In its strictest definition, investment is the act of spending capital on an enterprise in the hope of receiving a profit on the spent capital. For example, a business that spends its resources setting up a second manufacturing line can describe that process as an investment because it is doing so with the hope of earning more profits. Both Payback and Net Present Value (NPV) methods are used to determine which investments are worthwhile and which are not.
Purpose

Each investment can be described in a mathematical equation as a series of costs and revenues. Most can be described as one initial cost preceding a series of diminishing revenues in successive time periods. Both Payback and NPV methods use these mathematical formulas to determine which investments are desirable.
Payback Method

Payback method is limited in its uses and disadvantageous compared to NPV method. It calculates only one parameter of desirability: the payback period, or the length of time needed for the business to recover its spending. Payback method calculates this by deducting expected annual cash flows of the investment from the initial expenditure. For example, if a business spends $800 and expects to earn $300 per year over the next three years, the investment would be determined to have a payback period of three years. Payback method calculations produce no other useful information and do not take into account either the profitability of the investment or the time value of money.
Time Value of Money

Money in the present is worth more than the same amount of money in the future. This is because money in the present can be put to immediate use, including investing it to produce a profit. Future value is the amount of money available in the future that is worth the same as money available now, while present value is the amount of money available now that is worth the same as money available in the future. Both values can be calculated if the investor knows the interest rate for the time in between the two dates. For example, if the interest rate is 10 percent for the next year and the investor has $100 now, that same investor can calculate that $100 to have a future value of $110 in one year's time. This is done by multiplying the original sum by 1 + 0.1, where 1 represents the original sum carried forward in time and 0.1 represents the interest paid on the invested money. Assuming the same 10 percent interest rate for the year, the present value of a future sum can be calculated by dividing that same future sum by 1 + 0.1, this time with the 0.1 representing the interest that could have been earned had money been invested at the earlier time. Both present value and future value can also be calculated across multiple periods. For example, if an investor wanted to know the future value of $100 in two years if the interest rates for the first and second years are 10 percent and 12 percent, the calculation is $100 multiplied by 1 + 0.1 and 1 + 0.12, producing a future value in two years' time of $123.20.
Net Present Value Method

Since the present worth of future sums can be calculated, the NPV method determines the desirability of investments by calculating the present worth of all future sums and then adding them to produce the investment's net present value. For example, if an investment has an immediate cost of $100, is expected to pay out $100 one year and $200 two years from now, and knows the interest rates for those years to be 10 percent and 12 percent, that $100 can be calculated to have a present value of $90.91 and that $200 can be calculated to have a present value of $162.34. Added together with the cost of $100, that means the investment is worth $153.25 in net present value. Using this method, a net present value that is positive means that the business is making a profit while a negative figure means that the investment is not worth its cost. The higher an investment's net present value, the more profitable it is and the more desirable it is for the business.