Time Value of Money
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Time Value of Money

One dollar today is more valuable than one dollar tomorrow because of inflation, risks, and its usage potential. Between the time when costs are incurred and revenues are received there is always a substantial difference during which the value of money changes (decreases with few exceptions). This is why to compare revenues and costs all items have to be translated to the same time line, usually the beginning or the end of a project.

In the figure below r is the cost of money (for example opportunity cost of capital or interest). It represents in percentage how much more one dollar would cost in one year.

Data Analytics Creates Value

On the left the reference is at the beginning of the project. One year later the $1 will value $1*(1+r). The effect is compounded over time so after n years one dollar becomes $1*(1+r)n.

On the right the reference is at the end of the project. One year earlier the $1 would have valued $1/(1+r). If the analysis is done at the end of the project's useful life for example as a learning opportunity we can use the real cost of money instead of the expected average r. If ri is the cost of money for year i, then the value of 1$ at the end would translate into $1/[(1+r1)*...*(1+rn)] at the beginning of the project.