# Cost Function for Start Up

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1. Nov 21, 2015

### Entreprenewb

1. The problem statement, all variables and given/known data
Trying to determine appropriate cost function for my start up. Usually total cost= fixed costs + per unit cost* Q.
However, it is usually assumed your fixed costs are monthly recurring costs, like rent, utilities, etc. Many of the costs we face are one time development costs with no real time dimension. Let's say our monthly fixed costs are $4,500. We have one time costs of$25,000 right off the bat. I'm tempted to simply add a time dimension, but not sure if this is acceptable or if the resulting equation will be of any practical business use (IE, I'm not sure if it will have the same interpretation when I take derivatives, etc). We're not entirely sure what our per unit costs will be yet, but they are most likely very small, <$100. Can anyone think of any obvious flaws with my approach? I would greatly appreciate any input, and understand this is slightly off topic for this forum. 2. Relevant equations TC= FC + per unit cost* Q Where, TC= Total cost FC= fixed costs Q= units produced 3. The attempt at a solution TC=$25,000 + ( \$4,500*m) + (per unit costs *Q)

Where m= # of months.

2. Nov 21, 2015

### Entreprenewb

Update: I have been told that I can represent these one time costs as capital put into the business that will depreciate, or as a business loan with interest. However, I am still not sure how I would represent this in a cost function. Since I am paying all of these expenses out of pocket, it makes sense to view this as capital put into the business that will depreciate.

Does anyone know how to add this to a total cost function--or if this is even appropriate?

3. Nov 21, 2015

### Ray Vickson

Your equation in 3, is basically correct, insofar as it ignores the time-value of money.

A more basic issue is: for what purpose do you want to do these calculations? If, for example, you are contemplating several alternatives (such as alternative designs or product lines, or even alternative forms of business) then taking account of "time" effects is important. Several methods for doing this are discussed in Engineering Economics textbooks and in some on-line sources, such as
http://ocw.mit.edu/courses/nuclear-...ogy-spring-2004/lecture-notes/lec09slides.pdf

On the other hand, if there are not really any choices involved, but just "accounting" issues, then you can still apply various methods as discussed in the cited source, although the reasons for different choices are maybe less compelling. An important consideration is how the different accounting methods relate to the tax-payable. For example, depreciation is often listed as a line item and is applicable to the assessment of taxes (even though depreciation is not a true, actual cost at all---you don't actually pay out x actual dollars per month for depreciation). How to do it and the options available to you are to some extent jurisdiction-dependent, and so it would matter whether you are located in the USA, Canada, New Zealand, Japan, etc.

4. Nov 23, 2015

### Entreprenewb

Interesting. The purpose of running these calculations is to figure out how we should be pricing our service, and additionally, finding the point at which we will break even. I am in the US. I did not consider the tax implications of using different accounting methods. Thanks for the response.