# Time Value of Money

Time Value of Money

Time value of Money is a basic core principle in finance and investing, it is a must know idea if you want to understand much more complex problems in finance.  The idea is that money will be worth more in the future if invested in an asset that receives interest or some type of return.  The sooner you receive money and invest it, the sooner your money will generate value. In this review we will cover many different types of definitions and calculations to further your understanding and introduce you to some of the reasons we use the time value of money every day in finance and in investing.

We will start off with some basic examples.

Given:  Calculate the future value if you have \$100 to invest with your bank and they quoted you a 5% yearly return for 2 years.

Explanation:  After your first year your dollar will become \$105 [100 + (100 x 5%)].  After two years your investment will become 110.25[105 + (105 x 5%)].  Using the time value of money idea your money has grown from \$100 to \$110.25 in 2 years.  For this equation you could have just done 100 * (1.052).  The equation is listed below.

FV = PV * (1+r)n

FV:      Future Value

PV:      Present Value

R:        Rate of Return

n:         Number of Compounding Periods

Given:  Calculate the present value if you need \$200 at the end of 2 years and your rate of return is 5% or a real life problem how much would you need to invest right now so that you can meet your obligation of \$200 assuming you can generate a 5% return in the market.

Explanation:  This is just the inverse of the first problem.  The equation is 200/(1.052) = 181.4059.  Meaning you must invest 181.41 right now with a 5% yearly return to have \$200 in one year.  You can even check it against our previous formula.  181.4059 * (1.052) = 200.

The two examples above do not take into account contributions or payments made to the investor or to the creditor.  To calculate the present value or the future value of a cash flow you must “discount” or use our formulas above for each cash flow with “n” being the period the cash flow occurred.  Please see the excel worksheet below for examples of calculations. We will work through 2 problems in our worksheet. First, if we invest \$1000 and make additional \$100 yearly payments and second, what would be the present value of \$1000 dollars in five years with a yearly \$100 dividend. Our time value of money formula or function will work perfectly to solve our problems.

When an analyst is performing time value of money problems, they normally use a financial calculator or a function in a program like Excel.  Please see below for examples of such functions like “PV”, “FV”, and “PMT”.

This is just the beginning to your understanding of finance and valuations, but once you grasp this simple idea it will be much easier for you to understand much more complex valuation models.  For example the dividends discount model, free cash flow model, residual income model, etc….