You've probably been offered something like this: "I'll give you £100 today, or £110 in a year." Which do you take? Most people would think: £110 is more, so wait a year. But whether that's the right answer depends entirely on what you could do with £100 today. If you could invest it and earn 15% in a year, you'd rather have £100 now — you'd turn it into £115. If you could only earn 5%, take the £110.
This is the time value of money in its simplest form: money available now is worth more than the same amount in the future, because of its potential to earn in the meantime.
If you invest £1,000 today at 8% per year, what is it worth in 10 years? The future value formula:
FV = PV × (1 + r)ⁿ
FV = £1,000 × (1.08)¹⁰ = £2,159
At 8% for 10 years, £1,000 becomes £2,159. The power of compound growth in a single formula. The variables you can play with: the present value (PV), the rate (r), and the time (n). Increasing any of them increases the future value dramatically.
Present value is the reverse: what is a future sum worth today? If someone promises to pay you £2,000 in 5 years, and you could otherwise invest at 7% per year, what is that promise worth to you right now?
PV = FV ÷ (1 + r)ⁿ
PV = £2,000 ÷ (1.07)⁵ = £1,426
That future £2,000 is worth £1,426 to you today, given your 7% opportunity cost. If someone is selling you the right to receive that £2,000 for £1,800, it's a bad deal — you'd be paying more than the present value. If they're selling it for £1,200, it's a good deal.
This is the foundation of every investment valuation. When analysts say a stock is "worth £50" but trades at £40, they've calculated the present value of all its expected future cash flows and arrived at £50. Whether you trust their assumptions is a different question.
The discount rate is what you use in the PV formula. It represents your opportunity cost — what you could earn elsewhere at equivalent risk. If you could safely earn 5% in government bonds, any investment must offer more than 5% in present value terms to justify the extra risk.
When central banks raise interest rates, the discount rate used to value investments rises. Future cash flows become less valuable in today's terms. This is why rising interest rates tend to hurt growth stocks more than value stocks — growth companies' earnings are weighted further into the future, so they're discounted more heavily when rates rise.
A real example: a startup promises you £1,000,000 in 10 years if you invest £100,000 today. That sounds extraordinary — 10× your money. But discounting at 25% (appropriate for high startup risk): PV = £1,000,000 ÷ (1.25)¹⁰ = £107,374. You'd be paying £100,000 for something worth £107,374 — a 7% margin of safety. Not nearly as exciting as the 10× headline suggests, and that's before accounting for the very real chance the startup fails entirely.
NPV combines present value with the cost of the investment. If NPV is positive, the investment creates value. If it's negative, it destroys value at your chosen discount rate.
NPV = (sum of all future cash flows discounted to present value) minus the initial investment cost.
Companies use NPV to decide whether to build new factories, launch products, or make acquisitions. Investors use it to value stocks and bonds. You can use it to decide whether any financial commitment is worth making — including education, property purchases, or business decisions.
The concept to take away: every financial decision involves comparing values across time. The discount rate you apply reflects both the risk and your opportunity cost. Getting comfortable with this thinking — not necessarily the exact formula, but the intuition — puts you ahead of most people when evaluating any financial opportunity.
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