How to Calculate Opportunity Cost in Loan Analysis

If you use the Loan Analysis calculator, you’re likely familiar with the “Loan View” provision. This enables you to do a side-by-side comparison of two loans, or view each loan individually. There's also a fourth option: “Opportunity Cost.”

The function of this button is to more clearly show what Todd demonstrates in his comparison of a 15-year vs. 30-year mortgage. That is, you cannot separate a mortgage analysis from the time value of money.

In previous demonstrations, Todd has used the Financial Calculators, such as Present Value and Future Value, to show that the opportunity cost of both mortgages is the same. In fact, the opportunity cost of a cash payment is also the same. While using the Financial Calculators can help you break it down for a client, the Opportunity Cost button is a faster way to do the same calculations, if you already understand the principles.

The Cost of A Mortgage

In this example, say your client is shopping for a mortgage on a \$250,000 house. His bank is offering the same 4.5% rate regardless of the amortization schedule. His 15-year mortgage payment would be \$1,912.48 a month. For a 30-year mortgage he would pay 1,266.71 a month.

With Loan Analysis, you can input this information and compare the two. Then, by clicking “Cost Summary,” you can see the Net Cumulative Cost of each loan. From a pure cost perspective, the 30-year mortgage costs more. However, this is removed from the time value of money.

Solving for the Time Value of Money

This is where the Opportunity Cost button becomes truly fun. If you click on the button, it will look something like this:

If you’re wondering why nothing has changed, that's because you've got to include one more variable. In order to calculate for the time value of money, you must include the savings rate. After all, opportunity cost is a reflection of what those dollars could earn if not spent. So, under both loans, adjust the savings rate to 4.5% for each, and you’ll see this:

By adding the savings rate, you’re effectively doing what the Future Value calculator accomplishes: adding in the time value of money. In other words, what would the opportunity cost of this money be over 360 months at 4.5%?  The calculator applies this logic the same way a person would. For the 15-year mortgage, the opportunity cost is the cost of waiting 15 years to save the equivalent of the mortgage payment. The opportunity cost of the 30-year mortgage is the cost of only saving the difference between the mortgages instead of saving the whole thing.

Don’t Forget the Opportunity Cost of Cash

You may have noticed that when you toggle to “Opportunity Cost,” a CASH button appears. If you click that, you can calculate the opportunity cost of paying in cash. Input the same \$250,000 and add a savings rate of 4.5%. This represents what that money could become at the same rate over 360 months. Here’s what you’ll see:

The result? The opportunity cost of each decision is the same. And if you plug this information into the Future Value Calculator the old-fashioned way, it will confirm.

What the Opportunity Cost Button Represents

Using the Future Value Calculators is a simple-to-follow method of showing your client why the Opportunity Cost of each option is the same. It demonstrates the significance of the Time Value of Money, without getting too bogged down in the numbers. If you want to drive home the point, this might be the easier route. However, for your own calculations–or with a client who has a good grasp of the concept–the built-in Opportunity cost button can speed up your work.

There's also another powerful benefit to using the Opportunity Cost button: it actually shows the compounding effect of interest. In the column labeled “Compound Opportunity Cost @ 4.5%” what you’re seeing is the potential interest earnings of each monthly mortgage payment. The Future Value calculators don't have this level of detail, and can only prove that the cumulative result is the same. However, it's clear that on a month-by-month basis, the 30-year-mortgage actually has the lowest opportunity cost, because more money is being saved and therefore being EARNED.

The takeaway? The 30-year mortgage (Loan 2) really is the shining star of the mortgage world. The lower monthly payment provides more flexibility and freedom, while freeing up more money for opportunities as they arise.