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time value of money

Also called: TVM

A hryvnia today is worth more than a hryvnia next year, because it can be invested or used now and because future money is uncertain.

Time value of money is the idea that the same amount is worth more the sooner it arrives. Money in hand today can pay tutors, fund a launch or sit on a deposit and earn interest. Money promised for next year can do none of that yet, and it may arrive late, smaller or not at all.

Finance turns the idea into arithmetic. Pick an annual rate r that says what money could earn elsewhere at a similar risk. An amount today grows to amount × (1 + r)ᵗ after t years (future value); an amount due in t years is worth amount ÷ (1 + r)ᵗ today (present value). At 25% a year, 1,000,000 today becomes 1,250,000 in a year and 1,562,500 in two, because the second year earns on the first year's gain too.

For product people it shows up whenever money is traded against time: an annual plan paid up front versus monthly billing, a client who offers a bigger sum if they can pay later, a feature that costs money now and saves money over three years. Without it, a sum spread over years looks bigger than it is, and long payment terms look free.

Example

A Teams client, a logistics company, offers Klasna a choice for next year's English course: 600,000 UAH now or 690,000 UAH at the end of the year. The second number is 90,000 bigger, but it comes a year later.

At Klasna's rate of 25% a year: 690,000 ÷ 1.25 = 552,000 UAH in today's money, less than 600,000 now. At the 12% a deposit pays: 690,000 ÷ 1.12 = 616,071.43, more than 600,000.

The tipping point is 690,000 ÷ 600,000 − 1 = 15%: if Klasna's money earns more than 15% a year, it takes the cash now. To wait a year at 25%, the client would have to pay 600,000 × 1.25 = 750,000.

Common mistakes

  • Adding up sums from different years. 400,000 a year for three years is not 1.2 million in today's money; bring each year back to today first.
  • Treating payment terms as free. Every month a client waits to pay is a discount Klasna gives.
  • Not saying which rate. The same offer wins at 12% and loses at 25%; the rate belongs next to the answer.
  • Reducing it to inflation. Inflation is one reason, but the rate also covers what the money could earn and the risk that it never arrives.
  • Forgetting that delays cost money. A project that slips by a year is worth less even if every number in it stays the same.

Learn it in the course