Everyone’s probably heard the question; would you rather have $1000 today or $1000 a year from now? Clearly the same amount of money now is better than the same amount in the future, but at what value does that money in the future become more valuable than the present?
Define What Time Value of Money is:
Time Value of Money or TVM for short is the basic principle that money loses value as time goes on. This means $1,000 today is worth more than $1,000 in a month in the future. The logic behind this is that the economy is constantly growing each day causing inflation, so if that $1,000 doesn’t appreciate and grow at the same or greater rate as inflation then that $1,000 won’t have the same value or purchasing power in the future.
For example, take the classic Coca-Cola signs that advertise a bottle for 5¢. How far would that 5¢ go today compared to the past? Obviously, one couldn’t buy the same bottle of Coke now as in the past, and the same principle holds true for almost everything.
The time value of money can be thought of as a starting point and ending point, or in other terms present or future value. To get from one point to the other, two paths can be used depending on the direction. To get from present value to future value compounding is used, and when to go from future value to present value discounting is used.
Present Value (PV)
Present value can be thought of as the sum of money at the starting point of a period in time. don’t be fooled by the term, just because the term has present in it doesn’t necessarily mean that it’s the value of money right this second. The term is used to express the endpoint with the earliest time that is being considered.
An example of this case could be an analysis of an investment that would start in a month. Yes this is technically a future value of the current value of money, but it is being used as the starting point for a calculation of future value.
Future Value (FV)
Future value can be thought of the sum of money at an end point in a period of time. This value is important in understanding what type of growth the present value needs to undergo and how much present value there needs to be to have the future value.
Compounding
Compounding is the process to get from present value to future value. It is made up of rate of return or interest, and payments. Compounding is based on the idea that during a specified period a payment is made at a specified interest rate and that payment is added back into value to get the new future value. Compounding can be thought of the opposite of discounting.
NOTE: Interest rate and payment stay constant for the basic concept of time value of money. These variables can change but that gets into more complex mathematics (which I will dive into in later posts).
Discounting
Discounting can be thought of as the opposite of compounding. It is the process of getting from future value to a present value using discount rates (opportunity costs) and loss of earnings.
Time Value Function
The Time value function is an equation or formula using, n, i, pv, fv, and pmt. When any four values are known, the fifth values can be solved (PV, PMT, or FV may be zero). PV, PMT, or FV may be positive or negative, depending on the perspective n and i need to be expressed in the same terms, so if i must be an annual interest rate, then n is expressed in years. n, i and pmt were briefly touched on in the compounding and discounting definitions but their definitions are:
n (period) = is the total amount of periods compounded or discounted in the period of time between the PV and FV.
i (interest) = is the periodic interest rate or discount rate. The two most common interest rates used are APR (annual percentage rate) and APY (annual percentage yield) also known as EAR (effective annual rate).
pmt (payment) = an equal amount of money received or paid during each period (n). payments received are positive and payments paid are negative.
Types of Examples
Present to Future
- Compound a single amount to a future value, or FV.
- Compound an annuity to a future value.
- Sinking fund payments.
Future to Present
- Discount a single future amount to a present value, or PV.
- Discount an annuity to a present value.
- Determine a series of equal payments necessary to amortize a present value.
Money Now is Better than Money later:
Opportunity Cost
Is defined as the loss of potential gain from other alternatives when one alternative is chosen. It is the fact that a dollar invested today can earn interest while a dollar invested tomorrow doesn’t earn interest today. Money can’t work for you until it’s invested and earning a return on the investment through interest, and the opportunity cost of capital to an investor is the rate of return that is foregone when one form of investment is made instead of another.
Higher Purchasing Power
Purchasing power is the value of a unit of currency to buy a quantity or quality of a product/service. In simpler terms it’s how far your dollar will go. For example, in 2017 a gallon of milk went for $3.22 while in 2013 it cost $3.53 and 1913 cost .35¢. Each of these years it was the same product being sold however in different points in the economy the value of dollar changed. Usually Purchasing power decreases as time goes on since inflation takes place, but the markets do fluctuate.