity (PVA) or present value of an annuity due (PVAD), (2) the amount of each annuity payment, (3) the number of periods, n, and (4) the interest rate.

How to calculate the present value of a deferred annuity:

1. Calculate the PV of the annuity as of the beginning of the annuity period. 2. Reduce the single amount calculated in (1) to its present value as of today.

Simple interest

Computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used. For example, simple interest earned each year on a $1,000 investment paying 10% is $100 ($1000 x 10%).

PV =

FV / (1 + i)^n

FV =

I (1 + i) ^ n I = amount invested at the beginning of the period i = interest rate n = number of compounding periods

Monetary assets:

Includes money and claims to receive money, the amount of which is fixed and determinable. Examples include cash and most receivables.

Interest =

Interest rate x outstanding balance

Keys on a financial calculator defined:

N= number of periods %I= interest rate PV = present value FV = future value PMT = annuity payments CPT = compute button

Monetary liabilities

Obligations to pay amounts of cash, the amount of which is fixed or determinable. Most liabilities are monetary. For example, if you borrow money from a bank and sign a note payable, the amount of cash to be repaid to the bank is fixed.

Accountants use

PV calculations much more frequently than FV.

PV / FV =

PV table factor

Interest

The amount of money paid or received in excess of the amount borrowed or lent.

Future value (FV) of $1

The amount of money that a dollar will grow to at some point in the future. Equation: FV = $1 (1 + i)^n

Present value (PV) of $1

The amount of money today that is equivalent to a given amount to be received or paid in the future. Equation: PV = $1 / (1+i)^n

Future value of an annuity due (FVAD) of $1

The future value of a series of equal sized cash flows with the first payment taking place at the beginning of the annuity period. Equation: FVAD = [ ((1 + i)^n -1) / i ] x (1 + i)

Future value of an ordinary annuity (FVA) of $1

The future value of a series of equal-sized cash flows with the first payment taking place at the end of the first compounding period. Equation: FVA = ((1+i)^n -1) / i

Future value

The future value of a single amount is the amount of money that a dollar will grow to at some point in the future.

Present value of an annuity due (PVAD) of $1

The present value of a series of equal-sized cash flows with the first payment taking place at the beginning of the annuity period. Equation: PVAD = [ 1 - (1 / (1 + i)^n) / i] x (1 + i)

Present value of an ordinary annuity (PVA) of $1

The present value of a series of equal-sized cash flows with the first payment taking place at the end of the first compounding period. Equation: PVA = (1 - (1/(1 + i)^n)) / i

Effective interest rate

The rate at which money actually will grow during a full year.

Deferred annuity

When the first cash flow occurs more than one period after the date the agreement begins.

The first payment of an annuity due is made on the first day of the agreement,

and the last payment is made on the period before the end of the agreement.

Interest rates are typically stated as

annual rates.

Leases require the recording of an

asset and corresponding liability at the present value of future lease payments.

In an annuity due, cash flows occur at the

beginning of each period.

Monthly =

divide by 12

Semiannually =

divide by 2

Quarterly =

divide by 4

In an ordinary annuity, cash flows occur at the

end of each period.

In an annuity due, the first cash payment won't

include interest.

In an annuity due, the last cash payment will

include interest.

A common annuity encountered in practice is a

loan on which periodic interest is paid in equal amounts. For example, bonds typically pay interest semiannually in an amount determined by multiplying a stated rate by a fixed principal amount. Some loans and most leases are paid in equal installments during a specified period of time.

Pension plans are important compensation vehicles used by

many U.S. companies. These plans are essentially forms of deferred compensation as the pension benefits are paid to employees after they retire.

The time value of money means that

money can be invested today to earn interest and grow to a larger dollar amount in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now- the present value of the investment- and its $106 future value represents the time value of money.

Most monetary assets and monetary liabilities are valued at the

present value of future cash flows. In other words, we value most receivables and payables at the present value of future cash flows, reflecting an appropriate time value of money.

While the calculation of the future value of a single sum invested today requires the inclusion of compound interest,

present value problems require the removal of compound interest.

Daily computing of interest is common for

savings accounts

Compound interest Includes interest not only on the initial investment but also on

the accumulated interest in previous periods. Occurs when money is invested for multiple periods. It results in increasingly larger interest amounts for each period of the investment. The reason is that interest is then being generated not only on the initial investment amount but also on the accumulated interest earned in previous periods. For example, Cindy Johnson invested $1000 in a savings account paying 10% interest compounded annually. With compound interest at 10% annually, the $1000 investment would grow to $1331 at the end of the three-year period.

In situations when the compounding period is less than a year,

the interest rate per compounding period is determined by dividing the annual rate by the number of periods.

The higher the time value of money,

the lower is the present value of a future amount.

Four variables that are important in the process of adjusting single cash flow amounts for the time value of money:

the present value (PV), the future value (FV), the number of compounding periods (n), and the interest rate (i).

The present value of a single amount is

today's equivalent to a particular amount in the future.

Given a choice between $1000 now and $1000 three years from now,

you would choose to have the money now.