 Personal finance practice problem using OneNote. Tax equivalent yield calculation. Prepare to get financially fit by practicing personal finance. You're not required to, but if you have access to OneNote, would like to follow along. We're in the icon on the left-hand side. Practice problems tab in the 11030 tax equivalent yield tab. Also take a look at the immersive reader tool, the practice problems typically in the text area too with the same name, same number, but with transcripts. Transcripts that can be translated into multiple languages, either listened to or read in them. Taxes have a huge impact on our investment decisions because clearly when we invest, we want that money working for us. We want our investments to be growing. We want the money to be earning revenue and in an income tax system as we have in the United States anytime revenue is earned. We've got to think about what are the tax consequences of that. At first glance, we might say, well, if I'm investing anything I'm investing in, I want it to be growing and earning revenue. If revenues are the same across the board, maybe it will not have a big impact on my decision-making process. However, the revenue is not the same across the board. So for example, we might have different rates for things like capital gains revenue versus ordinary income revenue for example. And when we're thinking of investing in something like bonds, for example, we could have investments in say municipal bonds, which don't have the same tax consequences as other types of bonds like corporate bonds. So now we've got to think, well, if I'm trying to invest in these different kinds of investments, for example, these different kinds of bonds, I would like to look at it from apples to apples or same thing to same thing perspective. How much return would I need for a corporate stock to have an equivalent return as I would have on say bonds that are not subject to taxes? Now also note that you would think that this kind of calculation might come out to the same result for all taxpayers, but that's not gonna be the case either because we know that we have a progressive tax system. So more wealthy individuals are gonna be taxed at a higher marginal tax rate. And therefore the tax incentives of tax-free investments, such as municipal bonds, for example, is gonna be more attractive to them. It's gonna be make more sense for them. Lower income individuals, then it might not have as much of an impact because your taxes aren't gonna be as high. And we'll talk more about that in future presentations. So given that we've got the marginal tax rate, we're gonna assume here is at the 30%, the municipal bond yield is at the 5%. So we've got the yield or return at the 5%. The question is, well, normally if I can invest in a municipal bond or somewhere else, the somewhere else, which is subject to tax, is gonna have a higher rate of return because it has to because otherwise people would invest in basically the municipal bonds. The question would be then for me at this 30% tax bracket, how high would the like a corporate bond, for example, have to give a return to match the yield here on the municipal bond where I have a tax benefit. So calculation for that here is the tax equivalent yield formula. That's the tax-free bond yield, which is the 5% divided by one minus the tax rate. We're using the 30% here, noting that this tax rate also is the marginal tax rate, the highest tax rate. And when you look at the taxes, we have multiple tax rates that are gonna be assigned that we're gonna be paying taxes on because we have a progressive tax system. We could think of the rate as being an average rate, like the average that we pay, but when we make decisions at this point in time, we're making them on the margin as economists say, therefore we're gonna take the highest tax rate at that point. So then if we do this calculation, we're gonna say the tax-free bond yield is the 5%, and then I'm gonna, notice I'm breaking this formula out into a table. I think this is really good practice to do, and it also helps you to put together kind of worksheets that could be useful within your practice for multiple different kind of reasons, helping someone to kind of put something together and just do a data input type of format for it. You can also set this up in Excel so that you have your data up here on the left and set up your worksheets so that you can see transparently what is happening in the formula. So here I took the tax-free bond yield, which is the 5%, which is the numerator, and then on the denominator, I'm gonna put this in my table with one minus the tax rate, saying what I'm gonna do, I'm gonna pull that to the inside. I'm just gonna take one minus the tax rate, the top rate at 30%, that's gonna give us 70, 100%, minus 30%, 70%. And then we're gonna say that we've got the numerator and the denominator now so we can divide them out and get the 7.14. So in other words, we're taking the 0.05 divided by the 0.7, which is the 7.14, if I move the decimal two places to the right. So what does that mean? That means if I can invest in the municipal bonds and get a 5% yield and then I can invest in another bond where I don't have the tax benefit of it, I would have, they would have to have a return of at least the floor being 7.14 to compensate for the tax benefit. Let's double check that and see if that makes sense. So let's do our check figure, where we're gonna say that the earnings before taxes, if I had a $1,000 investment, which just assumed a $1,000 bond and I had the tax equivalent yield of the 7.14, this is estimated because it's in Excel. So it could be a little bit rounded to two decimals. That'll give us the 71.43 earnings. So we would say 1,000 times the 0.0714, 71.43, it's rounded again to 7.14. So it's a little bit different. And then the marginal tax rate times the 30%, meaning I'm gonna have to pay 30% of that 71 at my highest tax bracket, not my marginal bracket because I made this on the margin at the next decision point. So that means I'm gonna take that times the 0.3, we're gonna be paying 21.43, 42 about. So that means of the 71.43, I'm paying 21.43 to the government. That means that we really only got $50 in earnings, $50 in earnings. If I compare that $50 earnings to the 1,000 I invested, divided by 1,000, we're gonna get the 5%, which is the tax equivalent yield, which wouldn't have the tax consequences. In other words, if I calculated the same 1,000 and I didn't get any subject to taxes and they gave me a 5% return times 0.05, I would get $50, right? $50, which is the same I got here after I paid the taxes. So you can kind of work this out for yourself and be able to understand it. Thusly, I think oftentimes when we think about it in terms of just percentages, it can seem somewhat abstract. If you just apply out an investment and work through the problem and say, okay, yeah, I see that makes sense. Now, of course, you can go the other way as well. We can resolve for this and say, well, what if I have the tax-free bonds yield? What would then be the tax equivalent yield? So then you could solve for the tax-free bond yield in your formula, use your algebra, and I'm gonna do it down here in a table format. So if I knew the tax equivalent yield was the 7.14, how can we get back using our algebra back to the 5%? So we would take the one minus the marginal tax rate. So there's the one minus the 30%. That gives us our 70% again. And so that's gonna give us the 5% bottom line. And that would be the 0.0714 times 0.70%. And if I move the decimal over, it's about, again, there's rounding because it's in Excel, but it's about that 5%. So you could go that way as well. You could say, okay, well, if I had the tax equivalent yield, like the corporate bond that I have to pay taxes on, what would be the tax equivalent for if I didn't have to pay any taxes for the yield for a municipal bond, for example, in order for that to break even the 5% about? All right, so now we can see that at the 30%. The next time we'll take a look at it and we'll say, well, let's take a look at the range of tax rates because we have a progressive tax system and see the impact as the tax rates go up. And again, the higher your tax bracket is, the more beneficial to have a bond that's not subject to taxes. Because if you're a higher earner at higher tax rates, you're gonna have, it's gonna be more beneficial not to pay the taxes at those higher rates. So we'll see that in the following presentation.