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Smart Shopper Leasing vs. Purchasing
517 messages, Last post on Sep 17, 2009 at 12:47 PM
You are in the Smart Shopper Forum. Your Hosts are kirstie_h & tidester
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Replying to: kyfdx (Jul 19, 2007 7:18 am) Thanks so much for your replies! Maybe I will need to hire a auto consultant to help me through the car buying/leasing process! Is there somewhere I can learn about the terms such as money factor, baloon financing etc  Any suggestions on dealers that I should reach out to in Houston (I will be in zip 77007) if that matters. Thanks, Andy |
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Replying to: msindallas (May 29, 2007 10:43 pm) Your May 29 post stated, in part,... "Here is yet another perspective on this 4 year long debate -a mathematical description of the differences between the 2 modes of financing a car. I am a fairly recent member here, and wonder why someone has not done this analysis already on this thread. Disclaimer: I am not employed by Edmunds, or affiliated to any auto manufacturer or dealer. This article is not a solicitation for a sale or a lease of a vehicle. Summary: Do not lease, always purchase the car, and with cash. Target: Want to be behind the wheels of a new car every few years. Constraints/Assumptions: We want to (1) Buy only what we can afford. (2) Spread the expense evenly over the months we will be driving the car (3) Interest in a bank account is compounded every month (4) Have a car all the time for commuting and personal lifestyle (visiting family and friends, getting groceries, going to church, taking kids to school, etc)." I make no apology for resurrecting an old issue and certainly have no desire to torch your mathematical treatise but I do have some concerns. Risking pompousness, your analysis appears somewhat skewed triggering flaws due to asynchronous time lines and cash flow issues. Here are my observations... 1st. Your claim that one should always purchase with cash and never lease is seriously flawed. NEVER SAY NEVER. The way to do a credible lease v. buy decision is to examine incremental cash flows. There are many good capital budgeting textbooks available that discuss various methodologies (e.g., FV, NPV, IRR, MAPI, etc.) for analyzing competing alternatives. 2nd. Please remember that you will need to create a sinking fund in anticipation of making that very FIRST car purchase. This is very crucial. And so, while you're saving for that FIRST car, it is reasonable to conclude that you may not own a car although you may have access to one (that "old clunker" as you so eloquently describe). And so, at this stage, you can't use those monthly savings to compare to lease payments because they simply don't exist. Afterall, you're driving that "old clunker". When it's time to make that FIRST cash purchase, you should evaluate the cash purchase price (i.e., FV of the previous period's cash flows) v. the lease cash flows for that FIRST cycle. At this stage, the relevant question is: Which is cheaper; paying cash for the car or leasing it? It's probably best to disregard common costs (registration, tile, tages, gas, maint., etc). These, presumably, will be the same whether you buy or purchase. For all succeeding cycles, the money market streams can be compared with the lease cash flows. 3rd. I realize that you have proposed an exponential function with a negative growth rate (k) (decay/depreciation) of the form: V = Ce^-(kt) for illustrative purposes only and so I won't belabor the point other than to say that statistical estimation techniques (e.g., regression analysis) are generally deployed where historical data reflecting depreciation time line profiles are collected and analyzed in order to arrive at a suitable mathematical model. 4th. Another area that I take issue with is the "spreading" of taxes and fees over the holding period (q). Generally, these items are either (a) paid up front or; (b) amortized over the holding period. However, this is rather minor and so I won't belabor this either. 5th. It appears as though the right-hand side of your equation... M + M * (1 + i/1200) + M * (1 + i/1200)^2 + ... + M * (1 + i/1200)^(q-1) = M*q + (i*M/1200) * [q*(q-1)/2] which simplifies to... M*q * (1 + (q-1)*i/2400) was derived by using a power series expansion to find an approximating polynomial of degree 2 for (1 + i/1200)^q. Note that... (1 + j)^N = 1 + Nj + (j^2)N(N - 1)/2! + ... + j^n. Obviously, 1 + Nj + (j^2)N(N - 1)/2! bolded polynomial is substituted for (1 + j)^N in the equation for the sum of a geometric series, the right hand side of your equation is necessarily less than the left-hand side but not by very much. 6th. As I indicated above, it seems clear to me that the appropriate way to do a lease v. purchase analysis is to compare cash flows from both alternatives. In layman's terms... If the value that the consumer places on the future value of the dollars saved (invested at some oppotunity rate of investment or invested in durable goods and services) by leasing (usually, lease payments are lower than buy payments given identical holding periods) exceeds the net terminal value of the vehicle, then the financials say that it's best to lease. To reiterate, your buy strategy involves a savings provision where a sinking fund is established in anticipation of the next purchase. Payment streams for the next cycle's purchase are compared with the current lease payment streams. You seem to have forgotten that you must save for the purchase of that FIRST vehicle. Your analysis does not capture that initial stream of payments when you're still driving that "old clunker". 7th. Your mathematical expose is not a valid mathematical proof that buying is ALWAYS the better alternative to leasing because it only examines one particular case; which has a few flaws. FINALLY... Although not a bad idea, most people are not going to establish a sinking fund to purchase their next car. Money market rates haven't been that great (although they're starting to show some promise at the expense of higher borrowing rates) and are always in a constant state of flux. The high degree of uncertainty surrounding interest rates makes them very difficult to predict over a period of six months let alone one year. And so, it makes it very difficult to create a well defined savings plan for those big ticket items three or four years down stream. A reasonable expectation is that both payment streams and interest rates will vary over the planning horizon. John Medina, Ohio |
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Replying to: msindallas (May 29, 2007 10:43 pm) Another thing that needs to be clarified... According to your model, you should be comparing the FV of the money market cash flows (CF's) (which can be annuitized or levelized so that CF's can be compared directly) at the beginning of each cycle with the lease cash flows for that cycle. You have created a mismatch between the two competing cash flow sequences as the time lines are out of sync. Your comparable money market cash flows will always be lagging one cycle behind the comparable lease cash flows. Assumption #2 is unrealistic but, as I indicated in my previous post, I won't debate that. In addition, I have a slight problem with assumption #3. Banks seldom use monthly compounding for money market accounts. So, in most cases, you'll need to covert their Annual Percentage Yield to its nominal equivalent compounded on a monthly basis. For example, an APY of 6.13% on a suitable money market account is equivalent to 5.96% compounded monthly. And then, you'll need to consider one's marginal tax rate and convert the result to an after tax ROR. It appears as though you have considered the after tax issue on the money market side but not on the lease side. You'll also need to convert the annual inflation rate to its equivalent monthly compounding rate. For instance, a 2% annual inflation rate equates to 1.98% compounded monthly (not really that big a deal considering inflation rates are estimates anyway). Your post... "#423 of 459 Paying off a lease by msindallas Jun 01, 2007 (11:49 am) Bookmark | Reply Replying to: kyfdx (Jun 01, 2007 8:40 am) I'd be tempted to take the lease, then pay it off after 2-3 months. You'd be out the acquisition fee, but you would still be $3000 ahead. (unless the payoff reflects some sort of kickback to Volvo) This is new to me. Can you pay off a lease after 2-3 months? I thought you sign a contract for 24 or 36 months and become legally bound to complete the term, and if you don't, pay a huge penalty." contradicts your original premise that leasing is never a viable alternative. To wit... "Summary: Do not lease, always purchase the car, and with cash." Make sure you have collected all relevant and factual information. Gotta watch what you hypothesize. And, those universal all encompassing claims and assumptions can really bite you in the ass, fella. There are plenty of "gotchas" waiting to ambush you as one poster has already proven using the Volvo lease example. They can really leave permanent bite marks (kinda like egg on your face). You don't want any of that; do you? It's impossible to construct a mathematical proof that supports the fact that purchasing is always the better choice when compared with leasing because it just "ain't" so. I think what you're trying to do is impress everyone because you crave attention. However, it seems as though that you're the only one that is impressed. I can only hope that I'm not coming across that way. We have some very sophisticated folks participating in these forums. When people mention things like Hamiltonian dynamics (what's his name? tidewater?), LaPlace Transforms, Lagrangian multipliers, boundary layer conditions (from fluid mechanics/aerodynamics), third order non-linear partial differential equations, and the like; they're telling you something. Your equations do have some merit, though. I just think you need to (a) tweak your assumptions as well as your equations and (b) make sure that the time line profiles are aligned properly and you'll be fine. John Medina, Ohio |
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Replying to: delta737h (Sep 08, 2007 6:52 am)  
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Replying to: joel0622 (Sep 08, 2007 7:05 am) John |
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Replying to: delta737h (Sep 08, 2007 6:52 am) A 3 year old Cadillac STS has a wholesale value, with 45k on it, of about $18k. I could have bought my car for $39k. $21,000 in depreciation, $18k if I buy it and retail it after 3 years. I am paying, WITH TAXES amd 3 year registration, $517/mo/36mos with $1700  signing. That's a total cost of $20,312 including taxes over 3 years. Taxes are $1,000+, registration is a few hundred... etc... Do the math. Plus I get a tax deduction so my net cost is less... figure I can write off 80% or $16,000.. that's another $5-6k roughly back in my pocket. Back to the drawing board.
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Replying to: im_brentwood (Sep 08, 2007 9:04 am) I think that's what they have been doing!  tidester, host SUVs and Smart Shopper
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Replying to: tidester (Sep 08, 2007 9:57 am)
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| I have a small business and I was thinking of buying or leasing 2-3 company cars. which one should I do one. and if I do which one would benefit me more when it comes to taxes and liability. | |
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OK, you guys missed the whole point - let me re-iterate - When you lease - you are commited to how much money you spend every month (and at a high interest rate, money factor, etc). This is like borrowing from your future - living on credit. In contrast, when you buy (in my model) - you get to decide how much you save for your next purchase, and for how long. You have the freedom to adjust it - it's your money, and your car. If you need money for something else, you have the liberty to skip the car payments (to yourself) for a few months! As for the argument on the 1st car - no one says your 1st car has to cost $60,000 - most of us start our driving life with "an old clunker". For any debate, we need to use our judgment on boundary conditions - the analysis may not apply to a business that gets a tax write-off from leasing, or an individual who inherits millions or hits the jackpot. Lets go for it the non-math way - a car depreciates the same whether you lease it or buy it, and the cost comes out of your pocket. When you lease, there is an additional expense - you compensate the institution that pays for the car you drive (and owns it). This is why leasing will always be more expensive in the long run. You can build any model, but the above fact remains the same. In the simplified model I proposed, I suggested a way an individual can slowly build up the capital to buy his/her own own car and lease it to him/herself - without the hassles or making monthly payments on time or returning the car by a fixed date. Whether this fits his/her lifestyle, let him/her decide. I hate to point this out - but some of the arguments here sound like "There is no global warming, because the global climate models are wrong". Now I can't remember who said that. OK, I will get off my soapbox now. Cheers, - M.S.
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