Average life calculations are used in the syndication process when you're trying to sell loans that have potentially different repayment structures. Given that in most cases the repayment patterns of the loan are designed around the cash flows in every project, finance transactions, the loans will have a slightly different maturity profile, and that of course needs to be reflected in the pricing. An easy way of describing the maturity is through an average life calculation. Let's take a look at two loans here. In the first case, we have a loan, which is a bullet repayment. In year five, there is no repayments until the very last year of the loan. When it's completely paid off. That means interest, assuming we're calculating it from the beginning balance is five each year. To calculate the average life we take each year and we give it a weight, 1, 2, 3, 4, and 5, and then we multiply that weight by each repayment. So in this case, because you have no repayments in the first four years, you'll end up with zero. But in the last year, we have a weight of 5 and a repayment of 100. So 5 times 100 is equal to 500. Then what we do is we sum through all those weighted repayments and we divide by the original amount of the loan. And of course, in this case, you get five years. And the reason for that is that it is a bullet repayment loan. So the average life is five years. Now, let's compare this to a loan that has a staggered repayment pattern, likely similar to something in a project finance transaction. Here we have payments of 5, 10, 20, 25, and 40 from years one through five. So here we'll take the weight in. The first year of 1 times 5 is 5. In year two, 2 times 10 is 20. In year three, 3 times 20 is 60. In year four, 4 times 25 is 100, and in year five, 5 times 40 is 200. Then we'll sum the weighted repayments of 5, 20, 60, 100 and 200 together and get a total of 385. We'll identify by the original loan amount of 100, which will give us an average life of 3.9 years. So what this says is that the staggered repayment loan, ignoring the present value cash flows, but just on a simple weighted basis, is the equivalent of a loan that is a bullet repayment of 3.9 years.

So if you're comparing these two loans, even though the total maturity is five years, you would price the first loan slightly higher than the second loan because on average you're getting your money back sooner in the second loan, and therefore the risk is lower and the pricing should be lower.