Personal Finance practice problem using one note, investment earnings and after tax yield, prepare to get financially fit by practicing personal finance. Here we are aimed at one note, if you have access to one note we’d like to follow along you’re not required to but if we’d like to, we’re in the icon on the left hand side when the practice problems tab down in the 4150 investment earnings and after tax yield tab. Also note when using OneNote, take a look at the Immersive Reader tool.
Our presentations will also be in the text area with the same name, same number, but with transcripts, transcripts that can be translated into multiple different languages and either listened to or read in them. Closing the icon, we got the information up top calculations on down below, we’re going to take a look at the annual percent yield first and then we’ll move into consideration of the tax impact if we had earnings that were either tax free, or taxable possibly earnings from interest bearing items. So let’s first go up top and think of our investment and look at our annual percent yield.
Now this is just to remember that when you’re comparing and contrasting different types of investments, such as different types of savings accounts, when you’re starting to put the money into the savings account, you’re going to want to compare different rates of return that you might have, and compare them to other investments and so on so forth, how they would fit into your investment portfolio, you might also then consider the performance of something after time has passed. In this case, we’re saying a year has passed, we can add up the earnings that we have gotten in this case, we’re going to call it interest earnings that we have earned in say the savings account and try to figure out what the annual percent yield would be.
Because if we have the annual percent yield, we can compare it to the performance of other accounts meaning for example, we might have investments in say stocks and bonds or stocks, let’s say and we have dividends on them or gains on them, we can try to do a similar type of calculation to calculate what the percent earnings were because remember, or if I had another CD account or something like that at another bank, or if I had a savings account versus a CD account, and so on and so forth. Note, what I cannot do is I can’t generally just take this interest earnings and compare it to the savings I have in some other investment to compare and contrast, the quality of the investment that we have with regards to earnings because
I might have a different amount invested in the other areas, I might have 10,000 invested somewhere else, and only 1000 invested here. Therefore, we have to do some type of percent in order to in order to get a comparable number. And then we can do some comparisons. Now note that you could also you might also say, Well, if I did this for any period, meaning I can do the same ratio, the same percent calculation for any period, as long as I’m matching the same period. In other words you could do it for if it was three months in a year or two weeks or something like that, and you’re comparing the earnings of one investment to the other, you could do a ratio for that time frame.
And that would be fine. But if you want to compare it to other investments, what we would want to do is stand utilize the timeframe, which is usually a year. So remember what you’re usually thinking about when you’re looking at these rates. And comparing them, they’re usually going to give you the rates on an annual basis. And so that’s where that’s where you want to be when you compare to other areas. So let’s see what this would be we got the investment of 1000, the interest earned for one year from it.
So now we look at our books, we’d see that we have earned interest over time, possibly from an accounting software, we would get this or possibly from the bank itself 105 for one year, then we simply do the division problem, the interest earnings, the 105 over the investment would give us the percent earned for the time period covered which in this case was one year, which would give us 105 over 1000, moving the decimal two places over gives us the 10.5%. Now again, you can you can compare that 10.5%.
Then to other investments we might have, we could do a similar calculation, but have different dollar amounts in it, we can compare how much we earned compared to the investment. And we can then compare the percents where we could not have compared the dollar amount. And note you can do that for any timeframe as long as you have the same timeframe. So if you’re looking at your books, and we’re thinking about the first five months or something, or or even, you know, five years two, we could say for five years I’ve been earning this amount versus another amount and as long as you’re using the tape, same timeframe between the two, then it would be somewhat of a fair comparison.
But if you’re comparing to other investments that you want to invest in at this point in time, they are likely to give you options that are going to be on an annual basis. That’s the standard. So therefore you want to you want to generally break down your earnings to an annualized basis. So that you can then compare them possibly to other possible investments at that point in time, again, that typically being the standard. Okay, so now let’s take into consider the taxes. So what if we had a situation where we had a tax free yield of 7% in a taxable yield of the 8%.
So this could be the case where we have investments in say bonds, where we have tax free bonds, versus another savings account or something like that, where we have to pay taxes on it or in other words, typically, you have to pay taxes on your interest earnings on a savings account, and therefore, that’s going to lower your after tax basically earnings on it. Whereas if you put money into a tax free interest account, say, because you put money into government bonds, that government given you an incentive to finance their operations by making it tax free, that means your actual yield after taxes, your earnings after taxes will be better will be higher.
And so then the question is, well, how do you compare and contrast those two. Now remember, when you look at these, these two things, usually it’s going to be in this format, meaning the tax free yield is going to be less than the taxable yield, we’re earning only 7%, that’s worse right than the 8%, we could get, if we got the taxable yield in some other kind of investment account, that’s typically going to be the case because the market takes this into consideration.
And these percentages are driven in part, by by the market by the demand, that’s going to be, you’re going to be out there, however, it’s still going to be important because the you want to also compare this to your basically portfolio and see how you want your mix to be out between taxable amount and non taxable. And you may be able, if possible, if the interest was substantial, because we have a progressive tax rate, if you can get a substantial amount of your earnings from investments that are tax free, then you may actually be able to lower your your taxes, your tax rates, because we have a progressive tax system.
So if you were able to manage your investments, for example, to have 50% of your investments coming from earnings, that are tax free, even though the earnings were lower, and the other 50% being taxable, then your taxable income would be lower. And and that could have a significant impact, given the fact that we have a progressive tax system, meaning the tax rates actually go up as your as your income goes up. So that’s one kind of scenario you can kind of think about.
Whereas, you know, there’s going to be this kind of difference in that the market in and of itself will kind of evened out the gains, you would think on a free market between the gains that you’re going to get between these two. But if you put that into your personal portfolio, then then even given that case, you can kind of try to figure out what would be best for you given your particular circumstances, we’re going to be considering the marginal tax rate after 35%, which we’re going to just assume, as is our top tax rate.
Now, the marginal tax rate, you’ll recall, is not the average or effective tax rate, which is the average rate. So if you’re thinking about what rate should I use, because once again, I have this market, I have this progressive tax system. So I’m being taxed at multiple different rates, what should I use first thought would be average tax rate, right? Because that’s what an average pain, but no, because this next decision represents something you’re doing on the margin as accountants, which as economic economists would say, and the next decision we were making means we’re making a decision when we’re already at our highest tax bracket.
So whatever your highest tax bracket is, is your marginal tax bracket, which is going to be the marginal impact of the next decision, which we’re assuming is this investment decision. So we’re going to use our highest tax bracket generally. And then we’ll figure an investment so we can kind of figure this out without an investment first, and then we’ll think about the $1,000 investment just so we can put an investment number in. So So clearly, if we’re talking about the tax free yield, we don’t have to do anything because it’s tax free, we got an after tax yield of the 7%. What about the taxable amount, what’s the after tax yield, if I’m at a 35% tax rate on it, but we have the taxable, we have the taxable yield at 8%.
And one way we can calculate this is take the one minus the tax rate. So one minus the tax rate of the 35% means we have 65%. And so we’re going to take that 8% yield that we have and 35% of it’s going to be taken from us, therefore, we’re going to have the point oh eight or 8% times the 65 that we actually get to keep that’s not going to be taken from us. So the after tax yield is going to be the if I move the decimal two places over 5.2% and obviously that 5.2% is is now less than the tax free yield of the 7%. So the so it would the after tax yield will be beneficial to us. Now again, that’s because this might not be the case in the money.
Depends what the market looks like you would think that these two would kind of evened out for the most part in the market. But given the fact that we’re using a fairly high individual tax rate here, and if that was our particular scenario, then you know, we might have an advantage of a difference, you know, our situation might be different than the average of the market, which is different, which is driving this difference in the market. Okay, so then if I, if I go down, we can calculate this a couple different ways, it’s useful to kind of see this a few different ways.
So first, let’s just take that investment, and then say that we have that this is the the actual tax free yield, which would give us these 70%. So if I was looking at the tax free, how much would we earn in the yield? If we got to 7%? Well, there’s no tax impact, because it’s tax free 7% of the 1000, if we’re saying the investment was 1000, would be $70. And then let’s consider the taxable yield. Now, I’m going to do this a few different ways.
And I think it’s really useful to look at it different ways. Remember that the one way that you can see these types of calculations is the way that I believe is the most intuitive way to represent things. But that’s not usually the way that you’ll see things presented. If you’re seeing things in a book problem. The other way that they usually represent things is the easiest or shortest, most direct way with the shortest calculations to see things. And so you want to see things in that format.
And then and then also the fastest kind of to calculate type of format, which if you’re talking about professionals, tax pros, and working with other people that they’re good at, at trying and trying to look proficient, of course, and the more proficient you know, the quicker you do things and whatnot, the more proficient that can be there, they might not be as good as explaining type of thing. So you want to know how to do things in multiple different ways.
This is what I think is the most intuitive type of calculation, if you’re gonna say, all right, well, what if I invested $1,000? If I’m trying to compare these two things, and I just say, let’s just pick a number of $1,000. And let’s see what the impact would be between between these two rates of return. So if for the tax free, I got 70. And so if I had the 1000 times the taxable yield, which is the 8%. So 1000 times 8%. That means we would get $80. But it’s subject to taxes, and the marginal tax rate is 35%. So how much tax would we pay? Well, $80 times two times 230 5% will give us $28.
Let’s do this in the trusty calculator just for the fun of it, 1000. Starting at the top, again, times point oh eight, there’s our $80 times the tax rate times point three, five gives us $28. So the government would take $28 of it. So we had an original $80 that we earned minus 28. That’s going to the government that would give us then a difference of after tax return of let’s do that, again, at minus 28 would give us 52. And then we can we can figure out our after tax yields by saying
Well, my dollar amount would be 52. If I compare that to the original investment 52 divided by 1000, we get moving the decimal two places over 5.2%, our after tax yield, which we calculated up top here. Now we could do that a couple of different ways we can obviously do it this way, we could say well, if I take my investment, and I’m trying to get to two how much I would earn from it, we can just take that times the 5.2. Meaning do this calculation we did up top times 5.2% would get us directly to our earnings after taxes of 52.
Or the other way that kind of hybrid or in between method would be looking something like this the investment, and then we got the taxable yield is going to be the 8%. That means we would get $80. And then we’re sent instead of doing this kind of two step process of saying the IRS is going to take 35%, we’re simply going to take one minus the tax rate meaning 100% minus the 35% to give us 65. Because if the IRS is going to take 35% of the $80, we’re going to be able to keep the difference between 135% or 65%. So we can go directly from the $80 times to 65% is $52.
And then once again, if I compare that $52 to the 1000 that we invested, we can get to the after tax yield of the 520 5.2%. So this is often the way and this if you’re not used to this one minus the tax rate thing, it can be a little bit confusing, but you’ll see that often. And if you if you mull it over a little bit, it makes you know it makes sense. You know, okay, well yeah, you know, the government’s gonna take 35% so I get to keep 65% Okay, so I’m keeping 65% of the earnings of 80.
It’s a little bit more confusing when you do this calculation up here with it, when you’re taking this this one month. Minus 35%. Same thing, but now you’re taking 65% of a percent, which is a little bit abstract because this isn’t $1 amount, you’re saying, Well, I’m going to earn 8%. And then I’m going to get 65% of the 8% that I earned. That’s that’s like a double percent kind of confusion thing, if I actually have a numbered up here, like $80. And then I think, Well, yeah, the government’s going to take 35% of the $80, meaning I’m going to keep 65%.
That makes a little bit more sense, oftentimes, but mole mole both of them over because you’ll, you’ll probably see, in book problems, something more like this and more like this, more like this type of calculation, which is which is somewhat abstract. Then the more intuitive calculation, which I highly recommend, doing in practice doesn’t take much time to do if you have Excel to kind of move out the longer calculation. There’s nothing wrong with doing a longer calculation. In fact, it’s probably more transparent if you were to explain it to either yourself or to someone else. It’s not as useful or as handy to scrunch it up into a book answer problem. That way, though.