# Mathematical Analysis/Predictions of Internal Generated Revenue (IGR) in Some States in Nigeria

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## Mathematical Analysis/Predictions of Internal Generated Revenue (IGR) in Some States in Nigeria

ABSTRACT

In this paper, we apply the LINEST model of the Microsoft excel to the population, Nigeria (Naira) exchange rate with US Dollar and Internal Generated Revenue (IGR) of 2014 top-10 Nigerian states by IGR in billions of naira from 2010 to 2014 as in the data bases of National Population Commission (NPC), Central Bank of Nigeria (CBN) and National Bureau of Statistics (NBS) respectively. The indexed IGR is used as proxy for each state and the nation. The last census of 2006 by NPC is used as proxy to the national and states population, and the end of December CBN exchange rate with U.S. Dollar was used as well. The research which results into 14 equations (10 for states and 4 for the nation but all having and ) proves that the states in discuss (including Lagos, Rivers, Kaduna and Enugu) over spend/levy, against assets, tax and securities, the members of the states beyond the normal exchange rate in order to meet-up with the IGR target. This is seen in the negative “Difference” of the last/8th column in all the phases’ table of chapter 4; the highest (90%) resulting in 2013 indicated that the nation experienced subsidy removal from fuel at the end of the year in 2013. At the other hand, the positive “Difference” (highest in 2010-70%) indicated that the concerned states submitted an invalid data, indeed below their IGR. The study showed that fuel subsidy removal generates and stimulates excess charges and expenses in the Nigerian economy. The author recommends that Nigeria should maintain subsidy assistance to the member states; charges levied on assets, tax and securities should not exceed the CBN exchange rating. Again, the nation/states in concern should use the formulated equations for predicting or estimating the IGR to the dynamic/uncertain exchange rate of Nigeria Naira with US Dollar. The national IGR equation, in billions of Naira, is 35 376 39 5 5.

Certification Page i
Dedication ii
Acknowledgment iii
Abstract iv
CHAPTER ONE
1.0 Introduction 1
1.1 Concept of Revenue 1
1.2 Internal Revenue 2
1.3 Internally Generated Revenue (IGR) 2
1.4 Aims and Objectives of the study 2
1.4.1 Aims 2
1.4.2 Objectives 2
1.5 Scope and Limitations of the Study 3
CHAPTER TWO
2.0 Literature Review 4
CHAPTER THREE
3.0 Methodology 7
3.1 Model List 7
3.1.1 Linear Revenue Model 7
3.1.2 Simple Interest 8
3.1.3 Compound Interest 8
3.1.4 Annuity 9
3.1.5 Amortization 10
3.1.6 The LINEST Model And Its Variables Description 11
3.2 The Data And Data Source 12
3.2.1 The Data 12
3.2.2 Data Source 25
CHAPTER FOUR
4.0 Model Results 26
4.1 Result Description 26
4.2 Result Phases 26-40
CHAPTER FIVE
5.0 Conclusion/ Recommendation 41
5.1 Conclusion 41
5.2 Recommendation 41
References 42 – 44
Appendix A 45
Appendix B 46
Appendix C 48
Appendix D 49
Appendix E 50
Appendix F 51
Appendix G 52
Appendix H 53

CHAPTER ONE

INTRODUCTION

1.1 Concept of Revenue:

Revenue is always the price per unit times the number of units sold. The revenue resulting from one or more business transactions is the total payment received, sometimes called the gross proceeds. If R(x) is the revenue from selling x items at a price of m each, then R is the linear function R(x) = mx and the selling price m can also be called the marginal revenue. Revenue is a very important concept in economic analysis. It is directly influenced by sales level, i.e., as sales increases, revenue also increases. The concept of revenue consists of three important terms; Total Revenue, Average Revenue and Marginal Revenue.

1.1.1 Total Revenue (TR):

Total Revenue refers to total receipts from the sale of a given quantity of a commodity. It is the total income of a firm. Total revenue is obtained by multiplying the quantity of the commodity sold with the price of the commodity.
Total Revenue = Quantity × Price

1.1.2 Average Revenue (AR):

Average revenue refers to revenue per unit of output sold. It is obtained by dividing the total revenue by the number of units sold.

Average Revenue = Total Revenue/Quantity

1.1.3 Marginal Revenue (MR):

Marginal revenue is the additional revenue generated from the sale of an additional unit of output. It is the change in TR from sale of one more unit of a commodity.
Where:

Marginal revenue of nth unit;

Total revenue from n units;

Total revenue from (n – 1) units; n = number of units sold.
Source: (http://www.yourarticlelibrary.com/economics/revenue-the-meaning-and-concept-of-revenue-micro-economics/9089/) .

1.2 Internal Revenue

Monies collected by a government through imposition of levies and taxes on facilities, incomes, sale of goods and services, transfers of properties, and other domestic transactions, as opposed to monies collected from duties imposed on imports and other international transactions. Also called inland revenue. Source: (http://www.businessdictionary.com/definition/internal-revenue.html#ixzz3uwVYsw75 ).

1.3 Internally Generated Revenue (IGR):

Revenue generated internally apart from subventions, allocation, and grants from Govt. Examples of Internal Generated Revenue are student registration fees, rent of hall, rent of equipment, donations, dividends, interest, payment for transcript, payment for academic gown, etc.

Source: ( http://www.ui.edu.ng/sites/default/files/AUDITING%20OF%20INTERNAL%20GENERATED%20REVENUE.pdf )

1.4 Aims and Objectives of The Study

1.4 .1 Aims

The aim of this study is to formulate equations, using the LINEST model, which can predict or estimate the Internal Generated Revenue (IGR) of the states and the nation whenever the CBN exchange rate of Nigeria Naira with U.S. Dollar is given.

1.4.2 Objectives

The objective is to ascertain the uncertain prices of assets, in this case the Internal Generated Revenue (IGR), which has no generalized prediction in the economy.

1.5 Scope and Limitations of the Study

In this work, we are able to cover and indeed utilize the population, Nigeria (Naira) exchange rate with US Dollar and Internal Generated Revenue (IGR) of 2014 top-10 Nigerian states by IGR in billions of naira from 2010 to 2014 as in the data bases of National Population Commission (NPC), Central Bank of Nigeria (CBN) and National Bureau of Statistics (NBS) respectively.

We are limited to the indexed IGR which is used as proxy to the asset pricing in each state and the nation. The last census of 2006 by NPC is used as proxy to the national and states population, and the end of December CBN exchange rate with U.S. Dollar was used as well. Using these as basis, we can now formulate equations by the help of the LINEST model of the Microsoft excel, which can actually estimate only the IGR of each state and the nation.

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