Time Value Of Money

Introduction

The time value of money is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. The time value of money can be defined as the value of money received today instead of in the future. This is based on the premise that cash in hand today is more valuable than the same amount in the future due to its capability of earning interest. For investors, this is single most important concept in the world of finance. This paper will discuss the different financial applications of the time value of money. This paper will also describe the components of interest and highlight various methods of calculating time value of money using different interest scenarios.

Financial Applications of the Time Value of Money

Time value of money has many useful applications. One of the most important uses is that it helps to measure the trade-off in spending and saving. This can have important consequences for your personal budgeting. If market interest rates are at 5%, one may decide that the time value of money is greater in the future, and decide to invest. If rates are a meager 2%, it is easy to decide that the time value of money is higher today, and choose to spend.

In other words:

1. Is it profitable to borrow in order to invest?

2. Is a loan with a lower interest rate always best?

3. What do I need to invest right now at 8% interest in order to have $1,000,000 in 20 years?

The basic notion behind the time value of money is that a dollar received today is worth more than a dollar received tomorrow. An important caveat to this concept is that a dollar received today could be invested in order to increase its worth and purchasing power. The earlier a dollar is received, the earlier it can be put to work in the capital and financial markets to increase cash flows and net worth.

Companies, governments and individuals all compete for funds in the capital markets with companies and governments (entities) typically seeking capital through the issuance of stocks and bonds and individuals providing capital while seeking opportunities to increase the purchasing power of their dollars in the future (Block, 2004). While raising capital, entities must decide what cost is warranted to have capital available today. Specifically, an entity needs to be confident that their return on investment is greater than the cost of financing the debt. By comparing the future value of raising capital and of planned investments, the entity may determine that borrowing today to invest is worth more in the future under various scenarios. Armed with this data, the entity may make informed decisions and successfully leverage debt. For example, the City of Fairfield was able to invest bond proceeds to earn 2 percentage points more than the cost of issuing the bonds, effectively leveraging their position to create future wealth for the City.

Individuals, like corporate and government entities, must also make determinations using present and future values. Take car loans for example. By comparing the future value of 2 loans with varying terms, an individual may be surprised to learn that a 4 year loan at 7.0% costs less than a 5 year loan at 6.0% due to the power of compounding interest (over $701 difference on a $25,000 loan principle, see Exhibit A). Using present value, an individual may determine the investment required at 8% interest to have $1,000,000 in 20 years. Exhibit B demonstrates the one-time investment of $202,971 invested at 8% will equal $1,000,000 in 20 years.

Components of a Discount/interest rate

Interest rates are the "price" that lenders charge for lending their money to borrowers. There are many components to interest rates, each reflecting a form of compensation to the lender. These include real interest rate that compensates the lenders for postponing their own spending during the term of the loan, an inflation premium that compensates the lenders for the inflation they expect and liquidity risk premiums that compensates lenders for giving away risky loans such as to borrowers with questionable credit ratings.

There are two time periods that are typically important when discussing the time value of money. These are present value and future value. Present value is considered with a discount rate, or the adjustment to current dayÐŽ¦s value, and future value, that is considered with an applied interest rate. The calculations are similar but the differences are key in getting the correct answer.

Calculations for present value and future value are basically in one of four categories. Present value and future value of a fixed amount and the same for an annuity are easily determined using simple formulas. Understanding that interest can be calculated as simple or compound also becomes important when performing the final calculation. Simple interest applies when interest is paid only on the principle and not on the interest earned over time. Compound interest pays interest on the original amount and the earned accumulated interest. For an investor or a business it is more desirable to have income based on this. The opposite is true for the debtor.

The calculation for determining future value of a single amount is as follows.

FV- Future Value

PV- Present Value

i - interest rate (this is an interest rate because it is