Annualisation Explained for Dummies

What is annualisation?

Annualisation occurs when a short-term rate or a portion of a year amount is converted to an annual rate or a full-year amount. The Collins English Dictionary explains the concept annualise as follows: ‘Annualise is to convert (a rate of interest) to an annual rate when it is quoted for a period of less than a year.’ (Accentuation by the article writer.) Typically, annualisation enables analysts and investors to predict the financial performance of a security, an asset, or business for the following year. In addition, annualisation is used to compare the yields of different types of investments.  

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Examples and calculations of annualisations

Annualised income

What is an annualised income?

An annualised income is an estimation of the amount of money that a business or individual earns during a specific year.  

Examples of annualised incomes

Example #1 The business Tough Times generates an income of R20 000 over a period of 3 months, which is one quarter of a year. The annualised income of Tough Times is calculated as follows: R20 000 x 4 = R80 000 The answer of R80 000 is the expected income for business Tough Times over 4 quarters (= one year).   Example #2 Pete, a salesperson with a commission-based job, received the following income for the financial year starting at 1 March:

• March: R20 000
• April: R23 000
• May: R18 000
• June: R21 000

To annualise Pete’s income, the total of the income earned for the 4 months is multiplied by the ratio of the number of months in a year (12) divided by the number of months for which the income amounts are available. Thus, Pete’s annualised income will be calculated as follows: (R20 000 + R23 000 + R18 000 + R21 000) x 12/4 = R82 000 x 12/4 = R246 000  

Annualised salary

What is an annualised salary?

An annualised salary refers to the amount an employee would earn during a year, even when he or she is not employed for 12 months of a year. An annual salary varies from an annualised salary because it refers to an employee’s total yearly earnings, the amount a person can expect to earn as a salary during a given year. For instance, when an employee receives a fixed monthly salary of R20 000, his/her annual salary is R240 000 (12months x R20 000). Calculating annualised salaries is useful for businesses when budgeting for part-time workers and employees who will not be employed for the entire financial year.  

Examples of annualised salaries

Example #1 (Employee with a monthly salary) Employee B receives a monthly salary of R15 000. Her annualised salary is R180 000 (R15 000 x 12 months).   Example #2 (Employee with a semi-monthly salary) Employee C’s conditions of employment state that he is entitled to a semi-monthly salary of R8 000 that is paid in the middle and at the end of a month. The calculation of his annualised salary is as follows: R8 000 x 24 (12 months x 2 payments per month) Annualised salary = R192 000   Example #3 (Employee who is not employed for a full financial year) Employee D who resigned 7 months after the start of the financial year of business XYZ, has received monthly salaries to the amount of R105 000 at that point in time. Employee D’s annualised salary will be determined as follows:

• Determine the monthly income

R105 000/7 months = R15 000

• Multiply the monthly income by 12 months

R15 000 x 12 months Annualised salary = R180 000   Example #4 (Part-time worker) Donald Duck is a part-time worker, working 18 hours per week for 50 weeks at an hourly rate of R25 during a given financial year of a company. The annualised salary of Donald Duck will look as follows:

• Calculate the number of working hours per year

18 hours x 50 = 900 hours

• Multiply the working hours with the hourly rate

900 hours x R25 Annualised salary = R22 500  

Annualised budget

What is an annualised budget?

An annualised budget allows a person or business to forecast revenue and expenses for an entire financial year, based on the year-to-date (YTD) figures at a specific point in time, for instance after the first six months. An annualised budget, also called an operating or master budget, allows an individual or business to estimate yearlong performances, adjusting projections based on actual figures as the financial year moves forward to its end. The annualising of the income and expenses is done in the following way: The YTD figure at a specific time is divided by the number of expired periods, such as months, for the given financial year to obtain an average per period. The average is then multiplied by 12 (months) to determine the estimated figure at the end of the financial year. For example, at the end of August (the sixth month of the financial year) the accountant of the business Bright Star finds the following totals with regard to the income and expenses of the business: Both the totals of income and expenses are divided by six months to calculate the average balances per month. The average balances are then multiplied by 12 months to determine the annualised income and expenses.  

• Annualised income

R581 000/6 = R96 833 = R96 833 x 12 =R1 161 996  

• Annualised expenses

R513 000/6 = R85 500 x 12 = R1 026 000 Thus, the annualised surplus of the business Bright Star is R135 996 (R1 161 996 - R1 026 000).  

Annualising concerning loans

Short-term loans

Interest rates on short-term loans can also be annualised. For instance, a rate of 5% on a loan for a quarter of a year does not seem to be exorbitant. However, annualising the rate equates to 20% (4 x 5%).  

Annual percentage rate

Furthermore, annualised costs related to loans are often expressed as an annual percentage rate (APR). Origination fees, additional fees, and interest charged on a loan are annualised to get the APR, which is a percentage of the amount borrowed. The annual percentage rate is defined as the annual rate of interest that a borrower must pay on a loan. APR applies to different types of loans, such as vehicle loans, mortgages, and credit cards.

Calculation of APR

Typically, the following steps are followed to calculate the annual percentage rate (APR):

1. Calculate the sum of the total interest charged over the duration of the loan, the origination fees, and all the additional fees.
2. Divide the sum by the loan amount.
3. Divide the answer of step 2 by the total number of days in the term of the loan.
4. Multiply the answer of step 3 to get the annual rate.
5. Multiply the answer obtained in step 4 by 100 to convert the annual rate into a percentage.

The formula to calculate the APR of a loan is expressed as: APR = ((Interest + Fees/Loan amount)/Number of days in the loan term) x 365 x 100 Where:

• Fees comprise origination fees, administrative costs, and additional fees.
• The loan amount refers to the principal amount, which is the initial amount of a loan.

  Example of an APR calculation: Let us say, Justin borrows R20 000 from a bank at an interest rate of 8% for 3 years. Fees entail an origination fee of R1 000 and an administrative cost of R800. Calculation of the APR on Justin’s loan:

• Determine the interest accrued
• Calculate the total accrued amount by using the simple interest formula:

A = (P (1+(R x T))   Where:

• A = total accrued amount
• P = principal amount
• R = interest rate
• T = time frame

Thus, A = (R20 000(1 + (0.08 x 3)) = (R20 000(1 + 0.24)) = (R20 000(1.24) = R24 800  

• Calculate the interest

A - P = R24 800 - R20 000 = R4 800  

• Find the sum of all the fees related to the loan

R1 000 (origination fee) + R800 (administrative cost) = R1 800  

• Apply the APR formula

APR = ((Interest + Fees/Loan amount)/Number of days in the loan term) x 365 x 100 = ((R4 800 + R1 800/R20 000)/365 x 3) x 365 x 100 = (R6 600/R20 000)/1 095) x 365 x 100 = (0.33/1 095) x 365 x 100 = 11% Thus, the APR on Justin’s loan is 11%.  

Types of annual percentage rate (APR)

There are two types of APR:

• Fixed APR

Regarding a fixed APR, the interest rate applicable does not vary. Therefore, the APR calculated based on the interest will also be fixed, implying the cost of money for borrowing the money stays the same.

• Floating interest rate

A floating interest rate, also called a variable interest rate, is an interest rate that varies according to the market, the prime lending rate of a country, or an index. When a floating interest rate increases, the APR increases, implying the borrower pays more to borrow the money.  

Annualised return

What is annualised return?

Annualised return, also referred to as annualised total return, refers to the average amount of money that investment has earned for an investor each year over a certain time frame if the annual return was compounded. Differently put, by calculating the annualised return of an investment, analysts are able to determine how much an investment has lost or gained during a certain period of time, taking compounding into consideration. Compounding implies that the returns of investment for consecutive years are interdependent. The annualised return of investment allows an investor to determine how effective investment has performed by comparing its return to corresponding investments.  

The difference between annualised returns and average returns

Contrary to annualised returns, average returns do not take compounding into account, only adding all of the annual returns of investment together and then divide the sum by the number of years applicable to the analysis. For instance, an investment of R10 000 performed as follows for the past 3 years: -20%, 15%, 10%. The average annual return for the 3 years = (-20% + 15% + 10%)/3 = 1.6%. Based on the calculation above, the total investment should be R10 160. However, this is not correct. An annualised return calculation indicates a more accurate picture as explained below:

• Value of investment at end of year 1: R8 000 (R10 000 - 25%)
• Value of investment at end of year 2: R9 200 (R8 000 + 15%)
• Value of investment at end of year 3: R10 120 (R9 200 + 10%)

The total of R10 120 at the end of year 3 indicates that the investment’s three-year annualised return is 1.2%. The average return is also called simple average return or mean return.  

The calculation of annualised return

The formula to calculate the annualised return of investment is: (1 + Return) ^ (1/N) - 1 Where:

• Return = the overall return, calculated as follows: (ending value - beginning value)/beginning value
• N = number of periods measured

For example, R12 000 was invested in a portfolio and after 5 years its value increased to R30 000. Thus, the overall return is (30 000 - 12 000)/12 000 = 1.5 The calculation of the annualised return of the investment will look as follows: (1 + 1.5) ^ (1/5) - 1 = 2.5 ^ 0.2 - 1 = 0.20 = 20%

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