Time Value of Money

Move every cash flow to the same date: forward multiplies, backward divides.

The idea

The time value of money is the principle that a dollar today is worth more than a dollar a year from now — not because prices might rise or the promise might be broken, but because today's dollar can be put to work. Deposit it, and a year from now you hold the dollar and the interest it earned; the dollar that only arrives next year missed that year of earning.

It follows that amounts of money at different dates cannot be compared or added directly. To value a contract that pays at several dates, we first carry every cash flow to one common date, usually today. Carrying money forward is familiar from Interest & Compounding: invested at rate $r$ per year, an amount $C$ becomes its future value $C(1 + r)^{t}$ after $t$ years. Carrying money backward, from a future date to today, is called discounting, and it is the first move in every valuation.

Ways to work on it

• Walkthrough. Derive present value from future value, discount a payment, and compare offers at different dates.
• Practice. Discount, grow, and compare single payments on clean numbers.
• Hardest. Value a whole payment stream, or find the rate that ties two offers.

Not sure where to start? Take the ten-question placement test.