 Personal finance practice problem using OneNote. Tax equivalent yield tax rate comparison. 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 11035 tax equivalent yield tax rate comparison tab. Also take a look at the immersive reader tool practice problems typically in the text area too. Same name, same number, but with transcripts. Transcripts that can be translated into multiple languages either listened to or read in them. In prior presentations we talked about the complexity that the tax system has on our investment decision making process because when we invest we want the investment to be working for us. Growing, earning revenue as we earn revenue in an income tax system as we have in the United States. We have to ask what are gonna be the tax consequences of it when we're looking at say bonds. We might have some bonds say municipal bonds that are not subject to taxes and we could have some other bonds say corporate bonds which are subject to taxes. How do we compare the yields between those two things given the fact that one subject to taxes and one is not that's our tax equivalent yield calculation. This time we'll do that calculation again but we also wanna think about the idea of what would happen then as our tax rates go up. In other words we would expect that as our tax rates increase and we're talking about marginal tax rates here not the average tax rate because we're gonna be taxed on multiple rates in the United States and we're making the decision at the market however therefore we're not using average we're using the top or marginal rate from an economic perspective we're making the decision on the margin. Therefore we would expect a tax benefit to be more beneficial to higher income individuals who are subject to a higher marginal tax rate. So you would think then that because of the market conditions playing on this dynamic that if you're in a lower income situation where you have lower marginal tax rates you might be able to get then a corporate bond that pays enough to kinda clear possibly the tax advantage that you would have and if you're a higher income individual with a higher marginal tax bracket it's more likely that investing in bonds would be a more attractive thing. So first let's do our tax equivalent yield. So we got the on just one point assuming the 30% as we did last time. So we've got the municipal bond this is the one not subject to taxes and the question is how much would the corporate bond the one that is subject to taxes have to be in order for it to give me an equivalent yield after I have to pay the taxes. So we could do that calculation we've got the 7% and then we've got one minus the tax rates that's one minus the 30% assuming the top tax rate the marginal tax rate that gives us the 70% pulling out the trustee calculator then we can then take the 77.07 divided by 0.7 to get the 0.1 or 10%. So we would need then a 10% rate yield on the corporate bonds in order to match the tax benefit incentive of the 7%. Now let's do that same calculation here and I'm just doing it in one cell so we can see what the benefit would be. We're gonna assume that we got the same 7% yield on the municipal bond and now we're doing this calculation here to get to the same rate the 10% that would mean we need the 10% on the corporate bonds but what if my tax rate was only at 28% well that would mean that I can get a corporate bond that would pay 9.72 which would be about equivalent yield after taxes what if I had 26% well then I can get a corporate bond that would yield less 9.46 what if I had 24% marginal tax bracket remember that we're still getting a yield from the municipal bond tax free of 7% the question is what other corporate bond could I purchase that would have a similar return well it could be as low as 9.21 if it goes and notice these are not actually the marginal brackets I'm just going down by 2% here so the marginal brackets will change and so on in terms of the marginal rates but this you get the idea if my top tax bracket was 22% then I can get an equivalent corporate bond at 8.97% and so on and so forth and if I'm down to say 15 or 14% that means that 7% return on the tax benefit bonds would be somewhat equivalent to an 8.14 of a corporate bond which is subject to taxes because I'm not paying as much taxes on it and then if I go all the way down to 10% you could see 7% on the municipal would be something like 7.78 down here so you would expect given this dynamic that the markets would react to this by basically pricing these returns in as the market reacts to the conditions and that would basically result in what you would think that these municipal bonds would be more advantageous for people that are at the higher marginal brackets because those are the people that are going to be desiring these bonds because they get the most benefit from it and if you're at the lower marginal tax brackets you would think that you might be able to get a corporate bond that has a yield that might be higher than what you can get given the fact of a tax equivalent kind of situation because you're not paying that much tax as compared to a high income individual who's paying a lot higher marginal tax rates so you would think from a practical standpoint that would be your kind of takeaway you would think generally that if my tax rate is fairly low on a marginal tax rate I might be able to most likely can find corporate bonds that would be paying me more even though there's a tax incentive and if I'm a high earning individual then it's more likely that the tax incentives are gonna be such that it'll be beneficial for me to be taking those tax incentives. Okay and so and then we graph this in Excel this is a nice little chart that's useful that you can just make a chart in Excel so if you wanted to do this calculations in Excel you can map this out and then we'll make this graph as we do the practice problem in Excel.