**Time Value of Money**

Consider your cheese steak hoagie business. Assume that Phillies will win another World Series, and your business will be hired to serve a party that will generate an additional $2,000 times 1.15X years from now the Phillies win the championship again. What would you choose the value of X equals 1, 2, 3, or 4 years from now? What factors would you consider to make your decision?

If you hoagie business owes money and is paying a high interest rate for the loan, you will certainly would like X to be 1. Or, if you do not owe money but you can invest the money to expand your business, you will prefer the money now. What about if instead of $2,000 now, you will receive $3,000 but X will be 4? The factors that you will need to evaluate your alternatives are:

Inflation

Interest rate

Opportunity cost

This is what is known as the time value of money (TVOM). The money has value trough the planning horizon and it will affected by an interest rate every time period. For example, you loan $4,000 to a bank at 10% and by the end of each year you will an interest rate to the bank, so at the end of year one you will owe to the bank $4,400 dollars. Also, you may have at the end of year 3 a positive cash flow of $3,000 and you decide to loan the money to a friend, so you can no longer invest the $3,000 in expanding your business and forego the opportunity to earn a return on your $3,000, which is know as the opportunity cost.

Other terms that are used to express the TVOM are interest rate, discount rate, hurdle rate, minimum attractive rate of return, and cost of capital.

What it is clear is that $4,000 today are not the same to $4,000 ten years ago, or 3 years for now. In other words, a brand new Honda Civic in 2004 cost approximately $11,500, and in 2009 costs approximately $18,5000.

Therefore, we can not add or subtract money that occurs at different time periods. If we want to do that then we need to bring the money to a same time period applying the corresponding mathematical operations and the corresponding discount rate. This is what is known as discounted cash flow (DCF) which has four DCF rules:

1. Money has time value of money;

2. Money cannot be added or subtracted unless it occurs at the same point(s) in time;

3. To move the money forward one time unit, multiply by one plus the discount or interest rate;

4. To move money backwards one time unit, divide by one plus the discount rate or interest rate.

Therefore, to evaluate different alternatives (or add money occurring at different points in time) we have to develop mathematical relationships of money at different points in the planning horizon. We will develop these relationships in the following chapters.