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Present vs. Future Value

Every financing decision, valuation, and retirement projection in this book reduces to moving money forward or backward in time. These two operations are how you do it.

Present Value (PV): This is the current value (worth) of money you’d invest or receive from future cash flows, given a specified discount rate.
Future Value (FV): This is the total amount of money you’ll have in the future, considering both your initial investment and the accumulated interest.

The discount rate is the hurdle rate of return an investor demands to compensate for the time value of money and the specific risks of that opportunity. A key factor that must be incorporated into the discount rate is expected inflation over the investment horizon. Other factors include the risk-free rate^$†$, equity risk premiums, and others.

The present value formula is:

PV = \frac{FV}{{(1 + r)}^{n}}

Where:

— Required Rate of Return (or interest rate)
— Number of Periods

For example, to calculate the present value of receiving $10,000 in 5 years at a 5% discount rate: $PV = \frac{$ 10, 000}{{(1.05)}^{5}} = $ 7, 835$

This means you’d need to invest $7,835 today at 5% to have $10,000 in 5 years.

The reverse calculation determines the future value of a present investment or recurring cash flows over time. The future value formula is:

FV = PV \times {(1 + r)}^{n}

Using our previous example, the future value of investing $7,835 today at 5% for 5 years is:

$FV = $ 7, 835 \times {(1.05)}^{5} = $ 10, 000$

For example, investing $10,000 today at 8% over 30 years grows to $100,626 — about $48,000 in today’s purchasing power at 2.5% inflation, which is still nearly $5 \times$ and, unlike the nominal figure, a number you can actually spend.

These two formulas answer most of the questions in this book. Should you take the pension lump sum or the monthly payment? Discount the payments and compare. Is a structured settlement offer fair? Discount it. Is the zero-percent financing better than the cash rebate? Discount both. Should you prepay the mortgage or invest? Compare the guaranteed return of the former against the expected return of the latter, both after tax.

One habit to build now: whenever someone quotes you a total — “you’ll receive $500,000 over twenty years” — your first move should be to discount it. Twenty annual payments of $25,000 at a 5% discount rate are worth $311,555 today, not $500,000. Selling the undiscounted total is the oldest trick in finance, and it works on almost everyone.

^$†$The theoretical rate of return on an investment with zero risk, e.g., treasury bonds.

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