INTERMEDIATE ACCOUNTING I

CHAPTER 6

ACCOUNTING AND THE TIME VALUE OF MONEY

Introduction

• Time value of money.
• Accounting applications -- bonds, pensions, leases, long-term notes.
• Personal applications -- purchasing a home, planning for retirement, evaluating alternative investments.

Nature of interest

• Interest is:
• payment for the use of money
• the excess cash received or repaid over and above the principal
• rates are generally stated on an annual basis unless indicated otherwise.



• Three components of interest:
• pure rate of interest (2%-4%)
• credit risk rate of interest (0%-5%)
• expected inflation rate of interest (0%-?%)



• Simple interest.
• Interest is computed on the amount of the principal only.
• Simple interest = p x i = n where
• p = principal
• i = rate of interest for a single period
• n = number of periods



• Compound interest.
• Interest is computed on the principal and on any interest earned that has not been paid or withdrawn.
• Interest may be compounded more than once a year.



• Terminology used in compound interest problems.
• Four fundamental variables:
• Rate of interest
• Number of time periods
• Future amount.
• Present value



• Single sum and annuity problems.
• Single sum problems involve a single amount of money that either exists now or will in the future.
• Annuity problems involve a series of equal periodic payments or receipts called rents.
• Ordinary annuity - the rents occur at the end of each period.
• Annuity due - the rents occur at the beginning of each period. The first rent will occur now.
• Deferred annuity - the rents occur in the future.
• Compound interest Tables.
• Interest tables provide in the text:
• Table 6-1: Future amount of 1.
• Table 6-2: Present value of 1.
• Table 6-3: Future amount of an ordinary annuity of 1.
• Table 6-4: Present value of an ordinary annuity of 1.
• Table 6-5: Present value of an annuity due of 1.

Steps in solving compound interest problems

1. Classify the problem into one of eight types. Use the chart on the following page to identify:
1. The computation to be performed.
2. The interest to be used.



2. Determine n, the number of compounding periods, and i, the interest rate per period.

• Draw a time diagram. This is helpful when the number of periods or number of rents must be figured out from the dates given in the problem.



• If interest is compounded more than once a year--
• to find n, multiply the number of years by the number of compounding periods per year.
• to find i, divide the annual interest rate by the number of compounding periods per year.



• In annuity problems, n is equal to the total number of rents paid or received. i and R should be stated in the same basis as n. For example, if interest is compounded semiannually, then n = the number of semiannual rents paid or received, i = the annual interest rate divided by 2, and R = the amount of rent paid or received every six months.
• If either n or i is to be solved for, proceed to Step 5.
• Use n and i to choose the proper interest factor from the interest table indicated in Step 1.

3. Solve for the missing quantity by performing the computation indicated in Step 1.

4. If n or i is to be solved for:

• First perform the computation indicated in Step 1 to obtain the unknown factor.
• Then find n or i by referring to the proper interest table to locate the factor in the appropriate column or row. Interpolation may be necessary.



• Single-sum problems
• Present value is always a smaller quantity than the future amount.



• The process of finding the future amount is called accumulation. The process of finding the present value is called discounting.



• The factors in Table 6=2 are the reciprocal of corresponding factors in Table 6-1. Therefore, all single sum problems can be solved by using either Table 6-1 or 6-2. For example, if the future amount is known and the present value is to be solved for, the present value can be found:
• by multiplying the known future amount by the appropriate factor from Table 62.
• by dividing the known future amount by the appropriate factor from Table 61.



• Ordinary annuities
• Present value of an ordinary annuity is always smaller than the future amount of a similar annuity.



• The factors in Tables 6-3 and 6-4 are not reciprocals of each other.



• In annuity problems, the rents, interest payments, and number of periods must all be stated on the same basis. For example, if interest is compounded semiannually, then n = the number of semiannual rents paid or received, i = the annual interest rate divided by 2, and R = the amount of rent paid or received every 6 months.



• For the purpose of looking up interest factors, n equals the number of "periods" and is always equal to the number of rents.



• Annuities due.
• The present value of an annuity due is always smaller than the future amount of a similar annuity due.

• The future amount (present value) of an annuity due is always larger than the future amount (present value) of a similar ordinary annuity with the same interest rate and number of rents.



• Deferred annuities



• A deferred annuity does not begin to produce rents until two or more periods have expired.



• A deferred annuity problem can occur in either an ordinary annuity situation or an annuity due situation.

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