In the previous section, we learned about the time value of money using a relatively simple model. In reality, there are more factors that affect the value of a potential investment. These factors will be described briefly in the following section.

In the previous example, we were blending the concept of “inflation” with another concept called “discount rate”. **Inflation** is how the price of goods generally increases, and can be an appropriate substitute for figuring out the future value of money. However, “discount rate”, is a term which is unique to individuals and business entities. A “**discount rate**” is the rate at which any given entity can *expect* to earn on their money invested. For example, most people keep money in banks. A bank will pay a customer interest for the customer to keep their money in the bank. The interest rate is typically extremely low, say, %0.05. So if you invest your $1000 in a bank for 10 years, you would get a predicted return as described above with a %.05 increase per year. If you invest your money in a stock, you might get a higher return than in a bank. Maybe you can get something like 4% return on your investment. If you can consistently get 4% return, that becomes your *discount rate*. That way, when evaluating what investments are good for you, you need to compare the investment’s rate of return against your own discount rate.

As you can see, an individual’s (or business’) discount rate is often different than the rate of inflation. But if the general purchasing power of money is decreasing (because the cost of goods increases – i.e. inflation), and you can grow your money at a different rate, how can you figure out how much cash you need **today**, in order to make a large purchase **in the future**? The formula for this is shown below.

The first step is finding the “Present Worth Factor,” F_{PW}.

Where i_{INF} again is the inflation rate, and d is the discount rate. “n” represents the number of terms (often years) of the calculation. Once the F_{PW} is known, you can calculate the “Present Worth” (PW) of an investment. The PW is the amount of money needed at the present (invested at d) in order to purchase something in the future (with an inflation rate of i_{INF}). The PW is:

Where C_{0} is the cost of the object you wish to purchase. An example below uses both discount rate and inflation to find the present worth.

*Example*: Your Company has recently installed a large utility scale PV power-plant. The overall plant cost is $100M and the plant is operational. There are dozens of large inverters as a part of the system, which will need to be replaced in about 7 years. If there are 20 inverters, which cost $20,000 each, how much cash does your company need to have now, invested at your company’s discount rate of 6%, in order to purchase the inverters in 7 years? Assume an inflation rate of 3%.

*Solution*: If your company would make the purchase today, it would cost $20,000*20 = $4M. However, the company will actually make the purchase in 7 years, and the cost of the inverters will go up, due to inflation. So instead we use the Present Worth formula. First we’ll calculate the present worth factor.

Now we apply the present worth factor to the cost of the inverters:

Therefore your company needs to have about $3.3M *today* invested at 6% in order to make the inverter purchase in 7 years.

Sometimes in order to make these large purchases, a company will need take out a loan from a bank. When a bank loans money to an entity, they consider it an investment, and expect more money in return. This money (from the perspective of the entity taking the loan) is called **interest. Interest** is paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt. If you take out a loan from a bank for $1,000 at an interest rate of 3%, you will need to pay the bank back $1,030 at the end of one year.