The Time Value of Money: Excel Calculations and Real-Life Examples

Time Value of Money Definition: The time value of money means that money today is worth MORE than money tomorrow because you could invest it today and earn something on it the future.

For example, if you have $100 today, that $100 is worth more NOW than in a year from now because you could invest that $100 today and end up with $105 or $110 in a year.

The time value of money is critical in valuation because it is the foundation behind Present Value and Net Present Value, which determine what assets and companies are worth.

You have to discount future cash flow to its Present Value based on your opportunity cost, i.e., what you would earn on it today if you invested it in other, similar opportunities.

Many people misunderstand this concept and think that future cash flow is less valuable just because of inflation.

It is true that inflation makes uninvested money less valuable over time.

However, the REAL reason that future cash flow is less valuable than cash flow today is because of the time value of money.

Files & Resources:

• The Time Value of Money – Examples (XL)
• Present Value Calculations – Examples (XL)

How to Apply the Time Value of Money in Real Life: Renting an Apartment

As an example of this concept, we’ll examine South Korea’s “unique” real estate system (yes, I spent some time there a long time ago).

When you rent an apartment there, there are two options: 전세 (Jeon-se) and 월세 (Wol-se). We’ll label these choices Options #1 and #2.

• Option #1: You pay an upfront deposit for 50 – 80% of the apartment’s value, but you pay no monthly rent, and you get the deposit back at the end.
• Option #2: You pay an upfront deposit for 5 – 10% of the apartment’s value, but you pay monthly rent, and you get the deposit back at the end.

Let’s use some specific numbers and say that the apartment is worth $200,000 ($200K).

Here’s what Option #1 looks like:

• Deposit of $150K (75% of apartment’s value).
• No monthly rent.
• Get back $150K deposit after 2 years.

And here’s what Option #2 looks like:

• Deposit of $10K (5% of apartment’s value).
• Monthly rent of $1K (Yearly at $12K, so $24K for two years).
• Get back $10K deposit after 2 years.

To many people, the options look like this:

With Option 1, you first pay a deposit of $150K, and you get $150K back in Year 2 with no monthly rent.

On the surface, it seems like you have not “lost” any money ($150K in Year 2 – $150K Deposit = 0).

With Option 2, it looks like you “lose” $24K because you pay a $10K deposit upfront and annual rent of $12K for two years, and then you receive back the $10K deposit in Year 2.

So, to many people, Option 1 sees like the better option because you do not lose the $24K of rent.

However, this is not an accurate comparison because of the following:

1. $150K received back in 2 years is worth LESS than $150K today. Even if we receive back “the same amount” in the future, it’s worth less than it is today.
2. Paying $140K more for the deposit means that you CANNOT invest that $140K elsewhere and earn something with it. So, there’s an opportunity cost associated with a higher deposit. You could have used that $140K to invest and earned more over these 2 years.

Let’s use Excel to illustrate these points:

If we look at the Opportunity Cost + “Money Lost” with Option #1, it’s $24K.

With Option #1, we pay no rent, but we do pay an extra $140K upfront.

To determine if Option #1 or #2 is better, we need to know what we could EARN with this extra $140K.

In this example:

• Year 1 Lost Earnings = $140K Deposit Difference * 8.2% Opportunity Cost = ~$12K
• Year 2 Lost Earnings = (~12K Lost in Year 1 + $140K Deposit Difference) * 8.2% Opportunity Cost = ~$24K

So, in total, you could have earned $24K extra by paying a $140K lower upfront deposit.

Therefore, in this case, the outcome is the same at an 8.2% opportunity cost, even though Option #2 “looks” worse due to the annual rent.

We use the deposit difference here because even with Option #2, we would still have to pay the $10K upfront deposit.

So, it would not be correct to use the $150K total deposit under Option #1 as the comparison point here.

If we use a higher percentage for the opportunity cost, the “Money Lost” is even greater with Option #1:

By contrast, Option #2 still costs us only $24K.

So, with this opportunity cost, Option #2 is superior even though it seems to result in more “money lost” on paper.

How to Apply the Time Value of Money in Investment Decisions

In investment analysis, the time value of money comes up most often when you are calculating the Present Value of an investment or the annualized returns (the internal rate of return or IRR).

For example, if you’re valuing an asset that will generate $100 of cash flow each year for 10 years, the $100 of cash flow in Year 10 will be worth much less than the cash flow in Year 1 because of the time value of money.

If you could earn an annualized return of 5% per year on other, similar assets, then the $100 of cash flow in Year 10 is worth:

• $100 / ((1 + 5%) ^ 10) = $61.4.

If you could earn 10% per year on other, similar assets, it’s even worse:

• $100 / ((1 + 10%) ^ 10) = $38.6.

This doesn’t mean that you shouldn’t invest in this asset.

Instead, it means that you should focus on the asset’s near-term cash flows because they are worth more to you today than the ones it will generate in Year 10, 20, or 30.

This “discounting” approach is widely used in Discounted Cash Flow (DCF) models and other valuation methodologies such as the Dividend Discount Model (DDM).

The time value of money also comes up in concepts such as bond valuation, bond yields, the yield to maturity, and leveraged buyout (LBO) models.

In these analyses, the assumption is that when an asset generates cash flows during the holding period, you re-invest these proceeds at the same rate as the overall annualized return.

Therefore, the time value of money influences the results because this re-investment assumption means that cash flows earned during the holding period become more valuable by the end.

There are ways to adjust for this, such as by using the MIRR function rather than IRR or XIRR; MIRR is the “Modified Internal Rate of Return” and lets you assume a different rate of return on the re-invested proceeds.

The Time Value of Money: Key Takeaways

The main points of this article are:

1) Discounting Future Values – Whenever an asset generates cash flow in the future, or you assume a sale of the asset in the future, you must discount it to its Present Value because money today is worth more than money tomorrow.

2) Upfront Payment vs. Paying Over Time – Many people claim that buying a house or paying a large deposit in exchange for no rent is always a better deal because “you can get your money back,” but this is not true.

It depends on what you could earn with the money you would have spent buying the house or putting down a larger deposit and how this compares to the ongoing rental cost of the property.

3) Comparing Assets and Investments – Finally, when you’re completing these types of exercises, you always want to compare similar types of assets and what you could earn on each one.

For example, it’s inappropriate to compare U.S. Treasuries (government bonds) with a real estate investment or the stock market because the risk and potential returns are completely different.

It is more appropriate to compare the potential returns on a real estate investment to those of other, similar properties in the same geographic region.