“Is there a formula on how much a car a person can afford? Is it based on net worth? Income?”
I’ve also wondered this in the past, and so I figured out a formula for myself, which I think is logical and plausible.
Here goes:
First, what should we be comparing car expenditure with? You suggest possibly net worth or income. I think the answer is neither. Your annual consumption budget is the right benchmark.
Expenditure on cars is a consumption item. Hence, net worth is not directly relevant, except in so far as it has already formed some prior input into your calculation for your total annual consumption spending. Income is more relevant, but again, not a great starting point.
You should base your car expenditure calculations around your annual spending. As a dedicated Boglehead, you will have already done a prior calculation in which you have calculated your annual spending, calibrated to smooth consumption over your lifetime, taking into account your current assets, expected future income, asset allocation, and conservative plausible rate of return assumptions.
Let’s call your annual consumption spending C.
Next, as a dedicated Boglehead, you are already putting aside a certain amount of money each year (X) in a sinking fund (perhaps a low-cost 30/70 (equity/bond) fund to cover the cost of replacing your car every N years.
Let’s call the depreciation rate on cars D.
Now, we could complicate the calculation by assuming you earn some rate of return on your sinking fund. I do this for my own calculations, but I think it is a bit of an unnecessary complication. The sinking fund is mostly bonds, and it is held outside of tax preferred retirement vehicles, so the post-tax inflation-adjusted return is close to 0. So let’s forget about the return generated in your sinking fund.
So, the problem becomes one of putting aside $X every year indefinitely, in order to purchase a car every N years, with the car’s purchase price being P, and with the car’s value depreciating at a constant rate D each year.
Given that the trade in value will be the depreciated value of the car, we have the following condition at each point in time that a new car is purchased and the old one is sold:
P(1-D)^N + X * N = P
Solve this for the value of P
P = {X*N} / (1 - (1-D)^N)
This formula intends to find the balance where your savings of X over N years directly contribute to acquiring the new car by covering the depreciation of the old one.
Now let’s move to make the equation more useful.
Let’s set the value for $X as a given proportion of your annual expenditure budget:
X = S * C
where S is the share of your annual consumption spending dedicated to covering the cost of replacing a car of value P every N years.
Now, let’s calculate the ratio of the car purchase price to annual consumption P / C. Let’s call this ratio R.
R = P / C = {S*N} / (1 - (1-D)^N)
So, I think this is the type of formula you looking for.
The value of R is the ratio of the capital cost of a new car purchase to your annual spending budget, expressed as a function of: (a) the share of your annual budget you are happy to allocate to your car sinking fund, (b) the number of years you intend to hold your cars on average, and (c) the depreciation rate on cars.
What is a plausible value for R? For that, we need plausible values for S, N and D.
D is hard to know, but a bit of a given. You can influence it a bit by how well you care for the car, but it largely depends on market forces, technological obsolescence, and physical wear and tear. I think a plausible depreciation rate on cars is about 15% p.a., so let’s set D = 0.15.
Values for S and N are more in the realm of personal preference. But we can use economy-wide data to generate some plausible values.
Perhaps someone can check the latest BEA national accounts input-output tables, but I think they would show that a plausible value for S is about 0.04 (based on the share in total U.S. household consumption of purchases of motor vehicles at tax- and margin-inclusive prices, which I think is about 3 per cent, but I'll set S = 0.04 on the basis that (i) expenditure elasticity for motor vehicles is greater than 1 and my sense is that bogleheads generally have higher than average income; (ii) the economy-wide average spend is not quite right, because some households do not have cars, and so pull the national average down).
Google tells me that the average age of the U.S. passenger car fleet is about 12 years, so let’s set N=12.
Plugging these into the equation for R, we have R = 0.56.
That is, if someone is happy to commit to putting aside 4% of their consumption budget each year, and turn over their cars every 12 years, then each time they buy a new car, they can buy a car valued at 56% of their annual consumption budget.
I’ve also wondered this in the past, and so I figured out a formula for myself, which I think is logical and plausible.
Here goes:
First, what should we be comparing car expenditure with? You suggest possibly net worth or income. I think the answer is neither. Your annual consumption budget is the right benchmark.
Expenditure on cars is a consumption item. Hence, net worth is not directly relevant, except in so far as it has already formed some prior input into your calculation for your total annual consumption spending. Income is more relevant, but again, not a great starting point.
You should base your car expenditure calculations around your annual spending. As a dedicated Boglehead, you will have already done a prior calculation in which you have calculated your annual spending, calibrated to smooth consumption over your lifetime, taking into account your current assets, expected future income, asset allocation, and conservative plausible rate of return assumptions.
Let’s call your annual consumption spending C.
Next, as a dedicated Boglehead, you are already putting aside a certain amount of money each year (X) in a sinking fund (perhaps a low-cost 30/70 (equity/bond) fund to cover the cost of replacing your car every N years.
Let’s call the depreciation rate on cars D.
Now, we could complicate the calculation by assuming you earn some rate of return on your sinking fund. I do this for my own calculations, but I think it is a bit of an unnecessary complication. The sinking fund is mostly bonds, and it is held outside of tax preferred retirement vehicles, so the post-tax inflation-adjusted return is close to 0. So let’s forget about the return generated in your sinking fund.
So, the problem becomes one of putting aside $X every year indefinitely, in order to purchase a car every N years, with the car’s purchase price being P, and with the car’s value depreciating at a constant rate D each year.
Given that the trade in value will be the depreciated value of the car, we have the following condition at each point in time that a new car is purchased and the old one is sold:
P(1-D)^N + X * N = P
Solve this for the value of P
P = {X*N} / (1 - (1-D)^N)
This formula intends to find the balance where your savings of X over N years directly contribute to acquiring the new car by covering the depreciation of the old one.
Now let’s move to make the equation more useful.
Let’s set the value for $X as a given proportion of your annual expenditure budget:
X = S * C
where S is the share of your annual consumption spending dedicated to covering the cost of replacing a car of value P every N years.
Now, let’s calculate the ratio of the car purchase price to annual consumption P / C. Let’s call this ratio R.
R = P / C = {S*N} / (1 - (1-D)^N)
So, I think this is the type of formula you looking for.
The value of R is the ratio of the capital cost of a new car purchase to your annual spending budget, expressed as a function of: (a) the share of your annual budget you are happy to allocate to your car sinking fund, (b) the number of years you intend to hold your cars on average, and (c) the depreciation rate on cars.
What is a plausible value for R? For that, we need plausible values for S, N and D.
D is hard to know, but a bit of a given. You can influence it a bit by how well you care for the car, but it largely depends on market forces, technological obsolescence, and physical wear and tear. I think a plausible depreciation rate on cars is about 15% p.a., so let’s set D = 0.15.
Values for S and N are more in the realm of personal preference. But we can use economy-wide data to generate some plausible values.
Perhaps someone can check the latest BEA national accounts input-output tables, but I think they would show that a plausible value for S is about 0.04 (based on the share in total U.S. household consumption of purchases of motor vehicles at tax- and margin-inclusive prices, which I think is about 3 per cent, but I'll set S = 0.04 on the basis that (i) expenditure elasticity for motor vehicles is greater than 1 and my sense is that bogleheads generally have higher than average income; (ii) the economy-wide average spend is not quite right, because some households do not have cars, and so pull the national average down).
Google tells me that the average age of the U.S. passenger car fleet is about 12 years, so let’s set N=12.
Plugging these into the equation for R, we have R = 0.56.
That is, if someone is happy to commit to putting aside 4% of their consumption budget each year, and turn over their cars every 12 years, then each time they buy a new car, they can buy a car valued at 56% of their annual consumption budget.
Statistics: Posted by JamesG — Wed Mar 06, 2024 6:12 pm — Replies 74 — Views 3602