Interest and growth
Present value and discounting
Turn future amounts into today's money — the core move behind every valuation.
Learning objectives
- Discount a future amount to its present value
- Build discount factors in a worksheet
- Explain why higher discount rates lower present values
Discounting is compounding in reverse. If 1,000 grows to 1,080 in a year at 8%, then 1,080 received in a year is worth 1,000 today at an 8% discount rate.
The discount rate is the return you could earn elsewhere on an investment of similar risk — your opportunity cost.
PV = FV ÷ (1 + r)ⁿ = FV × discount factor
- FV
- amount received in the future
- 1 ÷ (1 + r)ⁿ
- discount factor for period n
The intuition. A present value answers a practical question: how much would I have to invest today, at the discount rate, to end up with that future amount? If 36,751.49 invested at 8% grows to exactly 50,000 in four years, then a promise of 50,000 in four years is worth no more than 36,751.49 to someone who can earn 8%. Paying more than that for the promise would be worse than simply investing the money.
Choosing the rate. The discount rate is not the bank's deposit rate by default. It is the return you give up by putting money here rather than in the best alternative of similar risk. A payment from a government is close to certain, so it is discounted at a low rate; a payment that depends on a start-up's success deserves a much higher one. Later tracks show how companies estimate this rate; for now, remember that riskier or more distant cash is worth less today.
A decision it settles. A fictional distributor, Saqr Trading, is owed by a customer who offers either SAR 95,000 now or SAR 110,000 in 2 years. Saqr's money earns 8% elsewhere. The later payment is worth SAR 94,307 today, so taking SAR 95,000 now is better by about SAR 693. The two options are equal at a rate of 7.61%: any business that can earn more than that should take the cash today.
A step-by-step method for a stream of payments: (1) draw a timeline and write the year of each cash flow; (2) compute each year's discount factor, 1 ÷ (1 + r)ⁿ; (3) multiply each cash flow by its factor; (4) add the results. The challenge at the end of this lesson does exactly that, and the next lessons build on it.
Data
| Discount rate | Present value |
|---|---|
| 0% | 50k |
| 2% | 46k |
| 4% | 43k |
| 6% | 40k |
| 8% | 37k |
| 10% | 34k |
| 12% | 32k |
| 14% | 30k |
| 16% | 28k |
| 18% | 26k |
| 20% | 24k |
Calculate
A customer offers to pay 120,000 in 3 years instead of a discount today. Your discount rate is 9%. What is the payment worth today?
Check your understanding
The discount rate used to value a fixed payment due in 5 years rises from 6% to 9%. What happens to its present value?
Challenge: Discounting a stream of cash flows
For each year, calculate the discount factor 1 ÷ (1 + r)^year in column C and the present value (cash flow × factor) in column D. Then total the present values in D8. Link every factor to the rate in B1.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Discount rate | 8.0% | ||
| 2 | ||||
| 3 | Year | Cash flow | Discount factor | Present value |
| 4 | 1 | 5,000.00 | ||
| 5 | 2 | 5,000.00 | ||
| 6 | 3 | 5,000.00 | ||
| 7 | 4 | 20,000.00 | ||
| 8 | Total PV |
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