COURSE CONTENTS:

1. Introduction

2. MATHEMATICAL MODELLING OF UNCERTAINTY IN BUSINESS

3. Case Study No. 3

Course 3

MATHEMATICAL MODELLING OF UNCERTAINTY IN BUSINESS

Uncertainty is the expression of the incomplete and approximate character of information about factors influencing our future activity.

Risk is characterised by the possibility of describing a probability law for the expected results.

1. Introduction

1. MATHEMATICAL MODELLING OF UNCERTAINTY IN BUSINESS

Measuring uncertainty in business consists of calculating an estimated profitableness rate of the business (project) thus:

(1)

n

1iirpiRer

where,Rer – the estimated profitableness ratepi – the probability associated to the variant i;ri – the expected profitableness rate of the variant i;i - the variant of the alternative scenario;n – the number of the variant.

We have a business plan. Each business plan has three variants:- the optimistic variant; - the realistic variant;- the pessimistic variant.In relation number 1, we have two elements: “pi” and “ri”.For every variant, it is calculated the probability associated to the variant (the expected probability) noted pi – the probability associated to the variant i;Pi, the probability associated to the variant “i” is: for optimistic variant: pi >0,50; for realistic variant: 0,30 < pi< 0,50;For pessimistic variant: pi < 0,30.

The second element is the expected profitableness rate of the variant i.It is according to the relation:

233

221

)1()1(1 rrrFnFnFnCu

where, Cu = used capital; Fn = the expected cash flow; r = the expected profitableness rate

Replacing in the 2nd relation: 1+ r = u and knowing that Fn1 = Fn2 = Fn3 = Fn,the relation becomes:

We can determine the value of “u”, then the value of “r” results . r = u – 1Solving a third degree equation means applying the following graphical methods: the tangent, the chord and the bisectional interval.

.

01uuuFn

Cu 1uuu

Fn

Cu

u

1

u

1

u

1

Fn

Cu 232332

3

After having determined the expected profitableness rate for every variant, we calculate the business estimated profitableness rate for every variant, according to relation 1.The table below results:

Scenario Associated

probability

Cash flow

Fn

Estimated

profitableness

rate

the optimistic

variant

0.60 300,000€ 0.25 0.15

the realistic variant

0.20 200,000€ -0.15 - 0.03

the pessimistic

variant

0.10 100,000€ 0.25 - 0.02

0.10

n

1iirpiRer

- 0.80

pi

ri0.10

- 0.10

0.10

0.80

0.80

r1

r2

r3

Rer = 0.10

CONCLUSION: The narrower the distribution of the probability of the expected profitableness rates of a business (project), the more probable it is that the real profitableness would be closer to the expected profitableness and the lower the business (project) risk would be.

n

iiierrpR

1

33

221

)1()1(1 rrrFnFnFnCu

Scenario Associated

probability

pi

Cash flow

Fn

Estimated

profitableness rate

ri

Rer

the optimistic

variant

0.60 300,000€

0.25 0.15

the realistic variant

0.20 200,000€

-0.15 - 0.03

the pessimistic

variant

0.10 100,000€

0.25 - 0.02

0.10

1

2

pi

ri0.10

- 0.10

0.10

0.80

0.80

r1

r2

r3

Rer = 0.10

.

01uuuFn

Cu 1uuu

Fn

Cu

u

1

u

1

u

1

Fn

Cu 232332

3

The international company “Anastassia Oill” with headquarters in TBILISI was founded in 2007, its businesses focusing on fuel – lubricants production and trade, activity with a great future on the Romanian market. In order to settle a retail outlet in Romania, moreover in the county of Braşov in 2011, the managerial team of the company elaborated two variants of location, presented below:

PROJECT X. THE AREA OF THE RAILWAY STATION OF BRAŞOV (Project 1);

PROJECT Y. THE BARTOLOMEU AREA (Project 2).

For both projects, there were taken into account three variants: OPTIMISTIC, REALISTIC and PESIMISTIC.

CASE STUDY NO. 3

12

SCENARIO

Pi Fln ri Rer

O 0.60 300,000 ? ?

R 0.30 200,000 ? ?

P 0.10 100,000 ? ?

SCENARIO

Pi Fln ri Rer

O 0.50 250,000 ? ?

R 0.30 200,000 ? ?

P 0.10 50,000 ? ?

n

1iirpiRer

n

1iirpiRer

PROJECT X

Cu=600,000€

PROJECT Y

Cu =500,000€