# The most profitable commodity will be identified by calculating the contribution case study

## Management accounting.

– The profitability of the two commodities can be calculated as follows:

Product X,
Total revenue= 25×20, 000= 500, 000
Variable cost= 20×20, 000= 400, 000
Contribution = 500, 000-400, 000
=\$100, 000

## Product Y

Total Revenue = 50×40, 000= 2000, 000
Total cost = 40×40, 000= 1600, 000.
Contribution = 2000, 000-1600, 000
=\$400, 000

## Product Y is more profitable compared to X by \$300, 000.(400, 000-100, 000)

– Commenting on the pricing system used in table 1. It is basically a cost plus method of commodity pricing because from the table 1, the selling price is calculated as a percentage of the cost.(a profit of 25%is charged on every single unit of output).

## Initial fixed costs allocation by machine hours:

New fixed costs = 1. 1*480, 000
=\$528, 000.

## The new allocation of fixed costs will be in the same ratio (2: 1)

This will give the below values:
528, 000 *2/3= \$352, 000. (i)
528, 000 *1/3 = \$ 176, 000 (ii)

## Now based on the above fixed costs, the total cost functions will be expressed as follows:

TC (Y) = 176, 000 + 40Q
TC(X) = 352, 000 + 20 Q

## Whereby Q represents the quantity produced in each scenario.

Multiplying each equation by Q to represent the quantity produced, the below equations are obtained.
P= MR-MC
SO MC= 176, 000Q +40Q2
Again, in equation ii, MC = 352, 000Q + 20Q2

## Differentiating the two equations (established Dc/DQ,)

The following will obtained:
P1 = 80Q +176, 000.
P2 = 40Q +352, 000
Now profit is maximized when MC = MR

## This level of production will define the optimal production.

4 In equations expressed in No. 3 above, analysis has been based on differentiation which is based on economist’s point of view. It will thus be optimal to produce at the minimal costs as expressed by MR – MC = 0.

## REFERENCES.

H. Coombs, D. Hobbs, E. Jenkins, (2005) Management Accounting: Principles and Applications, Sage publications, London.
J. G. Siegel, J. K. Shim, (2006), Accounting Handbook, Barrons Ed. Systems, New York.
P. J. Eisen(2007), Accounting, Barrons Ed. Systems, New York
P. J. Eisen(2003), Accounting the easy way, Barrons Ed. Systems, New York