Time value of money

The term time value of money refer to all aspects of converting the value of cash flows at one point of time to the equivalent values at another time. To facilitate the financial decision process, it is important that we know the value of current and future cash flows.

Every decision has future consequences that will affect the value of the firm. These consequences will generally include both benefits and costs.  A decision is good for the firm’s investors if it increases the firm’s value by providing benefits whose value exceeds the costs. But comparing costs and benefits is often complicated because they occur at different points in time, may be in different currencies, or may have different risks associated with them. To make a valid comparison, we must use the tools of finance to express all costs and benefits in common terms

The calculation for the present value of a series of cash flows may be used to find out how much an investor will be willing to pay for an investment. Because the investor has a specific required rate of return, it is unlikely that a rational investor will pay more than the present value for an investment.

The term net present value refers to an investor's position after making an investment. To calculate the net present value of an investment, we modify the present value formula by subtracting the initial investment from the present value calculation.

When we compute the value of a cost or benefit in terms of cash today, we refer to it as the present value (PV). Similarly, we define the net present value (NPV) of a project or investment as the difference between the present value of its benefits and the present value of its costs:

NPV = PV ( Benefits) - PV (costs)

NPV = CFt (1/(1+r))^t - CFo

Where ,
CFt =Cash flow in period t
R = Discount rate (required rate of return)
T = Number of cash flows generated by the project
CFo = Initial cash investment
A positive NPV means that the investor paid less than the present value for the stream of cash flows. A negative NPV means that the investor paid more than the present value for the stream of cash flows
Example:

Project A requires a capital investment of $2,000 and promises a payment of $1,000 at the end of Years One, Two, and Three. If the investor's required rate of return is 12%, what is the NPV of the investment? We can use the NPV formula with the values CF1, CF2, and CF3 = $1,000, CF0 = $2,000, T = 3, and R = 0.12.

NPV = $1,000[1 / (1.12)]1 + $1,000[1 / (1.12)]2 + $1,000[1 / (1.12)]3 - $2,000
         = $401.83

A positive NPV means that the investor paid less than the present value for the stream of cash flows. A negative NPV means that the investor paid more than the present value for the stream of cash flows.