In plain English
100 today is worth more than 100 next year, because you could put today's 100 in the bank and have more than 100 next year. That is the whole idea. Interest is the rent paid for using someone's money, and discounting is running that rent backwards to ask what a future amount is worth today.
The advanced view
Discounting is the pricing of a cash flow by the opportunity cost of capital appropriate to its risk. Compounding is exponential because interest earns interest, so growth over n periods is multiplicative rather than additive. Every valuation technique you meet later — bonds, DCF, options — is a rearrangement of the same present-value machinery.
Simple interest pays on the original amount only: 100 at 10% for three years gives 130. Compound interest pays on the interest too: 110, then 121, then 133. Over one year they agree; over twenty years they are not remotely the same. Nearly all real finance compounds.
Discounting is the mirror image. If money grows at 10% a year, then 110 a year from now is worth 100 today — divide instead of multiply. The number you divide by is the discount rate, and it stands for what you could have earned elsewhere at similar risk. A higher rate means the future is worth less today, which is why rising interest rates push asset prices down.
Three lines and one trick
Future value = PV × (1 + r)^n Present value = FV / (1 + r)^n Rule of 72: years to double ≈ 72 / interest rate in %
Essential vocabulary
- Interest rate
- The price of money over time, expressed per year.
- Compounding
- Earning interest on interest already earned.
- Discount rate
- The rate used to bring future money back to today. Reflects both waiting and risk.
- Present value
- What a future amount is worth today, once discounted.
- NPV
- Net present value — the present value of everything coming in, minus what you pay now. Positive means do it.
Common pitfalls
- ×Adding cash flows from different years together without discounting them first.
- ×Using a monthly rate with a yearly number of periods, or the other way round.
- ×Assuming a high discount rate is 'conservative' — it can make a genuinely good project look bad.
Why it works
Money can be invested, so a krona at two different dates is two different goods. Discounting converts them into the same unit — today's krona — which is the only way to add them up honestly. Every 'is this worth doing?' question in finance reduces to that conversion.
How it is used — value a small project in your head
Step 1 of 6
- 1Spend 100 now, receive 60 at the end of each of the next two years. Discount rate 10%.
Deeper
Deeper: discounting shortcuts you can do out loud
In an interview you will not use a calculator. Learn three shortcuts. The rule of 72: money doubles in roughly 72 ÷ r years. A perpetuity is CF ÷ r, and a growing perpetuity is CF ÷ (r − g). A short annuity can be approximated by treating the discount factor as roughly linear over the first few years: at 10%, factors are about 0.91, 0.83, 0.75, 0.68, 0.62.
The dangerous part is the terminal value. In a five-year DCF at a 10% discount rate and 2% growth, roughly three-quarters of the value sits in the perpetuity. That means your answer is mostly an opinion about g and WACC, and you should quote a range rather than a point.
Must know cold
- ✓PV = FV ÷ (1 + r)^n. FV = PV × (1 + r)^n.
- ✓Perpetuity = CF ÷ r. Growing perpetuity = CF₁ ÷ (r − g).
- ✓Rule of 72: doubling time ≈ 72 ÷ r (in %).
- ✓NPV > 0 means the project earns more than its cost of capital.
Exercises
Try each one on paper before revealing the worked solution.
Exercise 1
A project costs 100 today and pays 30 a year for five years. At a 10% discount rate, is it worth doing? Estimate without a calculator.
Exercise 2
Cash flow next year is 12, growth 3%, discount rate 9%. What is the value, and what if growth is 4%?
Each bar is 100 received in that year, shrunk to what it is worth today. The grey part is the discount. This one picture is the whole idea behind present value, NPV and every valuation you will build later.