Present Value & the Time Value of Money
A dollar today is worth more than a dollar tomorrow, because today’s dollar can earn interest. Present value converts a future cash flow back to its worth today by discounting it at an interest rate. It is the single idea behind every bond, loan, and valuation in the course.
Why it matters
Discounting is compounding run in reverse. If money grows at the interest rate going forward, then to come back from a future amount you divide by that same growth. The higher the rate or the further away the cash flow, the less it is worth now.
Formulas
Worked examples
How much is $100 received in one year worth today if the interest rate is 5%?
PV = 100 / 1.05 = $95.24. Put $95.24 in the bank at 5% today and it grows to $100 in a year, which is why the two are equivalent.
Common mistakes
- ✗A dollar is a dollar whenever you get it. Timing matters. A future dollar is worth less today because of forgone interest.
- ✗A higher interest rate raises present value. The opposite. A higher discount rate shrinks the present value of any future cash flow.
Revision bullets
- •Present value discounts a future cash flow to today
- •Discounting is reverse compounding
- •Higher rate or longer horizon means lower present value
Quick check
Holding the amount fixed, raising the interest rate makes a future cash flow’s present value
Connected topics
Sources
- Mishkin (2018), Ch. 4Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.Introduces present value and discounting as the foundation of interest-rate analysis.