Time Value of Money and Fair Value Accounting. Dr Jae K. Shim
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unobservable inputs for the assets or liabilities.
Level 2 inputs are those except quoted prices included within Level 1 that are observable for the asset or liability, either directly or indirectly. Level 2 inputs include:
In the case of Level 3, unobservable inputs are used to measure fair value to the degree that observable inputs are not available. Unobservable inputs reflect the reporting company’s own assumptions about what market participants consider (e.g., risk) in pricing the asset or liability.
Financial Applications
In addition to accounting and business applications, compound interest, annuity, and present value concepts apply to personal finance and investment decisions. In purchasing a home or car, planning for retirement, and evaluating alternative investments, you will need to understand time value of money concepts. Other financial applications include determination of sinking funds--the contributions necessary to accumulate a fund for debt retirements and installment contracts--periodic payments on long-term purchase contracts or leases, periodic payments of an amortized loan, and valuations of businesses, stocks, bonds, real estate, and other financial securities.
Time Value Fundamentals
The following four variables are fundamental to all time value problems (Exhibit 1).
Exhibit 1: Fundamental Variables*
1. Rate of interest. This rate, unless otherwise stated, is an annual rate that must be adjusted to reflect the length of the compounding period if less than a year.
2. Number of time periods. This is the number of compounding periods. (A period may be equal to or less than a year.)
3. Future value. The value at a future date of a given sum or sums invested assuming compound interest.
4. Present value. The present worth of a future sum or sums discounted assuming compound interest.
* Given any two variables of 1,2,3, or 1,2,4, one can determine the third variable. Many situations will be illustrated later in the book.
Exhibit 2 depicts the relationship of these four fundamental variables in a time diagram.
Exhibit 2: The relationship of four fundamental variables
Exhibit 3 shows all the tables we will be using throughout this book.
Exhibit 3: Summary of time value tables*
* Future and present value table values are truncated to three decimal digits for simplicity. In practice, you are advised to use financial calculators or Excel to ensure maximum accuracy.
** Hereafter in this book, the terms payment and receipt will be used interchangeably. A payment by one party in a transaction becomes a receipt to the other and vice versa,
How Do You Calculate Future Values? - How Money Grows
Simple Interest
Simple interest is the interest calculated on the amount of the principal only. It is the return on (or growth of) the principal for one time period. The following equation expresses simple interest.
Interest = p x i x n
Where p = principal
i = rate of interest for a single period n = number of periods
Example 1
Barstow Electric Inc. borrows $10,000 for 3 years with a simple interest rate of 8% per year. It computes the total interest it will pay as follows.
Interest = p x i x n = $10,000 x .08 x 3 = $2,400
Compound Interest
Compounding interest means that interest earns interest. The future value of a dollar is its value at a time in the future given its present sum. The future value of a dollar is affected both by the interest rate and the time at which the dollar is received. For the discussion of the concepts of compounding and time value, let us define:
Then,
The future value of an investment compounded annually at rate i for n years is
where FVF(i,n)=T1(i,n) is the future value (compound amount) of $1 and can be found in Table 1.
Example 2
To illustrate the difference between simple and compound interest, assume that Nolan Company deposits $1,000 in the First Bank, where it will earn simple interest of 8% per year. It deposits another $1,000 in the Second Bank, where it will earn compound interest of 8% per year compounded annually. In both cases, Nolan will not withdraw any interest until 3 years from the date of deposit.
Simple interest:
$1,000 × .08 × 3 years = $240; the future value = $1,240
Compound interest:
Note: Simple interest uses the initial principal of $1,000 to compute the interest in all 3 years. Compound interest uses the accumulated balance (principal plus interest to date) at each year-end to compute interest in the succeeding year. This explains the larger balance in the compound interest account. Obviously, any rational investor would choose compound interest, if available, over simple interest. In the example above, compounding provides $20 of additional interest revenue. Simple interest usually applies only to short-term investments and debts that involve a time span of one year or less.
Example 3
You place $1,000 in a savings account earning 8 percent interest compounded annually. How much money will you have in the account at the end of 4 years?
From Table 1, the T1 for 4 years at 8 percent is 1.360. Therefore,
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