Time Value of Money Paper
In order to understand how to deal with money the important idea to know is the time value of money. Time Value of Money (TVM) is the simple concept that a dollar that someone has now is worth more than the dollar that person will receive in the future, this is because the money that the person holds today is worth more because it can be invested and earn interest (Web Finance, Inc., 2007). The following paper will explain how annuities affect TVM problems and investment outcomes. The issues that impact TCM will also be discussed: Interest rates and compounding (with two problems), present value, future value, opportunity cost, annuities and the rule of ’72.
The idea of TVM allows managers or investors the capability to understand the advantages and future cash flow of the cost of an investment or project. TVM 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 (Getobjects.com, 2004).
“Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per period of time, usually one year” (Getobjects.com, 2004). An interest rate is a very important factor in all financial decisions. The two types of interest rates are simple and compound (Brealey, Myers ; Marcus, 2003). A simple interest rate for example, occurs when a person borrows money from a lender and he or she will have to pay the lender a fee, this fee is the simple interest rate (Brealey, Myers ; Marcus, 2003). Simple interest is normally used for a single period of less than a year, such as 30 or 60 days simple interest = p x i x n (Getobjects.com, 2004). For example, a calculation for this problem would be: Say you borrow $50,000 for 60 days at 5% simple interest per year (assuming the year is calculated at 360 days per year).
Interest = p x i x n = 50,000 x .05 x (60/360) = 416.667
A compound interest occurs when the money earns interest on itself (Brealey, Myers ; Marcus, 2003). “Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously” (Getobjects.com, 2004). So in order to understand this, another problem can be solved: $50,000 is borrowed for two years at 6% annual interest.
Interest year 1 = p x i x n = $50,000 x .06 x 1 = $3,000
Interest year 2 = (p1 + i1) x i x n = ($50,000 + $3,000) x .06 x 1 = $3,180
The total compounded interest over two years is $3,000 + $3,180 = $6,180.
Money has a time value and the value today of future cash flow is referred to as the present value (Brealey, Myers ; Marcus, 2003). The present value of a future amount is worth less the longer one waits for it (Brealey, Myers ; Marcus, 2003). “The future value is the amount of money that an investment made today (the present value) will grow to by some future date. Since money has time value, we naturally expect the future value to be greater than the present value. The difference between the two depends on the number of compounding periods involved and the interest (discount) rate” (Getobjects.com, 2004). In order to calculate each of these two formulas can be used: PV = FV 1 / (1 + i)n for present and FV = PV (1 + i)n for future; FV = Future Value, PV = Present Value, i = Interest Rate Per Period, and n = Number of Compounding Periods (Getobjects.com, 2004). Once the present value and the future value are known along with the number of periods a rate of return can be calculated.
Opportunity cost is another important concept in making financial decisions. “For example, if an asset such as capital is used for one purpose, the opportunity cost is the value of the next best purpose the asset could have been used for” (Web Finance, Inc., 2007). Opportunity cost can also be referred to as rate of return. A rate of return is the total income per period per dollar invested (Brealey, Myers ; Marcus, 2003). To do this the formula i = ( FV / PV) (1/n) -1 can be used (Getobjects.com, 2004). Opportunity cost is the benefit or cash flow forgone as a result of an action (Brealey, Myers ; Marcus, 2003).
An annuity is a sequence of equally spaced levels of cash flows (Brealey, Myers ; Marcus, 2003). Some examples are car payments, loans, mortgages, or utilities. Annuities can be set monthly, bi-monthly, weekly, quarterly or annually. “The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due” (Getobjects.com, 2004).
There are two places that annuities fall under, present and future. The present value of an ordinary annuity is the value of equally spaced payments in the future (Brealey, Myers ; Marcus, 2003). Which can be calculated as PVoa = PMT (1 – (1 / (1 + i)n)) / i PVoa = Present Value of an Ordinary Annuity, PMT = Amount of each payment, i = Discount Rate per Period, and n = Number of Periods (Getobjects.com, 2004). “The present value of an annuity due is identical to an ordinary annuity except that each payment occurs at the beginning of a period rather than at the end. Since each payment occurs one period earlier, we can calculate the present value of an ordinary annuity and then multiply the result by (1 + i) or PVad = PVoa (1+i)” (Getobjects.com, 2004).
“The future value of an ordinary annuity (FVoa) is the value that a stream of expected or promised future payments will grow to after a given number of periods at a specific compounded interest FVoa = PMT ((1 + i)n – 1) / i” (Getobjects.com, 2004). The future value of an annuity due is the same to ordinary except each payment occurs at the end. So when calculating out the (FVoa) the formula that is used is FVad = FVoa (1+i) (Getobjects.com, 2004).
The rule of ’72 is a method for estimating an investment’s doubling time, or halving time (Wikipedia, 2007).It basically is a quick way to find out how long it would take for an investment to double. “The rule of 72 is an old accounting rule. This rule tells us that if we divide the number 72 by the rate of return, say 6%, how long it will take to double the money? We use 6% because it has long been recognized as a very good long-term rate of return. If we divide 72 by 6%, we would learn that money would double in 12 years” (Dobbs, 2007).
Each aspect that is involved in TVM is very important to everyone, not just managers and investors. When making purchases such as, a home or car, or deciding on an investment it is essential to the financial decision making process to know what interest rates, present value, future value, opportunity cost, annuities and the rule of ’72 are.
Time Value of Money Paper