6. Purchasing with an Annuity

Now that we know what annuities are, we're gonna take a look at using an annuity to purchase a piece of equipment or really to purchase anything. So we're gonna look at purchasing with an annuity. For example, let's say you bought something, your company bought something, and you agreed to pay $13,000 for, we'll say, five years, and the interest rate is 7% compounded annually. So what this looks like is you bought something today, and you took a note for it, and you have to pay one, two, three, four, five times $13,000 at the end of each one of these years. Now, the question is gonna say something like, "Record the entry here."

So you're gonna have equipment that goes up. But how much did the equipment actually cost? Well, we know it's not $13,000 times 5. If we did $13,000 times 5 and got $65,000, this is the value of the note. This, however, is not the value of the equipment, because in this $65,000, you also have to remember that we're paying some interest because we didn't pay right up front. You'll remember we're paying over the next five years. And money isn't free. We don't get to just borrow money for free. So over the next five years, we're paying 7% a year to be able to borrow that money.

So of this $65,000, part of it goes to equipment, and part of it goes to interest. Now the question is, what part goes to equipment? And this is one of those times when ordinary annuities are actually useful. Because what we're wondering is, if we didn't pay interest on any of these things, what would the amount be? And that's effectively saying, let's bring out all these $13,000s, and let's bring them back to the present value to take out the value of interest. So what we do is we say that $13,000 times present value of an ordinary annuity for n = 5 and i = 7%.

So over five years at a 7% interest rate, $13,000 times whatever that factor is, that gives us the value of the equipment 'cause, essentially, that's telling us what is the value of this annuity without any interest at all? What is the present value of this ordinary annuity? And that factor: $13,000 times 4.1002. So this comes out to be $53,303. So the value of the equipment is $53,303.

If we had paid for the equipment up front, we would have had to pay $53,303. But we didn't pay up front, right? We got this note payable of $65,000. Now, because you're good at accounting, you know these two need to equal. So this difference, this $11,697, this is what we call the discount. That's the discount on notes payable, which at some point is gonna turn into your interest expense. This is how you record the purchasing of equipment with an annuity. You have to bring back the annuity to the present value to find out what does the equipment actually cost and what am I actually paying in interest?

Because wrapped up in this $65,000, which is going to be your total cash outlay, you're gonna pay $65,000. But part of that cash is going towards paying interest, and part of that cash is going towards paying the principal, which is the cost of the equipment.