Time value of money
A pound today is worth more than a pound in a year, because today's pound can be invested to earn a return. That simple idea is the foundation of bond pricing, DCF models, mortgages and pensions.
Future value
FV = PV × (1 + r)^n
£1,000 invested at 8% a year is worth £1,080 after one year and about £2,159 after ten, because each year's return earns returns of its own. That is compounding.
The rule of 72 is a quick shortcut: divide 72 by the annual return to estimate how many years it takes to double. At 8%, about nine years. At 4%, about eighteen.
Present value
PV = FV ÷ (1 + r)^n
Reverse the maths and you can value future money today. £1,000 received in ten years, discounted at 8%, is worth about £463 now. The rate you discount at is called the discount rate, and it reflects both the time value of money and the risk of not getting paid.
Why it matters for investing
- Valuation: a company is worth the present value of its future cash flows (lesson 6.3).
- Rates: when interest rates rise, discount rates rise, and the present value of distant cash flows falls most. That's why long-duration assets like growth stocks and long bonds are so rate-sensitive (lesson 1.9).
- Your own returns: small differences in annual return or fees compound into large differences over decades.
Key takeaway
Every valuation is a statement about future cash, discounted back to today. Get comfortable with compounding and discounting and the rest of corporate finance follows.
Educational content only, not financial advice. Investing involves risk and you can lose money.