What you will learn
- Explain why receiving a dollar today is better than receiving the same dollar later
- Calculate how much money will be worth after it grows at a fixed rate
- Discount a future payment to find what it is worth today
- Connect discounting to the way investors value financial assets
Would you rather receive 1,000 dollars today or wait a year for the same 1,000 dollars? Taking the money today is the sensible choice. That preference has a name: the time value of money. The idea is used to price bonds and value entire companies, and the calculations follow a clear pattern.
Time Value of Money
Finance and Quant Society teaches the reason money today is worth more than money later. Watch this before moving on!!
Why money today is worth more
- Opportunity cost: you can invest money that you have now and earn a return on it. Waiting gives up that opportunity.
- Inflation: prices tend to rise, so one dollar usually buys less next year than it buys today.
- Risk and uncertainty: someone may promise to pay you later, but that payment might never arrive. Money you already have carries no such uncertainty.
Key terms
- Present value (PV)
- The value today of money that will be received in the future.
- Future value (FV)
- The amount that today's money will grow to by a future date at a given rate.
- Discounting
- Working backward from a future amount to find its value today.
- Discount rate
- The rate used to turn future money into present value. A higher rate produces a lower present value.
Future value: move today's money forward
Money invested at a steady annual rate grows to a future value. The formula is FV = PV x (1 + r) to the power of n. In this formula, r is the annual rate and n is the number of years. You multiply the balance by one plus the rate for each year that it grows.
Grow 1,000 dollars for ten years
You invest 1,000 dollars for 10 years and earn 6 percent per year. What will the investment be worth at the end?
- List the inputs. PV = 1,000, r = 0.06, and n = 10.
- Calculate the growth factor. 1.06 to the power of 10 is about 1.7908.
- Apply it to the starting amount. 1,000 x 1.7908 is about 1,790.80.
Why it matters: The balance is multiplied each year rather than increased by the same fixed amount. The next lesson looks more closely at this process, called compounding.
Find the future value
You invest 2,000 dollars for 3 years at 5 percent per year. What is its future value, rounded to the nearest dollar?
Present value: bring future money back to today
Present value runs the calculation in reverse. To find today's value of a future payment, you discount it. The formula is PV = FV divided by (1 + r) to the power of n. Here, r is the discount rate and n is the number of years. The answer tells you how much less a future dollar is worth than a dollar you can use today.
Find today's value of 1,000 dollars next year
Someone promises to pay you 1,000 dollars one year from now. If you use a 5 percent discount rate, what is the payment worth today?
- List the inputs. FV = 1,000, r = 0.05, and n = 1.
- Set up the calculation. Divide 1,000 by 1.05.
- Finish the division. 1,000 divided by 1.05 is about 952.38.
Why it matters: About 952 dollars invested today at 5 percent would grow to 1,000 dollars in a year. That is why the two amounts have the same value at those points in time.
Find the present value
You will receive 5,000 dollars in two years. Using a 4 percent discount rate, what is that payment worth today? Round to the nearest dollar.
Introduction to present value (Khan Academy)
Present value gets a slower walkthrough here. It may help if discounting still feels backward after the examples.
Choose between two payments
You can take 1,000 dollars today or receive 1,030 dollars one year from now. You could safely earn 5 percent on money you have today. Ignoring taxes, which offer is worth more?
Grow the 1,000 dollars at 5 percent for one year. It becomes 1,050 dollars, so taking the money today is the better offer.Every valuation in finance brings future money back to today's value.
Explain the discount
Why are a company's future profits worth less today than the same profits received right now? Explain it in your own words and use the word discount.
Write an answer before comparing it with the model response.
Model answer
Money received now could be invested and allowed to grow. Inflation also reduces what future dollars can buy, and there is some uncertainty about whether future payments will arrive. Investors discount those future profits to find their value today before adding them together.
Later units use discounting in discounted cash flow models, bond pricing, and option valuation. Next, you will look at the other direction of the same math: how compound interest grows money over time.