[What I learn today] Models of Cost, Revenue, and Profit

I decided to dedicate every Thursday as "Research Method Day" for my entire duration of my Ph D. study. This is to allow me to "divide-and-conquer" my entire scope of study. By doing this, I can focus to understand (find a way or method) how to calculate all my research data later. So, let's learn Models of Cost, Revenue, and Profit.


Q: What area can benefits from Cost, Revenue, and Profit Model?
A: Production planning, sales quota projection, financial planning and other areas of decision making.

Cost and Volume Models
The cost of creating (producing or manufacturing) a sell-able product (items) is a direct function (f) of the volume (v) being produced. Cost usually consist of two sub-cost which are: fixed cost and variable cost.


Fixed cost  does not depend on the production volume. This cost remains the same regardless of number of products produced. Variable cost depends on and varies with the number of production volume (number of product produced).

Consider this simple example:
Mobilevertising, Inc. produces a variety of mobile websites for its clients worldwide. Mobilevertising's best-selling product is the costumed-made 5-page mobile website ready to deploy in 24-hours (5PMP-EBD). A setup cost is incurred each time a changeover is made for a new mobile website development. Suppose that the setup cost is RM500. This setup cost is fixed cost that is incurred regardless of the number of website created. Beside that, suppose that manpower (software developer), marketing, sales and material cost RM850 for each mobile website created. Thus, the cost-volume model for producing x units of the 5PMP-EBD can be written as:

                                          C(x) = 500 + 850x                                                           [E1]  

where:-

• C(x) : total cost to produce x units or total production cost
• x : number of product created

Once we have the production volume (in this case number of website created), the model in equation E1 can be used to calculate total production cost. For example, the owner decided (take decision) to produce x = 5 unit of website every months, would result in a total cost of

             C(5) = RM500 + RM850(5) = RM4750                                                    

Marginal cost in the above example is RM850. Marginal cost is the rate of change of the C(x) with relation to total number of production (volume). NOTE: Marginal cost may increase or decrease in more complex total cost model.

Revenue and Volume Model
Board of directors & shareholders of any company definitely want to know about projected revenue associated with selling a specified number of company products or services. Suppose that each mobile website of 5PMP-EBD sells for RM898. The model for total revenue can be written as simple as this :-

                                 R(x) = RM898x                                                                             [E2]  

 where:-

• R(x) : Total revenue when able to sell x units
• x     : number of items sold

Marginal revenue in the above example is RM898. Marginal revenue is the rate of change of R(x) in relation to sales volume. Note: Marginal revenue can decrease or increase in more complex revenue model.

Now we come to is the most interesting (and important) part.

Profit & Volume Model 
The main reason entrepreneurs (and technopreneurs) do business is to make profit. Period. They (business owner) need to know (before hand) the profit implications of their decisions in business.
Total profit is total revenue [E2] minus total cost [E1]. Thus, we can produce the following model:-

                P(x) = R(x) - C(x) =  898x - (500 + 850x) = -500 +48x                                [E3]

Here, I suggested that the model for total profit which is P(x) [should be] and can be easily derived from cost-volume and revenue-volume relationships.

Pretty easy, huh? Next, we want to know the "breakeven point" which can be done though "Breakeven Analysis". Let's the mystery begins....

Breakeven Analysis
From equation E3 above, we can know calculate profits associated with any production volume of x. Suppose figure taken from marketing team (taken from their 'famous' and fancy market research report) projected demand forecast indicates that 10 units of the famous 5PMP-EBD can be sold easily by sales team. Thus, the decision to create and sell the 10 units of 5PMP-EBD results in projected profit of :-

                           P(10) = -500 + 48(10) = -20                [* Loss projected profit calculation] 

In simple word, a loss of RM20 is predicted when the sales team only able to sell 10 units of 5PMP-EBD. If sales team are able to sale only 10 units (sales projection), the owner may decide NOT to produce the product.

However, if the demand forecast is 50 units, that new number would gives projected profit of :-

                         P(50) = -500 + 48(50) = 1900             [*Positive projected profit calculation]            

This projected profit of RM1,900 may be enough to justify to proceed with the creation and sell of 5PMP-EBD by the owner.

Breakeven point is when total revenues equals to total cost (meaning when business is generating exactly RM0.00 profit). How to compute the breakeven point for our example?

The breakeven point can be found (exactly) by setting the profit equation [E3] equal to zero (0) and then solving the production volume. Let's try with our available model:-

                 P(x) = -500 + 48x = 0    

                 48x = 500                        

                    x = 500 / 48                 

                    x = 11                 ***see note below   

*** I take next positive number for this calculation; because there will be no such thing as half-baked product that can be sold to client (even though a few sales person can do it anyway).   

With this new information, the owner know that the production and sales of the famous 5PMP-EBD must be at least 11 units before a profit can be expected from the business activities.



Wow! We just learn the basic key items for any business plan. Woo-hooo! While writing this article, I found a website that give a more detail about break-even analysis here.