Time value of money: why a hryvnia next year is worth less

A logistics company offers Klasna a choice for next year's English course: 600,000 UAH now, or 690,000 at the end of the year. Leo says 690,000, obviously: it's 90,000 more.

But the same sum is worth less the later it arrives. A hryvnia today can pay tutors, fund ads or at least sit on a deposit; a promise a year out may slip or never come. That is the time value of money.

To compare, bring the later amount back to today. Divide it by (1 + r) for every year of waiting:

PV = FV ÷ (1 + r)ᵗ.

r is the discount rate: what the money could earn elsewhere at similar risk. Klasna uses 25% a year.

690,000 ÷ 1.25 = 552,000 UAH.

In today's money the later offer is worth 48,000 less than the 600,000 now, despite being 90,000 bigger on paper. The slip is to compare the two totals as they are, or to subtract 25% (690,000 × 0.75 = 517,500) instead of dividing by 1.25.

The same pair of offers can give opposite answers at different rates.

• At 25%: 690,000 ÷ 1.25 = 552,000, less than 600,000. Take the money now.
• At 12% (Klasna's deposit): 690,000 ÷ 1.12 = 616,071.43, more than 600,000. Waiting wins.

There is a rate at which the two are worth the same today, the tipping point:

690,000 ÷ (1 + r) = 600,000 → 1 + r = 690,000 ÷ 600,000 = 1.15 → r = 15%.

The 690,000 offer is simply 600,000 growing at 15% for a year. So the rule reads: if Klasna's money earns more than 15% a year, take the cash now; if less, wait.

This is why every present value comes with its rate. "The later offer is worth 552,000" means nothing without "at 25%". When someone shows you a discounted number, the first question is which rate they used and why. The slip is to read the 90,000 difference as a 90% rate, or to pick the rate that gives the answer you wanted.

The discount rate is not a number you look up; it is a choice, and it should answer one question: what could this money earn elsewhere, at similar risk?

• A deposit rate (Klasna's 12%) is what money earns with almost no risk. It is the floor: no business should accept less than a deposit for tying up its cash.
• The business's own rate (Klasna's 25%) reflects what its cash actually does: it pays summer payouts, funds spring ads and builds features, and the people who funded Klasna expect a return well above a deposit for carrying its risk.

For decisions about Klasna's own money, Klasna uses 25%. At that rate 690,000 in a year is worth 552,000 today, and the 600,000 now wins. At 12% the answer would flip, which is exactly why the choice matters.

Where the 25% comes from, the cost of capital and the hurdle rate, is a later lesson in this module. For now the rule: the riskier and more useful the money, the higher the rate. The slip is to reach for the deposit rate because it is the only "real" number on hand.

For money further out, divide once more for every extra year. It is easier to work with discount factors: what one hryvnia in year t is worth today, 1 ÷ (1 + r)ᵗ.

At 25% a year:

Each year multiplies the factor by 0.8. At 25%, a hryvnia three years out is worth about half a hryvnia today.

Present value = amount × factor, year by year, then add up.

A tools vendor promises savings of 400,000 UAH a year for three years and calls it "1.2 million of savings". With savings at the end of years 1, 2 and 3:

400,000 × 0.8 + 400,000 × 0.64 + 400,000 × 0.512 = 320,000 + 256,000 + 204,800 = 780,800 UAH.

In today's money the 1.2 million shrinks to about two-thirds. The slip is to apply one factor to the whole sum (1,200,000 × 0.512) or to forget discounting entirely and quote the 1.2 million.

Because later money is worth less, moving a payment later is a cost, even when the amount stays exactly the same.

A feature expected to bring 1,000,000 UAH at the end of year 2 is worth 1,000,000 × 0.64 = 640,000 today at 25%. If the launch slips a year, the same 1,000,000 arrives at the end of year 3: 1,000,000 × 0.512 = 512,000 today.

Cost of the delay: 640,000 − 512,000 = 128,000 UAH, a fifth of its value. Each year of delay multiplies the value by 0.8.

The same applies to everything that shifts money in time:

• a project that slips costs money even if every number in its plan stays the same;
• payment terms Klasna gives a client are a discount in today's money;
• a client paying a year later, like the 690,000 offer, must pay more just to stand still: 600,000 × 1.25 = 750,000.

The slip is to treat a delay as free because "we still get the full amount". In today's money you don't.

Discounting has a mirror image. Instead of bringing later money back to today, you can take today's money forward: multiply instead of dividing.

FV = PV × (1 + r)ᵗ.

At 25%, 1,000,000 UAH today becomes:

• after one year: 1,000,000 × 1.25 = 1,250,000;
• after two years: 1,250,000 × 1.25 = 1,562,500.

The second year earns 25% not on the original million, but on 1,250,000, including the first year's gain. That is compounding, and it is why 25% for two years is 56.25%, not 50%.

Simple interest (adding 25% of the original amount every year) would give 1,500,000. The 62,500 gap is interest on interest, and it grows quickly with time: after four years compounding gives 2,441,406 against 2,000,000 simple.

The same logic runs backwards in discounting, which is why each extra year cuts value by a factor of 0.8 rather than by a fixed 25% of the original. The slip is to add the rate once per year to the starting amount.

When a client wants to pay later, the fair question is: how much would the later payment have to be to be worth the same as the money now? That is the future value of today's amount at your rate.

FV = PV × (1 + r)ᵗ.

For 600,000 UAH at Klasna's 25%:

• one year later: 600,000 × 1.25 = 750,000;
• two years later: 600,000 × 1.25² = 600,000 × 1.5625 = 937,500.

Check it backwards with the discount factor: 937,500 × 0.64 = 600,000. Future value and present value are the same calculation run in opposite directions.

This turns a vague "they want to pay later" into a concrete counter-offer: "600,000 now, or 750,000 at the end of the year". The client's own 690,000 offer falls short of 750,000, so it is worse for Klasna than the cash now.

The slips: adding 25% twice to the original (600,000 × 1.5 = 900,000) instead of compounding, or applying the deposit rate, which would make the counter-offer too cheap.

When clients offer different amounts on different dates, totals can't be compared directly. Bring each one to today with its discount factor, then rank.

Four offers Hanna has seen this year, at 25%:

• 600,000 now: factor 1 → 600,000;
• 900,000 in two years: × 0.64 → 576,000;
• 700,000 in one year: × 0.8 → 560,000;
• 1,000,000 in three years: × 0.512 → 512,000.

The biggest total is the least valuable, and the order of the totals is almost exactly reversed. A bigger sum that comes later loses to a smaller one that comes sooner whenever it doesn't grow faster than the discount rate: 1,000,000 in three years is 600,000 growing at only about 18.6% a year, below 25%.

This is the everyday use of time value: payment terms, installment plans, multi-year deals. Any "pay later, pay more" offer is a loan, and its rate is what decides. The slip is to rank by the amount on the contract.