# Average Life

Also referred to as Weighted Average Life, or WAL, the average life of a mortage loan refers to the number of periods (commonly denoted in years) in which half the time-weighted principal has been paid.

Lenders use this metric in a variety of ways, including to price the loan (i.e. as part of the benchmark calculation to arrive at an appropriate interest rate) and to compare the risk of two loans of similar loan maturity.

## Putting ‘Average Life’ in Context

#### Scenario

Sunshine Bank, a regional bank based in Miami, Florida, is considering issuing a senior loan to finance the acquisition of Bayside Residences, a recently developed and stabilized market-rate multifamily apartment complex. Bayside Residences is a 250-unit property located in the thriving Biscayne Bay area, with a stabilized value of \$50 million.

#### Protagonist – Sunshine Bank

Emma Rodriguez, a senior loan officer at Sunshine Bank, is responsible for evaluating the loan application submitted by Starfield Life Insurance Company, which is looking to acquire Bayside Residences as part of its core investment portfolio.

#### Use of Average Life

To determine an appropriate interest rate for the loan, Emma calculates the average life (also known as weighted average life or WAL) of the mortgage. The average life of a mortgage loan is the number of periods (years) in which half the time-weighted principal has been paid.

Emma is reviewing a 10-year loan term with monthly payments. To calculate the average life, she must account for the amortization schedule, which includes both principal and interest components. By calculating the average life, she can compare this loan to other loans with similar maturities and evaluate the associated risk.

#### Calculation of Average Life

Assume the loan amount is \$35 million at an interest rate of 6.00% with a 30-year amortization period. Emma uses the following formula to calculate the average life:

```WAL = ∑(t × Pt) / ∑Pt
```

Where t is the period and Pt is the principal payment in period t.

1. Calculate the monthly mortgage payment using the formula for a fixed-rate mortgage:
```    M = P × [r(1+r)^n] / [(1+r)^n - 1]
```

Where:

• M is the monthly payment
• P is the loan principal (\$35 million)
• r is the monthly interest rate (6.00%/12 = 0.005)
• n is the number of payments (30 years × 12 months = 360)

Plugging in the values:

```    M = 35,000,000 × [0.005(1+0.005)^360] / [(1+0.005)^360 - 1]
M = 35,000,000 × [0.005 × 6.022575] / [6.022575 - 1]
M = 35,000,000 × 0.030112875 / 5.022575
M = 35,000,000 × 0.005996
M ≈ 209,857.68
```

So, the monthly mortgage payment is approximately \$209,857.68.

2. Determine the principal portion of each monthly payment over the loan term.

The principal portion Pt for each month can be calculated by subtracting the interest portion from the monthly payment M.

3. Multiply each period t by the principal payment Pt to find the time-weighted principal payments.
4. Sum the time-weighted principal payments and divide by the total principal payments to find the weighted average life.

#### Results of Average Life Calculation

After performing the calculations, Emma finds that the average life of the proposed loan is approximately 11.92 years. This means that on average, half of the loan’s principal will be repaid by the 11.92-year mark.

#### Conclusion

Understanding the average life of the loan helps Emma price the loan appropriately, considering the risk associated with the time it takes for half the principal to be repaid. By comparing the average life of Bayside Residences’ loan to other similar loans, she can ensure Sunshine Bank offers competitive and fair loan terms while managing its risk effectively.

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