In this workout, we're going to compare two different loans and we're gonna assess which one is riskier from a credit perspective, and we're gonna use a formula known as the average life.

The first loan has an initial amount or beginning balance of 200.

So the ending balance for year one is simply the sum of the beginning balance and the repayment. We copy the beginning balance to the right over the five year period. And of course, we are gonna copy over the ending balance formula. And as you can see, the first loan gets fully repaid by the end of year 4, so it's got a maturity of four years. Now let's look at the second loan. The second loan has the same initial amount of 200.

Now we compute the ending balance as the sum of the beginning balance and the repayment, and we copy the formula's over the five years.

And as you can see, the second loan is fully repaid by the end of year 5.

So on the face of it, by looking just at the maturity, we can see that the second loan is riskier because it's got a maturity that is longer than the first loan. But is that the full story? Well, that's when the average life calculation comes in. So let's calculate the average life for the first loan.

The first thing we do is we compute the weighted payments. So what we do is we take the year, in this case, year 1, and we multiply times the payment. In this case, I'm gonna use a minus payment to make the number positive. And of course here it'll be zero. Now we copy this to the right and you can see now the weighted payments across all five years.

Next, we're gonna sum all of the weighted payments, and that's equal to 660. And the average life is simply the ratio of the sum of the weighted payments and the initial balance of 200. And that gives us 3.3 years.

Let's do the same calculation for the second loan, starting with the weighted payments. So I'm gonna take the year, multiply times minus the repayment that gives me 40. I'm gonna copy that to the right across all five years. Then I'm gonna sum all the weighted payments that gives me 600. And finally, to obtain the average life, I take the sum of the weighted payments and divide it by the initial amount, and that gives me an average life of three years.

Now, the reason bankers use this average life metric is because it's very helpful to have in one single number a way of comparing two loans that have different maturities and different repayment patterns. Now, in this case, the first loan has an average life or an average maturity of 3.3 years. While the second loan has an average life of three years, which means that on average, the second loan is gonna get repaid faster than the first loan. And this is why from a credit perspective, the second loan is gonna be less risky than the first loan. And the first loan needs to be priced slightly higher.