Investment Theory and Risk Management, + Website

Discounting Present Values of Cash Flow Streams

As individual consumers, we are always trying to maximize our intertemporal utilities by trading off future and present consumption. That is, we will consume a dollar's worth of goods today if we feel that the satisfaction we receive from doing so exceeds the satisfaction we'd get had we saved that dollar and consumed it somewhere in the future. The decision to consume intertemporally therefore depends on our abilities to compare wealth today with future wealth, which is what we mean when we talk about the time value of money. A dollar cash amount invested in the future will be worth after, say, one year. Therefore, the present value P of a cash flow C to be received one period from now is the future C discounted at rate r:

Alternatively, investing P for one period at rate r will generate value equal to . The present value of a cash flow received two time periods from now is therefore:

If the cash flow is received more than once (say, three periods), then it has present value:

An example of discrete discounting is net present value (NPV), ...