[buzzy_boy]

Very interesting thread. This is a question that I have already asked myself. I have tried to answer the question to myself using some mathematics. I will present the model here. It is not perfect, and I would love to hear members' feedback.

Basic premise

Point of diminishing returns for the price of a car = maximum cost of cheapest viable alternative

Explanation

Supposing regularly using public transport is a viable option for you, then the maximum cost incurred while using public transport is the point of diminishing returns for a car.

What is a viable mode of transport depends upon individual circumstances. So, let me analyse my specific case.

Background

We are a family of four with 2 kids. We have an Activa for city commute. Every weekend, we travel 700 KMs, two way, to our native place.

Hence, monthly usage is approx. 3000 KMs, mostly highways.

Cost Parameters

1. Initial cost of vehicle
2. Maintenance cost per KM
3. Yearly expenses (mainly insurance)
4. Cost of fuel per KM
5. Cost of tolls

Some assumptions

Cost of fuel per KM = (cost of fuel per litre/ avg. mileage of the vehicle)

Assuming an economical driving style for a diesel vehicle, we can extract a max. of 20 KMPL on highways.

Cost of diesel = 102 Rs. per litre

Hence, cost of fuel per KM = 102 / 20 = 5.1

Adding approx. 75 paise per KM for toll charges,

Cost per KM of using my car = 5.85

Since four of us travel together,

Cost per KM per person = 5.85 / 4 = 1.46

Cost of public transport

A 2nd AC train ticket (our viable mode of public transport) costs Rs. 1000 per person for approx. 400 KMs one way (note: the rail-route is longer than the road route)

Cost per KM of public transport = (1000 / 400) = 2.5 Rs. per person.

Cost per KM of public transport for the whole family = 10 Rs.

Adding to that, the cost of local transport of approx .25 Rs (adjusted for proportional distance, shared by the family), we get = 10.25 Rs. per KM.

So, it seems any diesel car that can give 20 KMPL for highways is infinitely valueable.

Depreciation

However, we have missed depreciation of the vehicle as an important factor.

We know that

1. Cost per KM of car transport for my circumstances = 5.85
2. Cost per KM of public transport for my circumstances = 10.25

So, it seems that a car that depreciates Rs. 4.6 per KM might still be valuable.

Depreciation cost

To calculate the cost incurred through depreciation, we need to make some assumptions.

1. Avg. Lifetime on an engine ~= 4,00,000 KMs
2. Avg. cost of maintenance for mass market cars ~= .75 Rs. per KM
3. Residual value of the vehicle = 20% of the original cost (for simplicity, assuming OTR price)
4. Assume an avg. Insurance cost of Rs. 15000 per year (averaged over the expected life of the vehicle).

Then, for my circumstances, I can expect to drive the vehicle for 4,00,000 / 36,000 = approx. 11 years.

Let OTR of the vehicle be X. Amortized cost of the vehicle for 11 years for my usage pattern = ((X - 20% of X) / 11) + 15000)/36000 per KM

Targetted cost of vehicle

Total depreciation cost per KM then becomes:

(((X - 20% of X) / 11) + 15000)/36000) + .75

Per our thesis, that cost should be no greater than 4.6 Rs.

Solving for X, we get

(((X - 20% of X) / 11) + 15000)/36000) + .75 = 4.6

Then X is approx. Rs. 17,00,000

Result

Then per my usage pattern, a diesel vehicle that costs approx. 17,00,000 is my point of diminishing return.