Matrix Accounting Illustrated: Contribution Margin

• Published date: 01 July 2016
• Date: 01 July 2016
• DOI: http://doi.org/10.1002/jcaf.22180

59

© 2016 Wiley Periodicals, Inc.

Published online in Wiley Online Library (wileyonlinelibrary.com).

DOI 10.1002/jcaf.22180

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Matrix Accounting Illustrated:

Contribution Margin

Melvin Hughes

INTRODUCTION

Before reading

this article, it may be

useful to put it side-

by-side with the pre-

ceding article (“The

Simple Analytics of

Matrix Account-

ing, Activity-Based

Costing and Linear

Programming”).

Rather than reading

the whole article, it may be use-

ful to look over the summary in

the appendix.

Here, I intend to make

good on my promise that the

analytics are simple. I said

that a typical executive chef

could use this model, so we

will go over the steps on the

computer in detail. This paper

stops before the discussion of

activity-based costing (ABC)

and linear programming (LP).

The second section reviews

some notation of matrix alge-

bra and reviews the matrices we

will be using. The third section

builds a case study of Coase

Vineyards, a small winery in

Napa Valley, California. This

is a good example, in that for

wineries, prices and quality

of grapes varies year by year.

The product mix can change

very often, and small winer-

ies don’t have the resources to

build specialized but inefficient

computer models of costs.

Even large wineries with cost

accounting software in place

may find this material

beneficial.

The fourth section builds

an example of a hotel banquet

kitchen, which again has vary-

ing costs of inputs. For brev-

ity, I do not include a separate

numerical example, but just

provide a verbal discussion of

how the hotel industry could

use the Activity-Based Linear

Economic Model (ABLEM)

for real-time price negotiations

in a fast-paced setting.

The final section

suggests further uses

of ABLEM by man-

agerial accountant.

The third article is

introduced, describ-

ing how manage-

rial accounting and

operations research

can be integrated

with the present

mathematical model

of the firm.

REVIEW OF MATRIX NOTATION

AND MODEL VARIABLES

Before reviewing matrix

notation, I have duplicated the

parts of the appendix from

the first article that we will be

using in the current article.

Recall that the indexing num-

bers are M = the number of

products used, and N = the

number of variable inputs.

Recall that matrices are

boxes of numbers. Let us look

at the matrix S, the standard

usages of variable inputs.

When we say that it is a N ×

M matrix, we are saying that

it has N rows and M columns.

The “element” of the matrix

s23 would be the number in the

This article is a follow-up to a previous arti-

cle, “The Simple Analytics of Matrix Accounting,

Activity-Based Costing, and Linear Programming”

published in the JCAF March/April 2016 issue. In

this issue, the author goes over the steps on the

computer used to solve these types of mathemati-

cal problems. Some notation of matrix algebra is

reviewed, followed by example case studies.

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