# Time value of money: why a hryvnia next year is worth less > Time value of money with examples: present value, future value, discounting and the rate you discount at. - Course: [Finance for Product People: From Unit Economics to Business Cases](https://productovi.com/courses/finance-for-product.md) - Module: Is this bet worth making? - Lesson 21/32, ~27 min - Source: https://productovi.com/courses/finance-for-product/time-value-of-money ## Now or in a year? **Alex Tutor:** Back at Klasna's product team: Hanna brings a choice offered by a Teams client. **Hanna:** A Teams client, a logistics company, gives us a choice for next year's English course: pay 600,000 UAH now, or 690,000 at the end of the year. **Leo:** 690,000, obviously. That's 90,000 more. **Sofia:** But the 600,000 arrives a whole year earlier. That has to be worth something. **Alex Tutor:** It is. 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**: the same sum is worth less the later it arrives. **Alex Tutor:** To compare, bring the later amount back to today: divide it by (1 + r) for every year of waiting. r is the **discount rate**, what the money could earn elsewhere at similar risk. Klasna uses 25% a year. $$ PV = \frac{FV}{(1 + r)^t} $$ *PV: present value, what the payment is worth today; FV: the amount paid later; r: discount rate per year; t: years until it is paid.* **Alex Tutor:** Try it on the client's second offer. > **Exercise:** What is the **present value** of 690,000 UAH paid in one year, at Klasna's discount rate of 25%? ## The discount rate decides **Leo:** Our deposit pays 12%. At 12%, isn't the 690,000 worth more? **Alex Tutor:** Check it: 690,000 / 1.12 = 616,071.43, above 600,000. At 12% waiting wins; at 25% the money now wins. Same offer, opposite answers. **Hanna:** The tipping point is 690,000 / 600,000 − 1 = 15%. If our money earns more than 15% a year, we take the cash now. **Sofia:** So which rate is the right one, 12 or 25? **Alex Tutor:** A deposit is almost risk-free, so 12% is the floor. Klasna's cash isn't idle: it pays summer payouts, spring ads, new features, and the people who funded Klasna expect more than a deposit. We'll see where 25% comes from later in the module. > **Exercise:** 600,000 UAH now or 690,000 in a year. At what annual discount rate are the two offers worth **the same** today? **Alex Tutor:** One more decision before the tables: which rate do we actually use? > **Exercise:** Klasna's deposit pays 12% a year. Its cash otherwise funds summer payouts, spring ads and new features, and the people who invested in Klasna expect more than a deposit. Which rate should Klasna use to compare 600,000 UAH now with 690,000 in a year? ## Discount factors: two, three, four years out **Sofia:** And money in two or three years? **Alex Tutor:** Divide once more for every extra year: 1 / 1.25 = 0.8, then 0.64, then 0.512. These are **discount factors**. At 25%, a hryvnia three years out is worth about half a hryvnia today. > **Discount factors at 25% a year** > > | Years from now | 0 | 1 | 2 | 3 | 4 | 5 | > |---|---|---|---|---|---|---| > | Factor | 1 | 0.8 | 0.64 | 0.512 | 0.4096 | 0.32768 | > > Present value = amount × factor. Each year multiplies the factor by 0.8. **Hanna:** A tools vendor says their platform saves us 400,000 a year for three years: "1.2 million of savings". I'd like that in today's money. **Alex Tutor:** Discount each year's saving with its own factor and add them up. Savings at the end of years 1, 2 and 3. > **Exercise:** A saving of 400,000 UAH at the end of each of the next **three** years. What is it worth today at 25%? ## Present value vs future value **Sofia:** Does it work forwards too? What 1,000,000 today becomes later? **Alex Tutor:** Multiply instead of dividing. At 25%, 1,000,000 becomes 1,250,000 after one year and 1,562,500 after two: the second year earns on the first year's gain too. That is **compounding**, and 1,562,500 is the **future value** of today's million. $$ FV = PV \times (1 + r)^t \qquad 1\,000\,000 \times 1.25^2 = 1\,562\,500 $$ *Future value: what an amount today grows to after t years at rate r.* **Hanna:** That's also why a project that slips by a year costs money even if every number in it stays the same. **Leo:** And why a "year of payment terms" is a discount we give. **Alex Tutor:** Hanna's point about delays is worth a number. > **Exercise:** A feature is expected to bring Klasna 1,000,000 UAH at the end of year 2. The launch slips, and the same 1,000,000 now arrives at the end of year 3. At 25% a year, how much **value in today's money** does the one-year delay cost? > **Exercise:** **True or false:** at 25% a year, 1,000,000 UAH invested today grows to 1,500,000 UAH after two years. **Alex Tutor:** Now take Klasna's own money forward instead of back. > **Exercise:** The client would rather pay in **two** years instead of 600,000 UAH now. At Klasna's rate of 25% a year, what is the **smallest** amount at the end of year 2 that is worth at least as much as 600,000 today? ## Bigger later or smaller sooner **Leo:** Other clients ask for other terms. Can't I just compare the totals? **Alex Tutor:** Only after bringing each one to today. A bigger sum that comes later can lose to a smaller one that comes sooner. **Hanna:** Four offers I've seen this year: 600,000 now; 700,000 in a year; 900,000 in two years; 1,000,000 in three. **Alex Tutor:** Multiply each by its factor from the table, 0.8, 0.64 or 0.512, then rank them. > **Exercise:** Rank the four offers by what they are worth **today** at 25%, from most to least valuable. ## Your turn: answer the client **Leo:** So what do I tell the logistics company? **Sofia:** That we prefer 600,000 now. And if they want to pay later, the later sum has to grow by our 25%. **Hanna:** Which is 600,000 × 1.25 = 750,000. **Alex Tutor:** Give Leo the comparison in today's money, the rate behind it and the counter-offer. > **Exercise:** Leo asks: "600,000 now or 690,000 at the end of the year: which do we take?" Klasna's money earns about 25% a year in the business; its deposit pays 12%. Write a short reply (3–5 sentences): compare the offers in today's money, say which rate you use and why, and suggest what to tell the client. > **Key ideas** > > - **Time value of money:** the same sum is worth less the later it arrives, because money now can be used and later money is less certain. > - **Present value** = future amount ÷ (1 + r)ᵗ. At 25%, 690,000 in a year is worth 552,000 today, less than 600,000 now. > - The **discount rate** decides: at 12% the same 690,000 is worth 616,071.43; the tipping point is 15%. > - At 25% the discount factors are 0.8, 0.64, 0.512, 0.4096: a hryvnia in three years is worth about half. Three yearly savings of 400,000 are worth 780,800 today. > - **Future value** compounds: 1,000,000 × 1.25² = 1,562,500. > - A delay, or payment terms you give, is a cost in today's money. **Alex Tutor:** Next time we use this to judge a whole product bet: money out now, money in over years. - Previous lesson: [Case: double marketing before exam season?](https://productovi.com/courses/finance-for-product/marketing-budget-case.md) - Next lesson: [NPV, IRR and payback for a product bet](https://productovi.com/courses/finance-for-product/npv-irr-payback.md) --- Productovi Learning. Free, no sign-up needed to read.