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Present Value of a Single Sum:

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1. Define and explain present value.
2. How is present value of a single sum calculated?
3. What are the uses of present value concepts?

Contents:

We can divide present value concept into two types. These are: (1) present value of a single sum and (2) present value of an annuity. In this article present value of a single sum is explained. To understand the concept of the present value of an annuity read present value of an annuity article.

Definition and Explanation:

The present value concept implies that a dollar in hand today is not equivalent to a dollar in hand at some point in future. It is because we can invest it to earn interest income and at some point in future we will have more than a dollar. Suppose \$1 is invested at 12% interest. It will grow to \$1.12 after one year because the interest is added to \$1. After second year, it will grow to \$1.2544 because the interest for the second year is calculated on \$1.12. After third year it will grow to 1.4049 as calculated below:

 At the beginning of the first year No interest \$1 At the end of the first year [\$1 + (\$1 × 12/100)] = \$1.12 At the end of the second year [\$1.12 + (\$1.12 × 12/100)] = 1.2544 At the end of the third year [\$1.2544 + (\$1.2544 × 12/100)] = 1.4049

Notice that the interest for the second year is calculated on \$1.12 - principle (\$1) plus interest for the first year (\$.12).  When interest is computed not only on the principle but also on the interest, it is called compound interest. The calculation of present value is the reverse of compounding process. The \$1 is the present value of \$1.4049 and \$1.4049 is the future value of \$1 at 12% interest rate. Thus, if the rate of interest is 12%, you would be indifferent to either \$1 today or \$1.4049 after three years.

Formula:

The present value of a single sum can be easily calculated by the the following formula:

 Where; PV = Present value FV = Future value 1/(1+i)n = Present value factor

Example:

A young man has recently received an inheritance. He wants to take a portion of inheritance and invest it for his later years. His goal is to accumulate \$300,000 in 15 years. How much of the inheritance should be invested if the money will earn 12 percent per year compounded annually?

Solution:

We want to calculate the amount of money that is required today to receive \$300,000 after 15 years at 12% interest. In other words, we want to know the present value of \$300,000 at a 12% interest rate. It is calculated as follows:

 FV = \$300,000 n = 15 i = 12% PV = \$300,000 × 0.18270* = 54,810

Uses of Present Value Concept in Business:

The present value concept is very often used in businesses to evaluate proposed projects which will generate cash flows in different periods. Today, \$20,000 of revenue is not equivalent to \$20,000 in revenue 10 years from now. Thus, businesses very often use the present value concept to translate all cash flows associated with a project into equivalent dollars at one common point in time.

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More study material from this topic:

 Methods for the evaluation of capital investment analysis Average rate of return or accounting rate of return method Cash payback method Net present value method Internal rate of return method Simple interest Future value of a single sum Future value of an annuity Present value of a single sum Present value of an annuity Qualitative consideration in capital investment analysis Capital investment analysis and unequal proposal lives Capital rationing decision process Difference between simple interest and compound interest Difference between nominal and effective interest rate Future value of \$1 table Present value of \$1 table Present value of ordinary annuity table Future value of ordinary annuity table

A D V E R T I S E M E N T

 Financial Accounting Topics Introduction to Accounting ---------------------------------------------------------------------------- Transactions and Accounting Equation ---------------------------------------------------------------------------- Analysis of Business Transactions ---------------------------------------------------------------------------- Journal, Ledger and Trial Balance ---------------------------------------------------------------------------- Accounting for Bills of Exchange ---------------------------------------------------------------------------- Special Journals ---------------------------------------------------------------------------- Cash Book ---------------------------------------------------------------------------- Bank Reconciliation Statement ---------------------------------------------------------------------------- Final Accounts ---------------------------------------------------------------------------- Work Sheet ---------------------------------------------------------------------------- Capital and Revenue Items ---------------------------------------------------------------------------- Valuation of Inventories ---------------------------------------------------------------------------- Accounts of Non-profit Making Organizations ---------------------------------------------------------------------------- Statement of Cash Flows ---------------------------------------------------------------------------- Accounting Ratios Analysis ---------------------------------------------------------------------------- Depreciation, Provisions and Reserves ---------------------------------------------------------------------------- Accounting Dictionary ---------------------------------------------------------------------------- Financial Calculators

 Managerial Accounting Topics Financial Statements ---------------------------------------------------------------------------- Cost Volume Profit Relationship ---------------------------------------------------------------------------- Variable Costing System ---------------------------------------------------------------------------- Materials and Inventory Cost Control ---------------------------------------------------------------------------- Activity Based Costing System ---------------------------------------------------------------------------- Standard Costing and Variance Analysis ---------------------------------------------------------------------------- Balanced Scorecard ---------------------------------------------------------------------------- Capital Investment Analysis/Capital Budgeting