Weighted Average Life - WAL

See: WACC.

Weighted Average Life: the actuarial table that life insurance companies use when they sell products to sumo wrestlers.

Also, it's a stat used in determining how long it takes to pay back the principal of a loan.

You loan a friend $50,000 at 5% interest, with a five-year term. They are going to pay you back in monthly installments. So 5% a year means $2,500 in annual interest, times five years, or $12,500 in total interest. Plus the $50,000 principal. All paid back in 60 installments (five years times 12 monthly payments each year).

Your friend will be sending you $1,041.67 a month for the next five years to pay back the loan. But some of the $50,000 principal will come back to you almost immediately. Part of that first $1,000 payment will include a repayment of a portion of the principal. Other dollars you won't see again until the 60th payment five years from now.

What's the average length of time your money will be away from you? That's what weighted average life measures.

The measure comes up most in comparing a certain kind of bond called "amortizing bonds." These debt instruments provide periodic repayments of principal over the course of the bond's life. These payments can be irregular, meaning they aren't the same over the course of a bond's life.

You buy a bond that has a $10,000 face value. It has a five-year maturity with the following payment schedule for its principal:

Year 1: $1,000
Year 2: $2,000
Year 3: $2,000
Year 4: $3,000
Year 5: $2,000

To figure out the WAL, you multiply the total for each year by the number of years that money will be outstanding. So for year one, you multiply $1,000 by one. It's $1,000 that will be repaid in one year.

For year two, you multiply $2,000 by two...$2,000 repaid in two years. That equals 4,000 dollar-years. And so on.

The products of the various years are added together. You get an equation like this:

($1,000 x 1) + ($2,000 x 2) + ($2,000 x 3) + ($3,000 x 4) + ($2,000 x 5) = 33,000 dollar-years.

Now that dollar-year figure gets divided by the face value of the bond...in this case, $10,000. So $33,000 dollar-years divided by $10,000. You get a WAL for this bond of 3.3 years.

Another way to think about it: you'll be half repaid in 3.3 years. At that point, you should have $5,000 back of the original $10,000 you loaned out as the bond's face value.