1.3 Present Value

This section looks at computing the present value of future amounts, under conditions of certainty -- where you know how much will be paid in the future, when in the future the amount will be paid, and what the discount (or interest) rate should be.

The discounted cash flow (DCF) models that you use here are the cornerstones for most (nearly all) financial valuations!

1.3.1 - Present value - first principles

To make decisions now -- really the only kind we make -- it is useful to know the "present value" of future money. Present value is the current dollar value of a future amount -- what would have to be invested today (at a given interest rate over a specified period) to equal the future amount. What is a dollar in the future worth? It depends on when it will be received and our current investment opportunities. (More 1.3.1>>)

1.3.2 - Single cash flow

We will first look at discounting a single cash flow or amount. The cash flow can be discounted back to a present value by using a discount rate that accounts for the factors mentioned above (present consumption preference, risk, and inflation). Conversely, cash flows in the present can be compounded to arrive at an expected future cash flow. (More 1.3.2>>)

1.3.3 - Present value of cash flow streams

The future is sometimes bumpy and sometimes cyclical and sometimes forever. Cash flows can come in a mixed stream or a pattern of equal annual flows or even a perpetual stream. (More 1.3.3>>)

1.3.4 - Present value of an annuity

When equal payments are made over time (an annuity), their present value can be determined using standard valuation methodologies. This can also be done in reverse - to calculate the equal payments over time equivalent to a current lump sump payment (loan amortization). Not surprisingly, questions of annuities often arise in legal contexts. (More 1.3.4>>)

1.3.5 - Present value of a perpetuity

Sometimes annuities last forever -- or so we pretend. What is the value of payments that are received indefinitely, like proverbial AT&T dividends? On first reflection, you might think that te value of perpetual payments would be infinite. But remember that $1 paid in 10 years may not be worth picking up from the sidewalk (assuming normal inflation and the inherent time value of money) and $1 paid in 100 years is worth even less. (More 1.3.5>>)

1.3.6 - Constantly growing perpetuity

What if we expect that future returns will grow -- with inflation and as an investment progresses? If returns grow at a constant rate (g), the DCF formula produces one of the most often-used formulas in stock valuation -- known as the "Gordon-Shapiro dividend discount model" or the "Gordon model." (More 1.3.6>>)