More dollars is not always more wealth.
Inflation changes what money can buy. Present value only works when cashflows and discount rates speak the same language.
Present Value Relations
Four connected lessons turn future cashflows into value today. Complete the first three to unlock the integrated CFO Decision Room.
Inflation, Real vs Nominal, and Wrap-Up
What you should understand in this lesson
Inflation changes purchasing power. Students must distinguish real and nominal returns and use consistent discounting in NPV calculations.
Inflation is not the same as the time value of money
Time value of money concerns money now versus money later. Inflation concerns what money can buy now versus later.
Real wealth depends on prices
If your wealth rises by 10% but the prices of everything you buy also rise by 10%, you have more dollars but not more real purchasing power.
Real return vs nominal return
The nominal return is what you see quoted. The real return is what your wealth can actually buy after prices move.
If nominal return is 10% and inflation is 10%, real progress is about 0%. If nominal return is 15% and inflation is 10%, real return is approximately 5%, but not exactly.
Fix invalid NPV setups
Each case states a cashflow and the language it is written in. Pick the discount rate that keeps the whole setup in one language. Mixing real cashflows with a nominal rate, or nominal cashflows with a real rate, breaks the NPV before any arithmetic begins.
Forecast by operations in the actual dollars to be received, with 3% price inflation built into every line.
Benefits fixed in today's purchasing power, with no inflation escalation written into the plan.
Rent is set in constant dollars and reviewed only for real wage growth, not for headline inflation.
The consistency rule
Discount nominal cashflows using nominal interest rates. Discount real cashflows using real interest rates. Never mix real cashflows with nominal discount rates or nominal cashflows with real discount rates.
Worked Example 5: Present value of future income
- 1Find the real interest rateReal interest raterreal = (1 + rnominal)(1 + π) − 1= 1.051.02 − 1 = 2.94%
What gets harder after this lesson
Real-world valuation adds frictions on top of the consistency rule. Each of these changes either the cashflows, the discount rate, or both.
What Present Value Relations gives you
- 1Assets are sequences of cashflows.
- 2Cashflows at different dates are different economic units.
- 3Present value converts future cashflows into today's dollars.
- 4NPV is the present value of benefits minus costs.
- 5Positive-NPV projects create value.
- 6Perpetuities and annuities are special cashflow patterns.
- 7Compounding affects the true annual rate.
- 8Inflation changes purchasing power.
- 9Real and nominal cashflows must be discounted consistently.
Answer all questions, then check your work. You can retry any time — mastery is based on correctness, not speed.
- 01
Which best distinguishes inflation from the time value of money?
- 02
Nominal return 15%, inflation 10%. Real return is approximately:
- 03
Real cashflows should be discounted with:
- 04
Nominal cashflows should be discounted with:
- 05
In the lifetime-income example, the real interest rate was 2.94% and the present value was about:
- 1Assets are sequences of cashflows.
- 2Cashflows at different dates are different economic units.
- 3Present value converts future cashflows into today's dollars.
- 4NPV is the present value of benefits minus costs.
- 5Positive-NPV projects create value.
- 6Perpetuities and annuities are special cashflow patterns.
- 7Compounding affects the true annual rate.
- 8Inflation changes purchasing power.
- 9Real and nominal cashflows must be discounted consistently.