Time Value Of Money

Time Value of Money

"The time value of money is a necessary concept of finance that allows us to equate money from its present value (PV) future value (FV), present value-annuity (PVA), and future value annuity (FVA)." (Wilkipedia, 2006. Money that is deposited in a savings account earns interest, but the future value of that amount will be equal to if not less, in the future. This is the prime reason why people prefer receiving money today rather in the future. Receiving the funds today allows them to invest their money and receive a greater increase presently oppose to the future. As mentioned earlier, there are several financial applications of time value of money. We will discuss such applications below in further detail.

Future Value/Single Amount

"Future value measures what money is worth at a specified time in the future assuming a certain interest rate. This is used in time value of money calculations" (Wilkipedia, 2006). Future value with compound interest and without compound can be calculated two ways: without compound interest FV= PV x (1 + rt)/ 6050=5000 x 1 + 0.10)2. PV being the principal, t being the period of years, and r being the annual interest rate. With compound interest: FV=PV x (1 + I)n. PV being the present value, n being the number of compounding years or periods(month to month) and I being the interest rate per period.

Present Value/Single Amount

Present value is the exact opposite of the future value. The present value "of a future cash flow is the nominal amount of money to change hands at some future date, discounted to account for the time value of money). A given amount of money is always more valuable sooner then later due to the fact this enables one to take advantage of investment opportunities. Because of this, present values are smaller than corresponding future values"(Wilkipedia, 2006).

Example: (Wilkipedia, 2006)

Present Value - Single Amount

Future Amount (at the end of n periods) $10,000.00

Number of Periods (n) 7

Interest Rate Per Period (per n periods) 12.00%

The present value is: $4,523.49

Calculating an Interest Rate

Future Amount (at the end of n periods) $10,000.00

Present Value $6,000.00

Number of Periods (n) 6

The interest rate per period is: 8.89%

Calculating the Number of Periods

Future Amount (at the end of n periods) $15,000.00

Present Value $8.00

Interest Rate Per Period (per n periods) 12.00%

The number of periods is: 66.50

Discount rates

"The discount rate is the interest rate charged to commercial banks and other depository institutions on loans they receive from their regional Federal Reserve Bank's leading facility--the discount window"(FRB, 2006). This type of borrowing is to meet short-term liquidity needs of the institution. Such discount benefits the institution in various ways. For example, if TBN Network borrowed $2,000 at a discount rate of 10%. The present value of the borrow sum ($1000) discounted at 10%, would be equivalent to $1,818.18 within a year's time (2000/[1.00+0.10]). Not only will TBN save 10% at the end of the year, but also from the funds borrowed they will be able to generate additional funds as they invest in property/merchandise that will be sold throughout the given year.

Applications

Comparing investments

Suppose a manager has x$ and he has to choose between 2 alternatives like investing in a plant that brings in a certain cash flow every month or investing in financial market with a 10% return. Knowledge of time value of money will help him select the best investment.

Loans

Businesses need cash for operation and one way of obtaining cash is short term borrowing or bank loans. TVM is important in evaluating the various borrowing methods. If present interest rates are low then borrowing money from banks may turn out to be a cheaper alternative. It also gives the manager an understanding of the monthly payment that needs to be made to repay the loan. He can then match this with his predicted future cash flow and see if the company will be able to meet the payment needs.

Mortgages

This is practical for everyone and not just businesses. Suppose an individual is planning to buy a house through a mortgage then he can determine his monthly payments for the principal amount for a given interest rate. Depending on his monthly payment ability he can decide on which home to buy, down payment etc... There is also tax benefits associated with interest payments on home loan and this can be taken into account in the cash flow calculations for an individual. Using TVM he can calculate the interest payments and the principal payments for each year. For business, it can decide if it should rent or buy the office space. It can also calculate interest payments etc which should be accounted in financial statements.

Retirement savings

Since a dollar today is worth only a fraction several years later it is important to know about TVM in planning retirement savings.