# Annualize

Convert an end result into an annual basis

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## What Does Annualize Mean?

To annualize is to convert a short-term or partial period result into an annual basis. Annualization is helpful when comparing the returns of two or more investments or if a borrower wants to know how much interest they would need to pay for taking a loan. A return of a short-term investment – e.g., Treasury bills that mature within one year – is annualized to compare it with a long-term investment. Annualizing, in such a case, helps an investor to make a decision in selecting the investment product that would yield the best returns.

Below is the formula for converting a return into annualized terms. For example, if the monthly returns on an investment are 2%. The annualized return using the below formula is (1 + 0.02) ^ 12 – 1 = 26.8%. ### Summary

• Annualization is the process of converting a short-term figure into annualized terms so that it’s easy to compare values to make an informed decision.
• The APR or the annual percentage rate is the annualized cost of taking out a loan, including the fees charged by the lender to the borrower over and above the interest rate.
• The equivalent annual cost (EAC) is the cost of owning an asset over its life. By calculating the EAC, the company can decide which asset will provide them with a cost-effective return on their investment.

### Benefits of Annualization

Suppose the employment in Toronto grew by 0.90% in the first six months of the year. In July and August, they grew by 0.10% and 0.15%, respectively. In order to know if employment in July and August were better than the first six months, we would need to annualize all the figures.

The six-month growth rate of 0.90% converts to 1.81% per year. The growth rate in July comes to 1.21% annually and 1.81% per year in August.

After the annualization of the growth rates, Toronto’s employment growth was down compared to the annualized growth rate in the first six months, while in August, the growth rate was flat compared to the first six months.

Annualization helps individuals and companies make significant comparisons. For example, a photographer currently earns weekly pay of \$1,000. If a different company offers \$78,000 annually, should the photographer apply for the new role?

Here, they would need to convert their current weekly pay into annual terms. By multiplying \$1,000 per week into 52 weeks in a year, the annual salary comes to \$52,000 per year. It clearly shows that the new role will pay \$26,000 more than the current salary, and hence, they should apply for the new role.

### Annual Percentage Rate (APR)

An interest rate on a loan is the extra cost that a borrower pays for taking the loan from the financial institution. However, it does not include the fees for the loan. Hence the APR comes into the picture. The APR includes the fees and the interest rate on the loan, which is expressed in terms of a percentage.

If the APR is higher, it is an indication that the lender is charging a higher fee for the loan. Since all the lenders are required to disclose the APR along with the interest rates, it helps the borrower to compare the products and make an accurate decision.

### Equivalent Annualized Cost (EAC)

Equivalent annualized cost (EAC) is the annualized price of owning an asset over its life. It is an important concept in capital budgeting that helps companies make decisions on which project to select.

Below is the formula to calculate EAC: Where:

• r = Discount rate or rate of return
• n = Life span of the asset

For example, suppose a transportation company is looking at buying a bus, narrowing it down to two buses. Bus A costs \$50,000 with a life span of five years, while bus B costs \$80,000 with a life span of seven years. The company is looking at a return of 10%, which is the discount rate. Bus A is expected to incur an annual maintenance cost of \$10,000, while bus B is \$8,000. Using the above formula, the EAC is calculated as below,

EAC (Bus A) = \$50,000 * 10% / [1 – (1+10%)-5] + \$10,000 = \$23,189.87

EAC (Bus B) = \$80,000 * 10% / [1– (1+10%)-7] + \$8,000 = \$24,432.44

It is clear that bus B is more cost-efficient, with a savings of around \$1,242.57 per year.

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