Present Value & Discounting

What a future cash flow is worth today

Finance FundamentalsThe Time Value of MoneyFree preview
⏱️ About 15 min
Present Value & Discounting — illustration

Someone promises to pay you $5,000 in five years. What is that promise worth to you right now?

💡
The big idea: Discounting is compounding run in reverse: dividing a future cash flow by the growth factor converts it into an equivalent value today.
🎯 By the end, you'll be able to
  • State the present-value formula and relate it to future value.
  • Discount a single future cash flow to the present.
  • Explain how the discount rate and horizon change present value.
📎 Helpful to know first

The lesson "Future Value & Compounding".

Reversing the growth

If pushing money forward multiplies by \((1+r)^n\), then pulling money backward must divide by the same factor. Solving \(FV = PV(1+r)^n\) for \(PV\) gives the present value:

\[ PV = \dfrac{FV}{(1 + r)^{n}} \]

The discount rate

Here \(r\) is called the discount rate: the return you could otherwise earn, which sets how much a future dollar is worth today. A higher discount rate or a longer horizon both make the present value smaller.

ℹ️ Same idea, two directions

Compounding and discounting are the same relationship viewed from opposite ends of time. Every valuation in finance is ultimately discounting future cash flows back to the present.

🎮 Present-Value Explorer LIVE
Predict first: as you slide the horizon from 1 year to 30 years, does the present value fall in a straight line or a curve?
Present value of a single future cash flow as the horizon and discount rate change.
📝 Worked example: What is the present value of $5,000 to be received in 5 years, discounted at 8% per year?
  1. Inputs: \(FV = 5000\), \(r = 0.08\), \(n = 5\).
  2. Discount factor: \((1.08)^{5} = 1.469328\).
  3. Divide: \(PV = 5000 / 1.469328 = 3402.92\).
✓ PV = $3,402.92
✏️ Practice: What is the present value of $10,000 to be received in 12 years, discounted at 6% per year?
💡 Hint
Compute \((1.06)^{12} = 2.012196\), then divide 10000 by it.
Answer
PV = $4,969.69

Check your understanding

1. All else equal, raising the discount rate makes the present value of a future cash flow:
A larger denominator \((1+r)^n\) makes the present value smaller: future dollars are discounted more heavily.
2. Present value and future value are related because discounting is:
Dividing by \((1+r)^n\) exactly undoes multiplying by it, so discounting is compounding in reverse.
🔎 Related lessons
Next: Annuities & Perpetuities
✅ Key takeaways
  • Present value is \(PV = FV / (1+r)^n\) - a future cash flow pulled back to today.
  • A higher discount rate or longer horizon lowers present value.
  • Discounting is the engine behind every valuation in finance.
➡️ Most real finance involves a stream of many cash flows, not one. Next we value level streams: annuities and perpetuities.
Want to test yourself on this? Try the Finance Fundamentals Aptitude test →
🎓 Go deeper: external courses & trusted references

External sites are listed for reference only. This course is independent and has no affiliation with, or endorsement from, the institutions named.

⚖️
Educational content only. This course explains finance concepts and the math behind them; it is not financial, investment, tax, accounting, or trading advice, makes no recommendations, and predicts no returns, prices, or outcomes. All figures are illustrative teaching examples. Consult a qualified professional before making financial decisions.