Average Life Calculation

What is Average Life?

Average Life is a metric used in finance to describe the average time until a loan or bond is repaid. It is particularly useful for loans with different repayment structures, as it provides a single number that represents the weighted average time to repayment.

Understanding Average Life

Average Life calculations are essential in the syndication process when selling loans with varying repayment structures. These calculations help reflect the different maturity profiles of loans, which are often designed around the cash flows of specific projects or finance transactions.

Uses of Average Life

Average Life is used to compare loans with different maturities and repayment patterns. It helps in pricing loans accurately by considering the time value of money and the risk associated with different repayment schedules.

This metric is particularly helpful for bankers and financial analysts to assess the credit risk and pricing of loans. Average Life gives investors an indication of how quickly they can expect returns. Most investors will choose an investment that offers the earliest financial returns and therefore prefer investments with a shorter Average Life.

Weighted-Average Life

Weighted Average Life (WAL) can be used interchangeably with Average Life and is the average time that each dollar of unpaid principal on a loan or mortgage remains outstanding. WAL helps investors understand the timing of cash flows from a bond or loan. It provides a more accurate measure of the investment’s duration compared to the bond’s maturity date.

How to Calculate the Average Life on a Bond

The calculation of Average Life involves summing the weighted average of the time periods until each principal repayment is made. The formula considers the amount of principal repaid at each time period and the total principal amount.

To calculate the Average Life of a bond, you need to:

1. Assign a weight to each year of the bond’s life (e.g. 1, 2, 3, etc)
2. Multiply the weight by the repayment amount for each year
3. Sum the weighted repayments
4. Divide the sum of the weighted repayments by the original loan amount

For example, if a loan has repayments of 5, 10, 20, 25, and 40 in years one through five, the weighted repayments would be 5, 20 (2×10), 60, 100, and 200, respectively. Summing these gives 385, and dividing by the original loan amount of 100 gives an average life of 3.9 years. This compares to a maturity of 5 years.

How To Calculate Weighted-Average Life (WAL) on a Loan

To look at another example of the Average Life calculation please enter your email to access the free Financial Edge template. This excel spreadsheet contains two loan examples and how calculate weighted-average life.

Follow these steps to complete the free Excel template and calculate WAL of the two loans:

1. Start with Loan 1 – create the Beginning Balance for Year 1 (cell D9) by linking the Ending Balance of the previous year (200 for year 1 in cell C11)
2. Calculate the Ending Balance in cell D11 (Beginning Balance + Repayment = Ending Balance)
3. Copy the Beginning Balance link across to the right for each year (row 9) and copy the Ending Balance calculation across all 5 years of the loan (row 11)
4. This shows that the first loan will be fully repaid by the end of Year 4, so will have a maturity of 4 years
5. Let’s now do same steps (linking Beginning Balance and calculating Ending balance) for Loan 2 which is for the same amount (200) and repays the same amount for Year 1 (40) and then varies in repayments
6. The calculations show that the second loan is fully repaid by the end of Year 5
7. Looking at the maturity we can see that the second loan might be riskier as its maturity is longer than the first loan (5 years vs. 4 years)
8. But let’s check the Average Life calculation of each loan in cell D13: firstly, calculate the weighted payments by taking the year (Year 1 would be 1) multiplied by the payment (and shown as a negative)
9. Once completed the calculation (Year 1 * –Year 1 Repayment) can be copied over to the right for each year (to cell H13)
10. Sum the total (660) and divide by the initial loan size (200) to get an average life of 3.3 years
11. Do the same for the second loan (Weighted payments by year, sum of the weighted payments) to calculate the average life of 3 years

This average life figure is helpful to compare two loans for the same amount which have different repayments and maturities. The average life calculation shows us the average maturity of the loans, in this case 3.3 years and 3.0 years respectively. This means that on average the second loan is going to be repaid faster than the first loan. From a credit perspective it is going to be considered less risky than the first loan. Thus, the first loan needs to be priced slightly higher.

Mortgage-Backed and Asset-Backed Securities

Mortgage Backed Securities (MBS) and Asset-Backed Securities (ABS) are types of securities that use Average Life to provide investors with insights into the expected repayment schedule. These securities often have irregular cash flows due to prepayments and defaults, making Average Life a crucial metric.

Special Considerations

When comparing loans with different repayment structures, it is essential to consider the average life. For instance, a loan with a bullet repayment (single lump sum at the end) will have a different average life compared to a loan with staggered repayments. The average life helps in pricing these loans accurately, as it reflects the time value of money and the risk associated with the repayment schedule.

Conclusion

Understanding the concept of Average Life is crucial for accurately pricing loans and assessing credit risk. By considering the weighted average time to repayment, financial analysts and bankers can make more informed decisions, ultimately enhancing the efficiency of financial transactions.

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