Calculating the cost

[Leif]

OK, not a puzzle as such, but I need help to calculate something...

I am campaigning to get speed restriction in our village - I won't bore you with the obvious details - but I am running up against bureaucratic buck-passing and want to press my case with some numbers.

Say we want a speed camera. I am told the cost is £10,000 for the local council to put in the post and connect power, and the camera itself costs £30,000 - a total of £40,000.
The annual 'running cost' - excluding deducting income from any fines at a minimum of £60 a go - is stated to be £8,000.

The Department of Transport itself estimates the 'cost' of a fatality to be £1,638,390.

Without the running costs, I could argue that there would have to be 1,638,390/40,000 = 40.96 years without a fatal accident for it to be more 'cost efficient' not to put a camera in place. What I want to calculate, is the equivalent number of years with running costs of £8,000 pa. i.e The cost after the first year will be £48,000, after the second £56,000 etc.
(I'm not too interested in the cost of inflation increasing the £8K as the initial £1.6M would probably rise similarly.)

And then I'd like to do the same for a 'serious accident' cost of £185,220.

Make sense?

TIA

[StuartR]

Isn't this as simple as

40,000 + 8,000n = 1,638,390

So n = (1,638,390 - 40,000) / 8,000 = 199.79 years

[HansV]

I don't quite agree with your calculation - the £40,000 is not a cost per year, so you shouldn't divide the cost of a fatality by £40,000. Let's say the camera and post last 10 years, then you could say that the fixed cost amounts to £4,000 per year. With the operating costs of £8,000, that'd be £12,000 per year. So if there is no fatal accident for more than £1,638,390 / £12,000 ~ 137 years, it'd be more cost efficient not to put in a camera.
For a serious accident, it'd come out at ~ 15 years.

See the attached workbook, where you can play with the numbers.

Costs.xls

[Leif]

Ah, thank you both! A spreadsheet and sensible way of looking at things was just what I was expecting hoping for

[StuartR]

If you had said you were going to use a spreadsheet then we could have suggested you do a calculation based on Net Present Value, to allow for the changing value of money over time

[Leif]

I'm still open to alternative methods! It is how to look at it overall - e.g. assuming a 10-year life for the camera - that I need help with.

That, and slowing the traffic down...

[HansV]

Have you seen Cost benefit analysis of traffic light & speed cameras (PDF file)?

[Leif]

I have now! - thanks again, something to read later...

[HansV]

Here's a slightly modified version of the spreadsheet in which the income from fines is taken into account.

Costs.xls

[StuartR]

Have you seen Cost benefit analysis of traffic light & speed cameras (PDF file)?

I'm pleased to see that they understood the importance of converting all the numbers to Net Present Value.