hbr case study time value of money

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Time Value of Money (TVM): A Primer

• 16 Jun 2022

Would you rather receive $1,000 today or the promise that you’ll receive it one year from now? At first glance, this may seem like a trick question; in both instances, you receive the same amount of money.

Yet, if you answered the former, you made the correct choice. Why does receiving $1,000 now provide more value than in the future?

This concept is called the time value of money (TVM), and it’s central to financial accounting and business decision-making. Here’s a primer on what TVM is, how to calculate it, and why it matters.

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What Is the Time Value of Money?

The time value of money (TVM) is a core financial principle that states a sum of money is worth more now than in the future.

In the online course Financial Accounting , Harvard Business School Professor V.G. Narayanan presents three reasons why this is true:

• Opportunity cost: Money you have today can be invested and accrue interest, increasing its value.
• Inflation: Your money may buy less in the future than it does today.
• Uncertainty: Something could happen to the money before you’re scheduled to receive it. Until you have it, it’s not a given.

Essentially, a sum of money’s value depends on how long you must wait to use it; the sooner you can use it, the more valuable it is.

When time is the only differentiating factor, the money you receive sooner will always be more valuable. Yet, sometimes, there are other factors at play. For instance, what’s more valuable: $1,000 today or $2,000 one year from now?

TVM calculations “translate” all future cash to its present value. This way, you can directly compare its values and make financially informed decisions.

“Cash flows expressed in different time periods are analogous to cash flows expressed in different currencies,” Narayanan says in Financial Accounting. “To add or subtract cash flows of different currencies, we first have to convert them to the same currency. Likewise, cash flows of different time periods can be added and subtracted only if we convert them first into the same period.”

Related: 8 Financial Accounting Skills for Business Success

How to Calculate TVM

How you calculate TVM depends on which value you have and which you want to solve for. If you know the money’s present value (for instance, the amount you deposited into your savings account today), you can use the following formula to find its future value after accruing interest:

FV = PV x [ 1 + (i / n) ] (n x t)

Alternatively, if you know the money’s future value (for instance, a sum that’s expected three years from now), you can use the following version of the formula to solve for its present value:

PV = FV / [ 1 + (i / n) ] (n x t)

In the TVM formula:

• FV = cash’s future value
• PV = cash’s present value
• i = interest rate (when calculating future value) or discount rate (when calculating present value)
• n = number of compounding periods per year
• t = number of years

Calculating TVM Manually: An Example

Imagine you’re a key decision-maker in your organization and two projects are proposed:

• Project A is predicted to bring in $2 million in one year.
• Project B is predicted to bring in $2 million in two years.

Before running the calculation, you know that the time value of money states the $2 million brought in by Project A is worth more than the $2 million brought in by Project B, simply because Project A’s earnings are predicted to happen sooner.

To prove it, here’s the calculation to compare the present value of both projects’ predicted earnings, using an assumed four percent discount rate:

PV = 2,000,000 / [ 1 + (.04 / 1) ] (1 x 1)

PV = 2,000,000 / [ 1 + .04 ] 1

PV = 2,000,000 / 1.04

PV = $1,923,076.92

PV = 2,000,000 / [ 1 + (.04 / 1) ] (1 x 2)

PV = 2,000,000 / [ 1 + .04 ] 2

PV = 2,000,000 / 1.04 2

PV = 2,000,000 / 1.0816

PV = $1,849,112.43

In this example, the present value of Project A’s returns is greater than Project B’s because Project A’s will be received one year sooner. In that year, you could invest the $2 million in other revenue-generating activities, put it into a savings account to accrue interest, or pay expenses without risk.

Now, imagine there’s a third project to consider: Project C, which is predicted to bring in $3 million in two years. This adds another variable into the mix: When sums of money aren’t the same, how much weight does timeliness carry?

PV = 3,000,000 / [ 1 + (.04 / 1) ] (1 x 2)

PV = 3,000,000 / [ 1 + .04 ] 2

PV = 3,000,000 / 1.04 2

PV = 3,000,000 / 1.0816

PV = $2,773,668.64

In this case, Project C’s present value is greater than Project A’s, despite Project C having a longer timeline. In this case, you’d be wise to choose Project C.

Calculating TVM in Excel

While the aforementioned example was calculated manually, you can use a formula in Microsoft Excel, Google Sheets, or other data processing software to calculate TVM. Use the following formula to calculate a future sum’s present value:

=PV(rate,nper,pmt,FV,type)

In this formula:

• Rate refers to the interest rate or discount rate for the period. This is “i” in the manual formula.
• Nper refers to the number of payment periods for a given cash flow. This is “t” in the manual formula.
• Pmt or FV refers to the payment or cash flow to be discounted. This is “FV” in the manual formula. You don’t need to include values for both pmt and FV.
• Type refers to when the payment is received. If it’s received at the beginning of the period, use 0. If it’s received at the end of the period, use 1.

It’s important to note that this formula assumes payments are equal over the total number of periods (nper).

Here’s the calculation for Project A’s present value using Excel:

Why Is TVM Important?

Even if you don’t need to use the TVM formula in your daily work, understanding it can help guide decisions about which projects or initiatives to pursue.

“Applying the concept of time value of money to projections of free cash flows provides us with a way of determining what the value of a specific project or business really is,” Narayanan says in Financial Accounting.

As in the previous examples, you can use the TVM formula to calculate predicted returns’ present values for multiple projects. Those present values can then be compared to determine which will provide the most value to your organization.

Additionally, investors use TVM to assess businesses’ present values based on projected future returns, which helps them decide which investment opportunities to prioritize and pursue. If you’re an entrepreneur seeking venture capital funding, keep this in mind. The quicker you provide returns to investors, the higher cash’s present value, and the higher the likelihood they’ll choose to invest in your company over others.

You now know the basics of TVM and can use it to make financially informed decisions. If this piqued your interest, consider taking an online course like Financial Accounting to build your skills and learn more about TVM and other financial levers that impact an organization’s financial health .

Do you want to take your career to the next level? Explore Financial Accounting —one of three online courses comprising our Credential of Readiness (CORe) program —which can teach you the key financial topics you need to understand business performance and potential. Not sure which course is right for you? Download our free flowchart .

About the Author

• Business Case Studies

Finance & Accounting

Time Value of Money: The Buy Versus Rent Decision

Time Value of Money: The Buy Versus Rent Decision ^ W14403

Want to buy more than 1 copy? Contact: [email protected]

Product Description

Publication Date: August 28, 2014

Source: Ivey Publishing

Industry: Real estate industry

A recent MBA graduate had been renting a condominium, and a similar unit next door had just been listed for sale. Now facing the classic buy-versus-rent decision, the young grad decided it was time for her to apply some of the analytical tools she had acquired in business school - including "time value of money" concepts - to her personal life.

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