I don't have the exact question but if someone has an example that would be helpful.

As I can recall the question goes like this:

FV is given
PMT is given but it's compounded quarterly or the coupon rate is compounded quartly
N is given
I is given but it's compounded semi annually

How do I calculate the PV?

I'm using a BA 2 Plus calculator;

I can get the calculations when the PMT periods or coupon periods is the same as the interest periods, but I'm not too sure how to approach these when they are different,

And another twist is for Cash Flows, if the I compounding period is different from the CF periods e.g.. I is in semi annually but the payments are in quartely, how do we calculate these

I've been trying to find an example off the internet so I can walk through this but without success.

Help?

Thank-you
Raymond

I can't help you with the calculator because I don't have that one. But that's semi-irrelevant, because the concept behind it is the same regardless of how you're finding the values.

I'm confused over the way you've presented the problem. You're talking about coupons, making it sound like bonds. I've never seen a bond compound differently than the payment periods. Plus, the bond itself doesn't actually compound -- that's used for figuring present values of bonds. So are you actually talking about an interest period going over the end of a year and having to accrue a quarter's worth of interest?

For instance. Interest is paid semi-annually on March 31 and Sept 30. At the end of Dec you would have to accrue a quarter's worth of interest as an adjusting entry, because those 3 months have to get into the current year but it hasn't been paid yet. If that is what you are doing, then you aren't "compounding" anything quarterly. You're just accruing part of the semi-annual interest at year-end. If the last payment was Sept 30, then you have 3 month's worth of interest to accrue, or half of a six-month amount. (If this is a bond, you'd also have to do half the amortization.) But there is no compounding going on at year-end.

There is a such thing as paying at a different time than what is compounding. You can also compound irregularly. But it adds an added complication and requires some manual work. You can compound more often than you pay. But paying more often than you compound is a little difficult, because the payment is going to change the amounts and you'd have to update everything.

Unless it doesn't change the principal. Like a bond... they make an interest payment but they aren't paying anything from the bond face value. But... there wouldn't be any point of compounding. The compounding concept for bonds is just to figure out present values. And I can't see any earthly reason why the compounding periods would be different. That just doesn't make sense.

So, a) it would be useful to know if you're doing bonds, or something else, and if something else, what? (bonds don't use FV either), and b) you need to figure out exactly what it is you're attempting to do, because what you're describing (especially if it's bonds) isn't making sense. Hard to make an example if I don't know what you're actually trying to do.

It's a bond question

I'll take one of the examples I know how to calculate and try to write it in the question I am trying to ask.

Bond issued on June 1, year 1, matures on June 1, Year 15. The presend date is June 1, Year 5, coupon payment has just been paid. The bond has a face value of $1,000, a coupon rate of 8% compounded quartly and a current yield of 10% compounded semi-annually. Ignorming taxes what is the current dollar price of the bond?

e.g.. PV.

I just took an example I know how to calculate and re-worded the coupon date to compound at quartly instead of semi annually. It was a question on an exam that I was stumped on =(

thank-you
Raymond

normally I'd take the $1000 x coupon rate so if it were semiannually I would take 1000 x 0.08/2 = $40 for the payment for my calculation
but if it's quartly then ? Take 0.08/4, hmm I'm having troubles finding an example of this particular problem since for all the problems I've seen so far the coupon rate and yield are compounded the same


about the Cash Flows, I'll try to dig up a better example e.g.. Cash flow is semi-annually but the I is given compounded quartly.

Well, I can only say that is darn weird. The bonds can make quarterly interest payments, but bond interest payments don't "compound."

Unless there's something weird here that I've never seen in my life, then I think the simple answer is just use the semi-annual amount like normal.

Bonds are like interest-only loans. If you took out a car loan, normally you'd have a payment that includes interest and principal. You get charged for one month of interest, and then you make a payment. They first take that month of interest, and the balance of the payment goes towards principal. So the principal goes down. So the next month the interest goes down because the principal has gone down. And so on. So using time value of money, you're using monthly compounding because the interest and principle amount both are changing every month.

But there are interest-only loans. i.e. each month you just pay the interest for the month and nothing goes towards principal. So the principal never drops. And therefore the interest never changes. You could use simple interest to figure that out because there isn't any compounding effect involved there.

That's what bonds do. They pay interest however often, and they pay nothing on the face value (principal), so the principal never changes and the interest payment never changes. There isn't any compounding on the bond itself.


normally I'd take the $1000 x coupon rate so if it were semiannually i would take 1000 x 0.08/2 = $40 for the payment for my calculation
but if it's quartly then ? Take 0.08/4,

You used simple interest to figure both of these out. When using simple interest, there's no compounding. . 08/4 is .02 which gives you $20. . 08/2 is .04 which gives you $40. $20 + $20 = $40. It's the same every quarter. There's no compounding going on here.

Let's just say this is your normal semi-annual one. You'd use $40 for the interest payment, and you'd use semi-annual compounding to figure the present value of the $40 payments. Notice you're using compounding to figure the present value of the payments. But you used simple interest to figure the actual interest payments. You did not compound the $40. That's simple interest. See? The actual interest payments don't compound. The interest payments and the present value of the interest payments are two different things and two different calculations.

I can think of two things the "compounding quarterly" could mean for the interest payments, and my original post included a lot of explanation about that. But both things sounded very weird to me and it made no earthly sense for a company to do either one. But just because it doesn't make sense for a company to do so doesn't mean I can't figure out the math. Math doesn't care if it makes sense to do it.

So I saved all that in case you want it, but right now I'm just going to ask. Are you sure it said it "compounded" quarterly rather than it just "paid" quarterly. If they're just paying quarterly, the semi-annual interest is still $40 and you'd use that to figure the present value. (I've never even seen the payments be different than the market, but I could see that working. But since you're trying to figure out market value semi-annually, you need to know the semi-annual payments, which are $40.) If you are absolutely sure it said the payments "compound" quarterly, then I'll put back in all the other jibberish I wrote.

Hmm, I took this example out of a previous national exam but it says semi annually instead of quartly, maybe it's the wording where it's acutally not worded properly and it means payment
But I do understand your point on the compounding part.

Much apperciated

Raymond

National exam? You've mentioned an exam a couple of times. What exactly is that? Like our CPA exam, or something you need to graduate?

I think I'd scare myself if I was actually able to do problems that you can't get on a national exam. I doubt I could pass such a thing at this point in time.