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An underlying principle in the financial measure of investments, including investments in software projects, is that the value of a given quantity of money today is worth more than the same amount at a date in the future. This first basic principal, the time value of money, can be stated succinctly as:

“A dollar today is worth more than a dollar tomorrow” [29]

It is intuitive that given a choice between receiving a dollar today and a dollar at a later time, even tomorrow, that today is preferable. There are two factors that explain this preference:

1. Money received today is immediately available for other investments. 2. Future events have uncertainties.

Suppose that a choice exists between receiving $100 today and a greater amount one year from now. How much additional money would be required to make the later payment preferable? A simple way to determine this is to look at possible investments at a similar risk. Assume that in this example, the future payment is guaranteed; investments with zero risk should be considered. Suppose that a U.S. government bond offers a 5% interest rate. Presumably, even considering recent market turmoil and tremendous government deficits, U.S. government bonds have no risk of default. Suppose that $100 is invested today at a 5% interest rate.

100 * (1 + interest rate) = 100 * (1 + r) = 100 * (1 + 0.05) = 105, where r is the rate of return.

Equation 1 Future Value Of $100, One Period At 5%

The above equation states that given a 5% interest rate, the future value of $100 today is $105.

PV * (1 + r) = FV, where FV is the future value and PV is the present value.

Equation 2 Future Value After One Period

From another perspective, suppose that a payment is offered at a later date. What is the value of that payment today? Equation 2 can be manipulated to solve for the present value in terms of the future value.

PV = = FV * ( )

Equation 3 Present Value After One Period

The term, ( ), is known as the discount factor, with r being described as the discount rate.

As a concrete example, suppose a payment of 110.0 is offered in one year. What is the present value of this payment? Assume that alternative, equivalent risk investments are available at a 5% rate of return.

PV =

Assuming a 5% rate of return, or equivalently, a 5% discount rate, the present value of $110 one year from now, is $104.76. This means that $104.76 received today is of equal value to $110 received in one year.

Equation 2 and Equation 3 can be used to calculate future value and present value over one time period, in the examples, over a period of one year. The future value over multiple periods can be determined as follows.

Period 1:

Period 2:

….. Period N:

Equation 5 Future Value After N Periods

Solving for PV yields

Equation 6 Present Value Of An Amount To Be Received in N Periods

As can be seen from above, money has a time value. The value of a quantity of money spent or received today is different from the value of the same quantity of money at a future date. To evaluate any investment, all payments and outlays are converted into dollars valued at the same point in time, usually the present. This is referred to as calculating the net present value. “Present value” indicates that all money is converted into its worth today. “Net” indicates that all payments and outlays are summed. Efforts

with positive NPVs are worthy of consideration. This is best understood via a simple example. Suppose that a project to develop a new commercial software product, perhaps a word processor, is being considered. Suppose that the costs include payment of $100,000 to a team of requirements engineers today and payment of $300,000 to a team of developers six months from now. Further suppose that the final product will be completed in one year and that it can be sold to another company or on the market for $420000 at that time. Should this project be conducted? The answer to this can be determined by calculating NPV1.

Assume US government bonds are available at an interest rate of 6% per year or 0.06/12 = 0.005% per month. Individual cash flows (both revenue and outlays) can be designated by Ci.

C0 = -100000 (today, cost of requirement engineers)

C1 = -300000 (six months from now, cost of development team)

C2 = 420000 (one year from now, sale of product)

r = 0.06/year = 0.005/month

NPV = -100000 + (-300000)/(1 + 0.005)6 + 420000/(1 + 0.005)12 = -100000 – 291155 + 395600 = 4445

Equation 7 NPV of Word Processor Project Example Assuming 5% Discount Rate

The general rule is a project is worth consideration when NPV is positive2. The NPV of

this project is positive. This indicates that given our assumptions, the organization will

1

The question is actually answered partially by the NPV calculation. As seen elsewhere in this thesis, value assessment is multidimensional. NPV calculations serve as a measure of worth in the financial dimension.

2 _{Value is multidimensional and NPV, or financial value, is only one dimension. Some classes of projects,}

gain wealth as the result of this project. The next question is whether the project should proceed based on this calculation. There are several implicit assumptions in this NPV calculation. How certain are the expenses ($100000, $300000 (in six months)) and the future revenue ($420000 (in one year))? Assume the discount rate (0.06) used was the interest rate available from zero risk government bonds. Is this the correct discount rate to use in this calculation? Using a risk free discount rate is appropriate for calculating the NPV of risk free investments. Unless the project is risk free, which is highly unlikely for any project, the calculation is not valid due to use of an incorrect discount rate. This project generates a future value of $420000 in one year given investments of $100000 today and $300000 in six months. Again, assume that a 6% return is available from safe government bonds. All projects have risk. Any rational investor would require a return higher than $420000 to undertake this effort. The same return could be return risk free from government bonds. This principal can be expressed as:

“A safe dollar is worth more than a risky one” [30]