Calculating proceeds from selling bonds

0:00- [Narrator] We're told that Maplewood Technologies bonds have a face value of $1,000 per bond, a coupon rate of 5.25% and a current market price of 92.75, quoted as a percent of face value. The bonds pay interest on March one and September one or March first and September first.

0:18And investor sells 15 bonds on November first, two months after the September first interest payment. The broker charges a commission of $7.50 per bond. What are the total proceeds from the sale accounting for accrued interest and commission? Pause the video. Have a go at that.

0:37All right, so first let's just think about the current market price as a percentage of the face value of the bond. So that would be $1,000 times 0.9275, because this is meant to represent 92.75%. As a decimal, it would be that right over there. And we can actually, we can actually calculate this part in our head.

1:07This would be $927 and 50 cents, but that's not all. The broker is also charging a commission. So we are going to sell, so this is proceeds we're going to get, but the broker charges a commission of 7.50, so we have to pay the commission in order to sell it. So that's going to come out of the money that we actually get.

1:33That is the commission right over there. And now we have to think about the accrued interest, and the accrued interest is the interest that we as the bond sellers get that we, that we've essentially accrued, that we haven't been paid yet in a coupon, and it's been accruing for two months.

1:51Now, I'm gonna give you a little quirk of corporate bonds. You might just say, "All right, let me count the days that we would with a, with a treasury, or with a government bond and see what fraction that is of 365." So to actually do the actuals, but with corporate bonds, for simplicity, and this goes back to the days that traders were trying to do the math in their heads.

2:10They just assume that every month has 30 days. And likewise, that there are 360 days in a year and they've just accepted that. Obviously it's not perfect, but that's just a convention in the corporate bond markets. So what we can, what we do is we say, "Okay, this has been two months."

2:27We assume each of those months have exactly 30 days, even though we know October does not have 30 days, it has 31 days. So we would just say, "Okay, that's two months, that's 60 days out of a total of 360 days." So that's how much interest, that's the proportion of the annual interest that we have accrued.

2:48And then the annual interest or the coupon payment, is 5.2, 5.25%. So I'll write this as a decimal, 0.0525 times the face value, times the face, times the face value. Now once again, this we can do in our head because the face value is a nice clean number, like a 1,000.

3:10See, if it was 52%, it would be 500 something dollars. So if, if we are 5%, so this would be right over here, this is $52.50 cents, and this right over here is the same thing as one sixth. So this is all going to simplify to that, divided by six. So it's gonna be $927, 927.50 minus 7.50.

3:35Actually, that math is pretty straightforward. So that is going to be $920. And then we are going to add to that, whatever that is. Let me get a calculator out for that part. So if I do 52.5 divided by six, that gets me 8.75 plus 920. 920, so these are gonna be the proceeds per bond after paying the commission.

4:09And how many bonds did I get or how am I, am I selling? Should I say I'm selling 15, so times 15. So my total proceeds are going to be 13,931. Let me write this over here. So this is going to be $13,931.25 cents. And we are done.