Today, you purchased a $1,000 bond that matures in 5 years. Th...

Question

Today, you purchased a $1,000 bond that matures in 5 years. The bond pays annual interest of 10%. Visualize these cash flows on a timeline.

Accepted Answer

All right. Let's see what we got here. Today you purchased a $1,000 bond that matures in 5 years. The bond pays annual interest of 10%, visualize these cash flows on a timeline. All right? So it's going to be paying annual interest of 10% and this is the annuity that we're generally gonna be working with in this class, is an annuity of interest payments. Alright? So let's go ahead and draw our timeline and then we're going to fill it in. So we've got 0, which is right now when we bought the bond. And I want to make a note that even though it's a $1,000 bond, that's the principal amount of the bond. It's not necessarily what we paid for it today. That could sound a little confusing and we're going to dive into bonds a lot more once we get to the liabilities, okay? But at this point, I just want you to know that even though it's a $1,000 bond, that's just the principal amount that's going to be paid out in 5 years. The value of the bond today could be some different number, all right? So what's going to happen is that we need to find the value based on our variables, right? We need to find what all the cash flows are worth today and that's going to be the price of the bond, the present value of the bond. So what are the cash flows in this case? Well, there's the cash flows for the interest payments, right? There's going to be annual interest payments of 10% of the $1,000 and then there's also going to be the $1,000 principal payment at the end of the 5 years. So let's go ahead and find out what that interest is going to be. So the interest, right? There's gonna be cash interest that's being paid and it's gonna be a $1,000 times the 10%, right? Each year, this bond pays 10% annual interest based on the $1,000 principal amount. So a 1,000 times 10%, that tells us that the interest is a $100 per year, right? This is an annual interest that gets paid once per year. And it's going to be paid every year for 5 years while it's maturing. So notice what we're going to have here. We're going to have a $100 here in 1 year, $100 here in year 2, in year 3, 100, year 4, 100 and year 5, 100 as well, right? Because time is passing and we're earning that interest. So we're going to get a $100 each year. And what does that look like to you already? We've got the same amount of money at equal intervals. We've got an annuity, right? These interest payments are an annuity. Okay? But those aren't the only cash flows involved in this bond. There's the interest payments, but remember there's the principal payment at the end, right? There's the $1,000 that this bond is worth. Well, after 5 years, we're going to get that $1,000 back, right? We purchased the bond for some amount and in 5 years, there's going to be this $1,000 payment. So this $1,000 is another cash flow. There's going to be this $1,000 cash flow in year 5. So it's not just the annuity of the interest payments, but there's also the principal which is a lump sum, okay? So there's 2 types of cash flows that we've dealt with. We've dealt with lump sums and that's when we were using our formulas earlier. With the present value equals future value divided by 1 plus r to the n. Right? Those formulas that we learned earlier in this lesson, well, those were for lump sums, such as this $1,000 principal payment in 5 years. But then we also learned about annuities, right? And annuities is going to be these interest payments. So once we get to our tables in a following lesson, you're going to see how we can use those tables to find what the value of this bond is today. Okay? So what that would take is it would take finding, 1, the present value of the annuity, which is the present value of interest payments, but we also need to know the present value of the principal payment, okay? And those together, when we add the present value of the interest payment and the present value of the principal, that is going to be the present value of the bond, okay? And that's going to be dependent on the same factors, right? We're going to have the number of periods, which in this case was 5 years. We're going to have the market interest rate. Remember when I told you r is the market interest rate? Well, in this problem they didn't tell us what the market interest rate was because we're not going to do all the calculations in this case. But there's going to be the market interest rate and there's going to be the future value of the principal payments and the annuity here, okay? So it gets a little tricky, right? There's a lot of moving pieces at this point. But I promise once we start getting to the calculations of finding what the present value of the bond is, it's not so tough once we're using the tables, alright? So let's go ahead and move on to that lesson now.

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Today, you purchased a $1,000 bond that matures in 5 years. The bond pays annual interest of 10%. Visualize these cash flows on a timeline.

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