 Personal finance practice problem using OneNote. Car lease versus purchase decision. Get ready to get financially fit by practicing personal finance. You're not required to, but if you have access to OneNote, we'd like to follow along. We're in the icon on the left-hand side, the practice problems tab in the 6180 Car lease versus purchase decision tab. Also take a look at the immersive reader tool. Our presentation should also be in the text area with the same name, same number, but with transcripts. Transcripts that could be translated into multiple languages and either listened to or read in them. We have the information related to the purchase up top and then down below we have information related to a lease so we can compare and contrast the process that we might go through when we're making this type of decision. Obviously the purchase of a car is a decision that might implement or impact multiple periods into the future. Therefore, we might want to put a more formal thought process or structure into our decision making as opposed to the more short-term decisions which we might make more on the basis of habit and routine. So the first thing we might want to look at is to just take a look at the cash flows that would be involved under the two methods over the periods that are going to be involved and then we might want to add into that the time value of money types of calculations that we'll do after this point. So first we got the cash flow related to the purchase. Let's imagine that we've got the down payment and we're going to finance part of it. Down payment of the 7,800 and then we have the monthly loan payment of the 1,100 and the years are going to be four years. The value of the car at the end is going to be the 15,000. So we're going to have the car we imagine for four years and then there's of course this problem with the residual value at the end of the time period and this is going to be one of the things that's a little confusing when you think about the purchasing decision versus a leasing type of decision because the lease might be for a fixed amount of time and when you make that purchase you don't really know how long you might have the car. You got to make some type of estimate in terms of how long the car is going to be lasting you for example when you're making a kind of comparison between the two and to do that one way to do that is to say well at the end of the term I'm going to say that there's a residual value I'm going to think that I can sell the car at that point in time possibly having a cash inflow at that point of the 15,000 then we've got the discount rate which we're going to say is 5% so we're going to say the down payment is going to be the 7,800 obviously that's going to be a cash flow upfront we have the loan payments that are going to be 1,100 if we think about them as just basically cash flows that's how much we're going to be paying and that'll include if it's a normal installment type of loan interest and the principal the months that we're going to be paying over is 48 that's going to be the four years times 12 so we got 48 payments and that will give us then the 48 times the 1,100 the 52,800 in terms of the loan payments in total so the cash flow then is going to be the 52,800 plus the 7,800 that's going to be the 60,600 in terms of the cash flow and obviously that's the cash flow for this timeframe of the four years that we have in place now after that point we're going to say the car's residual value is going to be the 15,000 if we were to sell it we can think about selling it at that point in time thinking that we could receive the 15,000 if we were to do that then of course it would be a cash flow or we might say that the value of the car that we might still be using is the 15,000 that we would still be getting use of it's easiest to kind of think about these type of comparisons if we can break things down to basically cash flows or cash flow equivalents typically so that's going to give us the net cash flow or the net flow which is going to be the 60,600 minus the 15,000 because that's going to be an inflow and that would give us the 45,600 so this is a calculation that's pretty straightforward because we're not really taking into consideration a time value of money considerations here also note that if the car was used for a job or something like that then you might have to take into consideration the tax implications that could be involved let's compare that to like a lease situation let's say the down payment for the lease is 3,200 the monthly lease payments are 950 and the length of the lease is four years so now we're comparing a four year lease here to the loan that would be extending over the four years if you've got different kind of terms in terms of how long the loan will be involved it could be a little bit more complex but the same kind of principles would apply here we would of course try to break it down to cash flows over the time frame that's being involved and then once we break it down to cash flows we can make some comparisons there we might then apply our present value kind of analysis which we'll do next so we'll say the cash flow here we've got the cash flow is going to be the down payment for the lease of the 3,200 upfront we've got the monthly lease payments then which are going to be paying 950 per month the number of months is 48 so if we take that 950 times 48 then we would get the 45,600 45,600 here for the total monthly payments and then at the end of the lease we've got charges so at the end of this lease of course we don't have the residual value of the car because we don't get the car at that point in time the car goes back but we might have some more charges that we have to take into consideration so in this case we're going to say plus the 1,500 into the lease charges that's going to give us then the hold on a second let's do that again we got the 3,200 plus the 45,600 plus the 1500 that's going to give us the 50,300 so that's the initial comparison we could make we got the 50,300 to the 45,600 we don't have any time value of money calculations but the time period that we're covering over this is fairly straightforward because we've kind of made it similar in that we've got the length of the lease similar to the loan and we basically cut out the end of the purchase at that end point by valuing the cash flow of the car kind of like it was a cash inflow as if we were to sell it at that point because once again we want to break things down to the cash flows now if this was if you had different terms for example if you were planning on holding on to the car longer or the loan had a longer or shorter term than the lease it gets a little bit more confusing but you could still break out this information and do this initial calculation with just simply the cash flows then on top of that you might then say well now I want to add into a little bit more complexity and take into consideration the time value of money that could be applied so let's use our present value type of factors for these larger types of purchases so typically what you'll do here is you're going to say let me let me take the term that this is being covered over we're going to go from zero to four years and then I'm going to use my present value calculations using a discount rate of the five percent to do that to take into consideration the time value of money because the flows that are happening in future periods are are going to be less in terms of present value terms than the flows that are happening in the current point in other words if I had a situation where I could basically purchase a car and pay the whole thing four years later instead of today I would be in a better situation than if I had to pay the whole thing up front today and then nothing after that point in time right because of the time value of money I'd rather pay it later typically because of the time value of money we're going to say that that time value of money is going to have the discount rate of the five percent the next thing we want to do is break out our cash flows on a year by year basis so I'm going to say here's the years here's going to be the cash flows related to the purchasing decision so in year zero we had to put down up up front that seven thousand eight hundred and then we had in year one the thirteen thousand two hundred which is going to be the amount of payments that we made which is the one one oh oh times twelve so there's the thirteen thousand two hundred as we make the payments for the loan for one two three and four and then also in year four notice I've got the four here twice we've seen at the end of that period we sold the car and we're assuming that there's a value that we have to put some value on it at this point in time that's going to be cash a cash value at that point in time so if we sold it we can get the fifteen that's going to help us to do the comparison because we got to break these down to basically cash flows right that's going to be the idea now if we present value each of these notice we can't really present value using an annuity we got to use the present value of one per period so anytime you got a more complex type of thing that's happening out into a longer frame into the future you can try to determine the cash flows on a year by year basis that might differ if they differ then you can't really use an annuity you could like try to do an annuity for like these few years or whatever but if you're using Excel you might as well just do the present value but then we can present value them we of course have to determine what we believe is an appropriate discount rate in order to do the present value type of calculation which we're going to determine is the five percent and you might think about that as kind of like the opportunity cost of the money what you could do with the money you know if you had it and you can invest it elsewhere for example so we got then the present value is going to be that I won't get into it the formula in too much depth here we do do this in Excel so if you want to work it in Excel you could do it in Excel but we're basically taking the present value of that 7800 at period zero which of course is the same value we use the same present value calculation but it's at period zero this one the 13100 we're bringing back to period zero bringing it back one year present value calculation would be the rate which is going to be the five percent and then comma the number of periods is going to be the one period so we took the one period here notice that we're kind of doing a little bit of of estimation or simplification because we didn't break it out to a month by month we could basically try to break this on a longer more extended point to a month by month breakout but it's often good if you're talking about longer years to try to estimate these to a year by year cash flow and then and then break it out on a year by year present value calculation which is what we do here so then we got the number of periods is going to be this one over here and then two commas because we're not going to have the payment because it's not going to be an annuity type of calculation and then the future value is going to be that 13200 that we're pulling back to the current period also notice that this amount here is absolute reference by the dollar signs that's because it's being pulled from outside the data set so when we pull this formula down it's going to be the same as you could see between these two this one the number of periods is going to be the number of periods is going to be from here which is this item and notice this one did allow us to pull it down because we want it to be pulling and changing from year to year and then this one as well is going to be the future value which is this amount is changing from time as we copy the formula down which is what we want which is why it's not an absolute reference okay spit it out so this is going to be the second one this 13200 is now being pulled back two years so same kind of calculation but now of course it's less because of the time value of money this one is going to be the 13200 discounted at 5% back three years giving us the 11403 this 13200 is discounted back at 5% for four years to give us the 10860 you could see it's going down of course and then we have the cash inflow related to the car assuming the value of the car at the end of the four years which we could sell it for is a cash inflow of the 15000 we discount that back for the four years as well giving us the 12341 and so now we're talking the 42266 so of course if I was just to look at the straight cash flows over this timeframe we've got the 4645 600 but if I apply the discounting to it we've got the 42266 which might be a little bit more accurate to then compare it to the cash flows related to the lease information so same kind of process we're going to say here's the periods of the years one through four and then we have the cash flows that we're going to be the down payment up front that's going to be the 3200 and then we made 950 monthly lease payments so again I'm not breaking it out per month on the cash flow calculations I'm going to annualize even though when I look at this annualized number that is going to be calculating as if it happened at the end of the period which is a simplification because it really happened throughout the period but this is all an estimate right so 950 times 12 is going to be the 11400 so we're going to annualize our cash flows and that's going to happen for year one year two year three year four and then year five we don't have the residual value of the car because it's not our car to sell at that point in time we're going to be saying that the end of the lease charges is going to be the 1500 and so we'll present value those items discounting it back at the 5% so the first one of course is at year zero so we still use the present value but it's at year zero so there's no change and then the second one is present value 5% there's the 5% it's going to be absolute that's why it's got the dollar signs and then the number of periods is one you can see that one change from 13 to 14 it's not absolute because it's going to copy down and then we had the skipping of the payments that's what the two commas is because it's not an annuity and the future value is the 11400 which you could see that one copied down from the 3 to with the 12 to the 13 so that's going to be the same thing going down we got the 11400 discounted back at the 5% two years gives us the 10,340 we've got the 11400 discounted back three years at the 5% giving us the 9484 we've got the 11400 discounted four years back at the 5% giving us the 9379 and then we've got the 1,500 that's the last end of the lease charges of the 1,500 discounted back at the 5% to give us the 1,234 if we add those up we've get to the 44,858 so now you can do the comparison on the total cash flows the 45,600 is lower than the 50,300 and then we've got the 42,266 also lower than the 44,850 but you can see how you can kind of break this down into the total cash flows and then possibly take into consideration the time value of money and you can apply this kind of strategy even if it got more complex than this for example if the years were different or if you're taking into consideration the value the other costs that might related to the selling of the car at the end of this timeframe if you take into consideration maintenance and that kind of stuff under the two scenarios if you take into consideration taxes as long as you can try to quantify what you think the cash flows will be on a year by year basis then you can use this kind of cash flow present value method which looks complex but quite is pretty easy to actually set up in Excel to do a fairly reasonable kind of side by side calculation it's all an estimate because of course we are going to be estimating the discount rate but it gives you a better idea than just kind of going with your gut on those long term decisions going with the gut works for short term habitual types of decisions oftentimes but you kind of want to put a more formal thing in process with the longer term decisions because we're not so good we don't make those all the time and we don't have the luxury of the trial and error and again one way to do that is to do your best to break down the cash flows on a year by year basis and then do your best to get your discount rate here and apply out a present value type of calculation and take a look at your comparisons also just realize that with this kind of comparison too you might take into consideration just the hassle which is hard to quantify in dollars right the hassle of going through the selling are you going to sell it after four years that's kind of a hassle to go through the selling process is that easier or less easy than upping the lease or releasing the car the ease on those types of things whenever you're getting into those intangible items well I like this because it's easier or I like this because I get you know this the value that there's certain values to me that you have to quantify those values if you're going to use a quantifiable term like that that's what the dollars are here for they're trying to give us a quantifiable measure so if we're saying yeah but I just like this better because it's easier for me to do then I've got to quantify you know I got to quantify that in some way if I'm going to do an accurate comparison from