### Author Topic: Another math question  (Read 11313 times)

#### gecko10x

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##### Another math question
« on: September 14, 2012, 11:38:17 AM »
Question:
Under what conditions (if any) does buying and holding a used car become sub-optimal?
Or: Assuming one has to drive a car, how much car can sit in my driveway before I'd be better off investing that money and leasing a car?

(Before lambasting me for suggesting leasing as an option, this is a financial exercise for those who have money and don't want to drive a really cheap car. BTW, I don't fall into this category yet.)

I think that there is a point at which the opportunity cost of having your money depreciate in your driveway is worse than leasing. Clearly, if you can buy a \$2000 car every 10+ years (without spending enormous amounts of money on maint.), then you'll spend very little. It's also obvious that buying a \$40k car every year is a colossal waste. (You could lease a Bentley for less than that.)
But what about buying a used \$10k car? \$15k? \$20k? If I want (for whatever reason) that much car, should my cash be sitting in my driveway?

So, unable to distill all the factors into an easy formula, I ran a couple of scenarios. Assuming 12% annual depreciation, and an investment return of 10%, it seems like if you (on average) have more than about \$7000 in your car, you could lease for less than the monthly cost (just over \$200/mo). If you assume 7% investment return, then it's more like \$8000+. In my calculations, I did not factor in maintenance costs. Also, I used a 20-25yr time horizon with 2-3 vehicle replacements; obviously the longer the time frame used, the more the opportunity costs will be. Also, does inflation need to be accounted for somehow? And I made no attempt to match lease costs to used purchase amounts (if that makes sense)- I only checked that you can lease vehicles starting around \$180/mo.

Can anyone do a better job? Did I miss something major? There are a lot of factors, and a lot of assumptions, so I challenge you!
« Last Edit: September 14, 2012, 11:43:16 AM by gecko10x »

#### arebelspy

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##### Re: Another math question
« Reply #1 on: September 14, 2012, 02:19:36 PM »
Often you can sell a vehicle for around what you bought it, if you buy and sell it right, making the only costs gas and maintenance.
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#### gecko10x

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##### Re: Another math question
« Reply #2 on: September 14, 2012, 02:33:27 PM »
Often you can sell a vehicle for around what you bought it, if you buy and sell it right, making the only costs gas and maintenance.

Since no one has bitten at the topic yet, I'll go ahead an follow the tangent for a bit: Have you done this? If so, what were the conditions? I find it extremely hard to believe this would be possible over any significant time period or mileage put on the vehicle.

#### gecko10x

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##### Re: Another math question
« Reply #3 on: September 14, 2012, 02:45:58 PM »
I just realized that this does bring up another point to the OP: maybe the depreciation is tied more closely to mileage, or is otherwise not as stable a value as I had assumed? I thought 12% was a largely accepted annual depreciation amount, but maybe this value is more variable.

#### AmbystomaOpacum

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##### Re: Another math question
« Reply #4 on: September 14, 2012, 03:16:47 PM »
Things that make this difficult:

1. Depreciation is not linear. New cars lose substantial value the day they are purchased. Older cars lose less value, even proportionally speaking, than newer ones.

2. Insurance is not constant. Newer cars cost more to insure.

2.5. If you finance, you generally have to have comprehensive/collision insurance, whereas you can just carry liability insurance if you have the car paid off. But in order to get this benefit, you suffer opportunity costs by paying the money upfront.

3. Maintenance is not constant. Older cars cost more to maintain. Older cars are also more susceptible to break down causing collateral damage (not just paying for repairs, but a rental car, etc.). Maintenance is also very irregular.

4. Buying cars costs money (and time) apart from the sale price. Taxes, registration, placing ads to sell your old car or spending money getting it sale-ready, etc.
« Last Edit: September 14, 2012, 03:20:13 PM by AmbystomaOpacum »

#### arebelspy

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##### Re: Another math question
« Reply #5 on: September 14, 2012, 04:08:15 PM »
Often you can sell a vehicle for around what you bought it, if you buy and sell it right, making the only costs gas and maintenance.

Since no one has bitten at the topic yet, I'll go ahead an follow the tangent for a bit: Have you done this? If so, what were the conditions? I find it extremely hard to believe this would be possible over any significant time period or mileage put on the vehicle.

Of the four motorcycles I've bought, they cost 1500, 1600, 1800, and 2600.  They sold for 1600, 1600, 2200, 4000, respectively.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
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#### \$_gone_amok

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##### Re: Another math question
« Reply #6 on: September 14, 2012, 04:19:25 PM »
Often you can sell a vehicle for around what you bought it, if you buy and sell it right, making the only costs gas and maintenance.

Since no one has bitten at the topic yet, I'll go ahead an follow the tangent for a bit: Have you done this? If so, what were the conditions? I find it extremely hard to believe this would be possible over any significant time period or mileage put on the vehicle.

I still have my Honda CRV that I bought used for \$4200 at 107K miles. 7 years and 110K miles later it is still great and is worth around 3000 (base on similar craiglist comparisons). I'm pretty happy with the \$200/year depreciation.

#### gecko10x

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##### Re: Another math question
« Reply #7 on: September 14, 2012, 05:24:47 PM »
All of the above examples of non-depreciating vehicles were fantastic deals for you. Being that they are all quite small values, I wonder if that's a prerequisite for getting that kind of deal?

#### velocistar237

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##### Re: Another math question
« Reply #8 on: September 14, 2012, 05:33:41 PM »
I imagine if you're deciding between buying a new car every 2 years vs. leasing, leasing might win. It's true that the monthly cost of a lease could be less than the monthly cost of owning and maintaining your own car, but that doesn't capture the difference. There's usually a down payment for leasing, for one. You could run the NPV, which could get a little involved, with insurance, warranty/maintenance, etc.

#### gecko10x

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##### Re: Another math question
« Reply #9 on: September 14, 2012, 05:38:12 PM »
Things that make this difficult:

1. Depreciation is not linear. New cars lose substantial value the day they are purchased. Older cars lose less value, even proportionally speaking, than newer ones.

True, but I was attempting to limit the discussion to used vehicles.

Quote
2. Insurance is not constant. Newer cars cost more to insure

True. I was ignoring this, but if someone wants to attempt to account for it, feel free.

Quote
2.5. If you finance, you generally have to have comprehensive/collision insurance, whereas you can just carry liability insurance if you have the car paid off. But in order to get this benefit, you suffer opportunity costs by paying the money upfront.

I hadn't considered this, and I don't know if it would be significant, but it is outside the scope of the OP, IMO.

Quote
3. Maintenance is not constant. Older cars cost more to maintain. Older cars are also more susceptible to break down causing collateral damage (not just paying for repairs, but a rental car, etc.). Maintenance is also very irregular.

Something else that I was ignoring in my calculations, but this would tilt the equation in favor of leasing.

Quote
4. Buying cars costs money (and time) apart from the sale price. Taxes, registration, placing ads to sell your old car or spending money getting it sale-ready, etc.

Good point. Something to consider if you plan to frequently buy & sell them. And taxes can end up being significant as the vehicle price goes up.

#### gecko10x

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##### Re: Another math question
« Reply #10 on: September 14, 2012, 05:49:55 PM »
I imagine if you're deciding between buying a new car every 2 years vs. leasing, leasing might win. It's true that the monthly cost of a lease could be less than the monthly cost of owning and maintaining your own car, but that doesn't capture the difference. There's usually a down payment for leasing, for one. You could run the NPV, which could get a little involved, with insurance, warranty/maintenance, etc.

According to the calculations I ran, this scenario isn't even a contest. Leasing came out ahead way faster than I expected, and I wasn't even considering maintenance. Also, from my experience, you don't have to have a down payment for a lease.

To be clear, I'm not talking about the monthly cost of owning. The point of the OP is the opportunity cost of having your money tied up and depreciating instead of working for you.

#### grantmeaname

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##### Re: Another math question
« Reply #11 on: September 15, 2012, 07:43:19 AM »
According to the calculations I ran, this scenario isn't even a contest. Leasing came out ahead way faster than I expected, and I wasn't even considering maintenance. Also, from my experience, you don't have to have a down payment for a lease.
Yeah, but you're explicitly ignoring most of the factors that make older cars cheaper in your post. With a bias like that there's no question which result you'll find.

Quote
To be clear, I'm not talking about the monthly cost of owning. The point of the OP is the opportunity cost of having your money tied up and depreciating instead of working for you.
I'm confused how this opportunity cost isn't the exact same thing as the cost of owning, given that owning is the alternative to renting. If that's not what you're talking about, you've totally lost me.

#### gecko10x

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##### Re: Another math question
« Reply #12 on: September 15, 2012, 11:39:45 AM »
According to the calculations I ran, this scenario isn't even a contest. Leasing came out ahead way faster than I expected, and I wasn't even considering maintenance. Also, from my experience, you don't have to have a down payment for a lease.
Yeah, but you're explicitly ignoring most of the factors that make older cars cheaper in your post. With a bias like that there's no question which result you'll find.

I ignored insurance because it didn't occur to me mostly, but I also don't know how to account for it. So, feel free to do so if you know how.

What else did I ignore? Maintenance would be in favor of newer cars.

Quote
Quote
To be clear, I'm not talking about the monthly cost of owning. The point of the OP is the opportunity cost of having your money tied up and depreciating instead of working for you.
I'm confused how this opportunity cost isn't the exact same thing as the cost of owning, given that owning is the alternative to renting. If that's not what you're talking about, you've totally lost me.

Sorry, in retrospect,  the way I worded that was NOT clear. Opportunity cost of tying up your money is the point of the OP.

#### menorman

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##### Re: Another math question
« Reply #13 on: September 15, 2012, 12:04:15 PM »
All of the above examples of non-depreciating vehicles were fantastic deals for you. Being that they are all quite small values, I wonder if that's a prerequisite for getting that kind of deal?
Well yea, the lower the initial value, the less it can depreciate. For most cars, a certain point is reached after they're between 15 and 20 years where they really don't depreciate much more no matter what. At that point, most specimens are worth the same on the open market. Mileage matters little, especially if the mechanics are in good working order. As a result, you can usually buy something in that age range, keep it a couple years, then sell it for close to what you bought it for, which is exactly what I did. When I bought my 1988 Honda Accord in 2006, I paid \$1300 for it. I just recently sold it to a friend who is paying me \$1000 for it. During my time of ownership, I drove about 65,000 miles* (bought at 251k, sold at 316). Spreading the depreciation yearly puts it at \$50/year, doing it by mileage is \$0.005/mile.

I ignored insurance because it didn't occur to me mostly, but I also don't know how to account for it. So, feel free to do so if you know how.
Comprehensive will often exceed the value of the car after a year or two, but liability can actually be higher in some instances. This is because of the demographics at work. While a brand new M6 might cost \$130k, those buyers generally tend to not be 17. As a result, liability-only insurance for a new M6 might literally be lower than liability for a decade old Civic due to who the drivers are. Generally, the cheaper cars tend to be teenage cars and teenagers have the highest accident rates. So if you want to know what not to buy, just stop by the parking lot of your local high school.

Quote
What else did I ignore? Maintenance would be in favor of newer cars.
Maybe, maybe not. That's highly dependent on many things including the model of car, how you drive, and how much you drive. But most importantly for used cars is how all those pertain to the previous owner. A used Civic that was flogged in traffic daily for 60,000 miles may not be as good of a buy as a Merc S550 that saw mostly long highway commutes for 200,000. As MMM has pointed out, most modern (i.e. last two decades or so) cars really don't require as much maintenance as in the past, especially if they're seldom used. Beyond that most maintenance isn't as hard or as impossible to perform at home, and thus not as expensive. Changing oil is not rocket science, neither is changing brakes, flushing coolant, or even adjusting valves. Now granted, some of those tasks are definitely easier in some vehicles than in others, but most cars on the MMM-approved car list can be pretty maintenance-free well into their 3rd mileage century.

*The mileage figure is actually quite a bit low because I average about 18k miles/year. The engine started showing its age quite a while back, so I finally got it rebuilt last year but never really got it running afterwards. So it sat for the last year of ownership. Otherwise, I would have driven a total of at least 80k miles which would work out to \$.00375/mile depreciation. However, I still could've sold it for at least what I bought it for, but probably at least \$1500. That's a profit, albeit small.

#### Lars

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##### Re: Another math question
« Reply #14 on: September 15, 2012, 01:49:54 PM »
OP have they convinced you that there are a large number of vehicle purchases that are better than leasing over your 25 year time frame?
If so I won't waste your time. If not, I think you made a couple of hidden assumption that led you to the wrong answer and I'd like to do some digging.

#### gecko10x

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##### Re: Another math question
« Reply #15 on: September 17, 2012, 02:36:49 PM »
OP have they convinced you that there are a large number of vehicle purchases that are better than leasing over your 25 year time frame? If not, I think you made a couple of hidden assumption that led you to the wrong answer and I'd like to do some digging.

Most of the responses up to this point have ignored or side-stepped the point of the OP. That's not to say they aren't good observations, but (without re-reading them all) no one has even attempted to pinpoint the maximum \$\$ that can sit in your driveway and still give you the best "return".

If no one is interested in the answer or the exercise, OK. Maybe there are too many variables (or maybe no one understands the question), but there are a few members who seem to like and have a good handle on math and spreadsheets, so I thought I'd throw it out there.

By all means, please point out whatever you think I've missed.

OP have they convinced you that there are a large number of vehicle purchases that are better than leasing over your 25 year time frame?

Once again, this was not the point. My intention was never to dispute the fact that there are a million ways to spend very little on a vehicle. Buy an old/cheap car, learn to fix everything yourself, learn to find/get great craigslist deals, buy from dealer auctions, etc. And the point was also not to say that leasing is a great way to spend your money. The point was/is that for someone that wants to drive a newer and/or more expensive vehicle, leasing may very well be a better use of your money than owning. Or at least that was the theory.

#### AmbystomaOpacum

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##### Re: Another math question
« Reply #16 on: September 17, 2012, 02:49:16 PM »
If we ignore maintenance, insurance and taxes, the attached spreadsheet I think does the necessary calculation.

Basically, enter how much you would spend if you bought, how much you would spend per month if you leased, how long you would keep the car if you bought (lease term is irrelevant because switching from one lease to the next costs nothing [assuming no payment due at signing]), your depreciation assumption and your investment return assumption.

The spreadsheet assumes you will invest an amount equivalent to what you would have spent buying if you lease (in other words, it assumes you have the cash and are not financing if you buy).

If you buy an expensive car or buy cars often, leasing comes out ahead. Otherwise, buying comes out ahead. To determine if buying is right for you (assuming buying wins on this sheet), I think you would look at the difference between the monthly costs for buying and leasing and see if you can hit this monthly for maintenance, taxes, etc. If you can, you come out ahead buying. If you can't, you come out ahead leasing.

Have at it.

Some other thoughts:

- Every month you own, depreciation is affecting you less. Every month you lease, you're earning interest on less money (because you have to make a lease payment from your investment). You'll never be earning enough interest to pay the lease with the interest, so you'll end up in the red eventually. A purchased car, however, will never have negative value.
« Last Edit: September 17, 2012, 02:53:37 PM by AmbystomaOpacum »

#### AmbystomaOpacum

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##### Re: Another math question
« Reply #17 on: September 17, 2012, 02:56:05 PM »
That sheet has a bug. It won't work with "months to keep car" greater than 84. Here is a fixed one that will work up to 120 (10 years).

#### gecko10x

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##### Re: Another math question
« Reply #18 on: September 17, 2012, 03:01:38 PM »
Every month you lease, you're earning interest on less money (because you have to make a lease payment from your investment).

This I did not account for! (at least, not in the way you did) Excellent point which appears to drastically change the outcome. I will have to look closer when I get a chance.

Edit: I don't have my spreadsheet with me, but I think I was assuming you had the cash flow to support the payment, and not reducing the investment amount.

Edit 2: I think that the way I did it, I should have accounted for the missed investment interest of each lease payment.
« Last Edit: September 17, 2012, 03:07:06 PM by gecko10x »

#### \$_gone_amok

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##### Re: Another math question
« Reply #19 on: September 17, 2012, 05:39:56 PM »
I believe cars are just tools that get you from point A to point B. However, I am very much a fan of fast and nice cars.

I don't believe small depreciation are only limited to cheap and reliable Japanese cars.  For example, a well maintained E30(maybe E36?) BMW M3 with manual transmission maintains it's value remarkably well.

Now for some math.
Let:
V = cost of buying a vehicle
x = lease term in years
Z = resell value of vehicle costing V after x years.
K = money earned by investing V over x years (unknown value based on many variables).
J = cost of leasing a vehicle over x years

if
|K - J| > V - Z

|K - J| < V - Z
lease is better

For this equation to work, only identical vehicles should be compared to keep operation cost the same.  For example, leasing a new 2012 VW GTI, vs buying a used one made in 2010.

Lets run this equation with the aforementioned vehicle.

V = fully loaded used 2010 GT = \$20,000 (quick search on craigslist)
Lease cost = \$369/mo (fully loaded 2012 GTI based on quick search on leasetrader)
assuming x = 3
J = 13,284 (total \$ spend on the lease)
Z = 12,000 (assuming 8K depreciation over 3 years).

|K - 13284| < 8000

In order to make lease the better deal. K needs to be at least 5284.

Now, if the investment return is higher than the cost of leasing the vehicle, then leasing is obviously a better choice, but this equation only looks at the real life examples such that there's a positive depreciation cost and a realistic investment return rate.

#### menorman

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##### Re: Another math question
« Reply #20 on: September 17, 2012, 05:47:00 PM »
OP have they convinced you that there are a large number of vehicle purchases that are better than leasing over your 25 year time frame? If not, I think you made a couple of hidden assumption that led you to the wrong answer and I'd like to do some digging.

Most of the responses up to this point have ignored or side-stepped the point of the OP. That's not to say they aren't good observations, but (without re-reading them all) no one has even attempted to pinpoint the maximum \$\$ that can sit in your driveway and still give you the best "return".

If no one is interested in the answer or the exercise, OK. Maybe there are too many variables (or maybe no one understands the question), but there are a few members who seem to like and have a good handle on math and spreadsheets, so I thought I'd throw it out there.

The question wasn't really clear before, and even this clarification still leaves a lot of assumptions to be made. A "used" 2012 Honda Accord (2013s are out now...) will still depreciate like crazy, while buying a 1988 BMW 318is probably is at the lower limit. If you're looking for a very specific dollar amount, I'd say \$1200-\$1500 for something running, depending on the local market and other factors. However, those cars will be far from new, probably at least 15-20 years old. After that point, the values keep pace with inflation and the cost of gas.

Of course, you could always put your car in one of those rental pools so that it actually earns money for you.

#### AJ

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##### Re: Another math question
« Reply #21 on: September 17, 2012, 07:38:48 PM »
V = fully loaded used 2010 GT = \$20,000 (quick search on craigslist)
Lease cost = \$369/mo (fully loaded 2012 GTI based on quick search on leasetrader)
assuming x = 3
J = 13,284 (total \$ spend on the lease)
Z = 12,000 (assuming 8K depreciation over 3 years).

|K - 13284| < 8000

In order to make lease the better deal. K needs to be at least 5284.

Love the math, gone_amok! Not to convolute the conversation too much, but wouldn't it be even better to buy the car and take financing? Using gone_amok's numbers, if you invested your own \$20k and borrowed \$20k @4% over a 5 year term, your payments would be roughly the same as the lease. After 3 years, you would own a car worth \$12k, have a loan balance of about \$8k, and also have your investment earnings and original \$20k.

#### AmbystomaOpacum

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##### Re: Another math question
« Reply #22 on: September 18, 2012, 08:29:37 AM »
Edit: I don't have my spreadsheet with me, but I think I was assuming you had the cash flow to support the payment, and not reducing the investment amount.

We can run the calculation this way too.

I set up this sheet to calculate your net worth after the given term if you buy, if you lease, and if you do nothing but invest all your money. Then I defined the cost of each option as the difference between your net worth if you do nothing and your net worth if you buy or lease.

It seems however that your starting balance and monthly income have no impact at all on the results. The only thing that matters is the purchase price, lease price, and term (as well as, of course, your assumptions on depreciation and investment return).

The results of the calculation are the same except that in my first sheet I just noticed I was calculating interest after making the lease payment each month whereas on this one I'm calculating it before making the lease payment; also on the new sheet I'm comparing with the value of the investment at the end whereas on the first sheet I was comparing with the initial balance.

The second sheet's numbers for monthly cost are probably the more interesting ones, but I could make the first sheet behave the same way simply by computing the value of your investment if you do nothing and using that as the point of comparison. Tracking cash flow doesn't make any difference.

Obviously, if you keep the investment amount fixed whether you are making a lease payment or not, leasing comes out ahead. But that implies that if you bought, you wouldn't invest the money saved by not having a monthly payment... which seems like an odd assumption.

--------------------------------------------

I think the takeaway is this:

The cheapest possible lease seems to be about \$180/month (this is based on a local advertisement for a Hyundai Accent, a very cheap car).

Once you know the baseline lease price, you can pick how long you want to keep a car and compute a sale price which will give you the same monthly cost as leasing over that term (hint: use Excel's goal seek function on this second sheet). So if you're going to keep a car for 36 months, you can buy a \$13,396.52 car and pay the same amount monthly as the cheapest possible lease. (This doesn't consider insurance and maintenance.) But the same Hyundai Accent is less that that, so if we're not consider insurance and maintenance, you get more car if you buy.

If we put a fixed monthly price on maintenance (say \$50) and assume insurance will be equal if you lease or buy, then we can use the same goal seek function and get a reasonable purchase price that's equivalent to a given lease price.

So for the \$180 lease...

36 months gives a purchase price of \$10,000
48 months, \$10,700
60 months, \$11,400
72 months, \$12,000

These are the prices that will cost you the same as leasing (including \$50 month maintenance). If you buy a cheaper car than these prices (or spend less on maintenance), you will come out ahead if buy. If you buy a more expensive car (or spend more on maintenance), you will come out ahead if you lease.

In time, if anyone wants, I'll set up a sheet where you can enter the lease price, the maintenance cost assumption, and automatically calculate the equivalent purchase prices at various lengths of ownership.
« Last Edit: September 18, 2012, 09:16:43 AM by AmbystomaOpacum »

#### AmbystomaOpacum

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##### Re: Another math question
« Reply #23 on: September 18, 2012, 10:10:04 AM »
I think I have it.

BIG DISCLAIMER: Please do not make any decisions based on this chart alone. It is just a first stab at a calculation that I'm not even sure is valid in the first place.

That said, here is what I am doing:

Enter lease price, depreciation, investment return, and maintenance cost. For each month, calculate how much money has been spent on the lease (lease payments plus opportunity cost of investing that money). Calculate how much has been spent on maintenance (including opportunity cost). Define the acceptable loss on your purchase to be the difference between the two. So if you've lost \$4000 total on the lease, and maintenance has cost a total \$1500, you can lose \$2500 between depreciation and opportunity cost on your vehicle and still come out ahead. Calculate total depreciation at that month. Calculate total investment opportunity at that month. The difference between investment opportunity and depreciation is the total loss of buying a vehicle in that month. Calculate what purchase price will produce that total loss percent. That price is assumed to be the price at which leasing and buying will be exactly equal in overall cost.

Hopefully some other people can look at this and tell me if it makes a lick of sense.

(Note that you can include taxes and whatever else you want in the "maintenance" cell. It's just a fixed monthly amount of additional expenses caused by owning a vehicle instead of leasing one.)
« Last Edit: September 18, 2012, 10:13:04 AM by AmbystomaOpacum »

#### Lars

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##### Re: Another math question
« Reply #24 on: September 18, 2012, 09:10:33 PM »
I feel like a bit of a slacker as I suggested a few assumptions were missing and missed a day or two of posting and everyone here found them while I was gone.

V = fully loaded used 2010 GT = \$20,000 (quick search on craigslist)
Lease cost = \$369/mo (fully loaded 2012 GTI based on quick search on leasetrader)
assuming x = 3
J = 13,284 (total \$ spend on the lease)
Z = 12,000 (assuming 8K depreciation over 3 years).

|K - 13284| < 8000

In order to make lease the better deal. K needs to be at least 5284.

Love the math, gone_amok! Not to convolute the conversation too much, but wouldn't it be even better to buy the car and take financing? Using gone_amok's numbers, if you invested your own \$20k and borrowed \$20k @4% over a 5 year term, your payments would be roughly the same as the lease. After 3 years, you would own a car worth \$12k, have a loan balance of about \$8k, and also have your investment earnings and original \$20k.

Excellent idea. I think whether buying is better than lease on the same new vehicle depends on the effective interest rate of the financing provided by the lease and the difference between what they offer to sell the vehicle at the end of the lease and the price you could sell the vehicle for if you owned it. I had no idea on the effective interest rates embedded in lease so I added to the great spreadsheet already posted and added on option on getting a loan as you describe. (I also got rid of those complex tables - excel has a formula for that function)

For the Hyundai info I could find, the effective lease interest rate was 4.25% which is very similar to 84 month loans from by credit union, so the cost difference between leasing and buying the 2013 accent was minimal (within my estimated errors). Of course, as has already been mentioned, depreciation dominates the overall cost for new and nearly new vehicle so anything that reduces depreciation will likely win with the lowest costs (comparing new leased vs 1 year old purchased, etc.)

Spreadsheet was done in openoffice. Hopefully it didn't screw up the formula in excel version.

#### gecko10x

• Bristles
• Posts: 418
##### Re: Another math question
« Reply #25 on: September 19, 2012, 10:52:37 AM »
Sorry it's taken me so long to respond- too many good additions to think through.

The above spreadsheets were not quite presenting the information the way my mind wanted to look at it, so attached is another take on it that looks at an investment horizon beyond any specific lease term. (There should be a graph of the green columns at the bottom. Hopefully the file will still be accessible after all my mucking with file formats.) You really have to skew the numbers to make leasing come out ahead over any significant time period.

#### totoro

• Handlebar Stache
• Posts: 2191
##### Re: Another math question
« Reply #26 on: September 19, 2012, 12:30:23 PM »
Holy, I have no idea how to do those sort of spreadsheets!   Clearly there are some math prodigies among us :)

Even if leasing was break even with buying if you wanted to always drive almost new, I would not do it.  I dislike the stress of worrying about interior damage or scratches that you are charged for upon return with a lease.  Having kids this is a likely scenario.

#### Lars

• Stubble
• Posts: 105
##### Re: Another math question
« Reply #27 on: September 19, 2012, 06:53:16 PM »
Sorry it's taken me so long to respond- too many good additions to think through.

The above spreadsheets were not quite presenting the information the way my mind wanted to look at it, so attached is another take on it that looks at an investment horizon beyond any specific lease term. (There should be a graph of the green columns at the bottom. Hopefully the file will still be accessible after all my mucking with file formats.) You really have to skew the numbers to make leasing come out ahead over any significant time period.

File came out no problem for me. I like the long term view. I found two mistakes:

You should be comparing column F and H not F and I as the monthly 200 cash used for investment will pay lease.
The formula for the investment value after replacement vehicles didn't fully account for effect of replacement vehicles.

The overall conclusion remains the same as yours though. Updated spreadsheet is attached.

#### gecko10x

• Bristles
• Posts: 418
##### Re: Another math question
« Reply #28 on: September 20, 2012, 08:04:27 AM »
You should be comparing column F and H not F and I as the monthly 200 cash used for investment will pay lease.
The formula for the investment value after replacement vehicles didn't fully account for effect of replacement vehicles.

The overall conclusion remains the same as yours though. Updated spreadsheet is attached.

You helped me realize my calcs weren't quite right- thanks.

I don't think your modifications makes sense though for what I was trying to show. I think the comparison should be of E/H or F/I. Here's what I was attempting to do:
E/H are the invested values; E is monthly payments invested, and H is initial lump sum invested.
F/I are the invested values minus the total costs; (F starts at the same place as E because the initial lump sum is already accounted for), I = H (i.e. the initial lump sum invested) minus the total spent on the lease. The lease cost should not be subtracted out within the FV calculation because you aren't removing that money from your investments.

Does this make sense? I've attached a new spreadsheet.

#### Lars

• Stubble
• Posts: 105
##### Re: Another math question
« Reply #29 on: September 20, 2012, 08:57:42 AM »
Yeah but I don't see how you are comparing what you think you are. Based on your formulas, the problem you are solving appears to be the following.

Starting with enough cash to purchase a vehicle outright and \$200 a month which option will come out ahead financially:

Spending Initial Cash to purchase vehicle and investing \$200/month. Every x years, the money in investment account is used to purchase new vehicle. (Column F)

Investing Initial Cash and using the \$200/month to pay the lease.  (Column H)

Column E would represent the investment value of the \$200 a month (no money is subtracted so this represents the case you never purchase another vehicle)

Column I represent value of initial invested cash minus \$200 a month for lease. Column F is always going to win because it get an extra \$200/month so it is not an apple to apples comparison. Do you see that? That is why I was comparing columns F and H.