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Net Present Value (NPV)
When making an investment, a central problem is how to compare dollars of benefits or costs today with dollars of benefits of costs that occurs in the future – say, three years from now. Economists approach this problem through the related concepts of discounting and Net Present Value.
Begin with the fact that banks and other institutions in the economy pay a rate of interest on deposits and charge a rate of interest on loans. To keep things simple, we will assume only one rate of interest in the economy – r.
If you put $100 in the bank today, one year from today, your account will have grown to $100x(1 + r). If you leave your deposit in the bank for a second year, it will have grown to $100x(1+r)x(1+r) or $100x(1+r)2, and so on.
Using this relationship, we take our original question – e.g. What is the value today of $500 that is paid three years from today? and we reformulate it as: If we want a bank account to be worth $500 in three years, how much do we have to deposit today? Assume the interest rate is 5% (= .05). If we define Z as the answer to the question, we can write:
Z*(1 + .05)3 = $500 or Z = $500/(1.158) = $431.92
When the interest rate is 5%, the last figure - $431.92 – is the value today - the discounted value - of $500 three years from today.
Below is a simple calculator for computing the value in today’s dollars of an investment that runs over eight periods – the investment’s Net Present Value. . The calculator’s upper line contains the investment’s costs (negative numbers) or revenues that occur each year. The lower line converts the values of those revenues and costs in today’s dollars. A basic test for undertaking an investment is that it have a Positive Net Present Value (also see discussion on Internal Rate of Return).
Begin by using the revenues and costs provided in the example. Experiment to see how high the interest rate must go before the investment has a negative Net Present Value – i.e. the investment is no longer worth doing. Then construct your own investment numbers and evaluate them at various interest rates.