Accounting chapter 7

List the variables in a single-sum problem.

1. Present value of single sum 2. Future value of single sum 3. Interest rate per compounding period 4. Time period or number of compounding periods

What is a deferred annuity?

A deferred annuity results from a variety of contracts where payments or receipts are delayed until a future period. For example, a company may receive annual payments of $50,000 for five years, but the payments will not begin until three years from today.

List the five primary variables of an annuity problem and explain the difference between an ordinary annuity and an annuity due.

Annuity problems can have five variables: 1. Present value 2. Future value 3. Interest rate per compounding period 4. Number of compounding periods 5. Amount of payments An annuity is a series of equal payments. For an ordinary annuity, those payments occur at the end of each period; for an annuity due, those payments occur at the beginning of each period.

You are provided with two time value of money tables. One is a present value of $1 table and one is a future value of $1 table. How can you tell which table is which type?

Because the future value of $1 is always greater than the present value of $1, the factors on the future value of $1 table are all greater than one such that the factor for one period is equal to one plus the interest rate and the factors for periods greater than one get progressively larger. Because the present value of $1 is always less than the future value of $1, the factors on the present value of $1 table are all less than one such that the factors for periods greater than one get progressively smaller.

How is the effective interest rate determined?

The effective interest rate is different from the stated interest rate when interest is compounded more frequently than yearly. First, compare the account balance (interest plus investment) at the end of the year with the beginning balance (interest plus investment) to determine the total amount of interest for the year. Then, divide that total amount of interest for the year by the beginning balance of the investment to determine the effective interest rate.

Why do accountants need to be familiar with present value concepts?

The time value of money concept is critical in several areas of accounting, particularly when valuing many of the assets and liabilities reported in the financial statements. For example, measuring assets and liabilities at fair value may require time value of money computations. Time value of money concepts determine the asset's value today based on the future cash flows it will generate. The same approach applies to determining the fair value of a liability. For example, a pension liability today can be measured using time value of money concepts and the future cash outflows a company promises to make to its employees when they retire.

You are provided with two-time value of money tables. One table provides factors for the present value of an ordinary annuity and the other provides factors for the present value of an annuity due. How can you tell which table is which type?

An ordinary annuity is an annuity where the cash flows occur at the end of the interest period and an annuity due is an annuity where the cash flows occur at the beginning of the interest period. Therefore, for any given number of periods, and a set interest rate, the present value factor for an ordinary annuity is always smaller than the corresponding present value factor for an annuity due. For the first period, the present value factor for an annuity due is always 1.0 for any interest rate while the present value factor for an ordinary annuity is always less than one (one divided by one plus the interest rate).

You are provided with two-time value of money tables. One table provides factors for the future value of an ordinary annuity and the other provides factors for the future value of an annuity due. How can you tell which table is which type?

An ordinary annuity is an annuity where the cash flows occur at the end of the interest period and an annuity due is an annuity where the cash flows occur at the beginning of the interest period. Therefore, for any given number of periods, and a set interest rate, the future value factor for an ordinary annuity is always smaller than the corresponding factor for an annuity due. For the first period, the future value factor for an annuity due is always 1 plus the interest rate for any interest rate while the future value factor for an ordinary annuity is always 1.0.

Explain how to determine the present value for any deferred, ordinary annuity by using only the table for factors of the present value of an ordinary annuity.

Assume the deferred annuity begins after d periods and is paid for n periods. First, determine the present value of an ordinary annuity of n + d periods. From this amount is subtracted the present value of an ordinary annuity of d periods. A mathematically equivalent procedure is to obtain the present value of an ordinary annuity factor for n + d periods and then subtract from that the present value of an ordinary annuity factor for d periods. This difference is multiplied by the value of each cash flow to determine the final present value of the deferred annuity.

What is the time value of money?

The time value of money concept means that a dollar received today is worth more than a dollar received at some time in the future. This statement is true because a dollar received today can be invested to provide a return.