## Need for simulation, Financial Management

Assignment Help:

Need for Simulation

If the mathematical model set up could always be optimized by the analytical approach, then, there would be no need for simulation. Only when interrelationships are too complex or there is uncertainty regarding the values that could be assumed by the variables or both, we would have to resort to simulation.

Example

Let us try to introduce some uncertainty in the illustration which we have already seen. As before, the competition price is Rs.10 and the firm is considering three alternative prices, namely, Rs.8, Rs.10 and Rs.12. However, for each price chosen by the firm, the sales volume is uncertain. The following table gives the possible values of sales for each price and also the corresponding cost of production and profit.

 Firms' Price (Rs. per unit) Competition Price (Rs. per unit) Qty.Sold (Nos.) Revenue (Rs.) Cost (Rs.) Profit (Rs.) 8   8   8 10 10 10 12 12 12 10 10 10 10 10 10 10 10 10 10,000 15,000 20,000   8,000 10,000 12,000   4,000   7,500 11,000 80,000 1,20,000 1,60,000    80,000 1,00,000 1,20,000   48,000   90,000 1,32,000 80,000    95,000 1,50,000    78,000    80,000    84,000    40,000    75,000    88,000 0 25,000 10,000   2,000 20,000 36,000   8,000 15,000 44,000

The table shows that if the firm chooses a price of Rs.8, its sales can take any one of the three values, namely, 10,000, 15,000 or 20,000 units. So also at prices Rs.10 and Rs.12.

If we try to use the analytical approach to solve the problem, assuming that the objective is to maximize profits, we may say that the firm should try to charge Rs.12 per unit.

This would bring in Rs.44,000 as profits. However, this is not a straight forward solution as the amount of profits can be earned, if and only if the quantity sold is 11,000. We know that when the price is Rs.12, the quantity sold could be 4,000 or 7,500 or 11,000. If only 4,000 were sold, the actual profit earned would be only Rs.8,000.

One way to solve problems involving uncertainty is to assign probabilities of occurrence for each sales quantity and then find the price which maximizes the expected profit.

We would still use the analytical approach for the modified version of the illustration by assigning probabilities. Let us complicate the illustration further to approximate it to a real-life situation.

Suppose the competition price is not known with certainty. However, it is known that it could be anywhere between Rs.8 and Rs.12. We could describe the competition price as a random variable which is uniformly distributed between 8 and 12. The firm is considering three pricing strategies as before:

1. Price equal to that of competition

2. Price two rupees below competition

3. Price two rupees above competition.

Let us further assume that given the firm's price P and the competition price Pc, the firm's sales volume is a normally distributed random variable with mean given by QM = 18,000 - 500P + 100Pc and standard deviation 2,000.

If, for instance, the competition price is Rs.10 and the firm's price is Rs.8, substituting these values in the above equation, the mean or expected sales quantity will be 15,000. However, the actual sales quantity is distributed normally with mean 15,000 and standard deviation 2,000.

Let us further assume that the costs are also uncertain. For any production volume Q, the mean unit cost is Rs.7, the actual unit cost is normally distributed with mean 7 and standard deviation of Re.1. Uncertainty in costs may be due to the break down of machinery, uncertain supplies and prices of some raw materials, etc.

Since we express the behavior of the variables in terms of a distribution, the model is called stochastic model of the system. This model is based on the following assumptions.

1. There is a probability distribution for the average selling price of competitors.

2. The mean sales volume is related to the firm's price and competition price and there is a probability distribution of the actual sales volume around this mean.

3. There is a probability distribution of unit cost.

Optimizing a model, which sets relationships of random variables through analytical approach is extremely difficult. Though our basic mathematical model of profit = PQ - CQ has not altered, P, Q and C are all random variables. The alternative is to arrive at the solution through simulation. However, to carry out simulation we need to know something about random number generation.

#### What are the financial management problems, What are the financial manageme...

What are the financial management problems Traditional approach was challenged was that the treatment was built too closely around episodic events, like incorporation, promotio

#### International bonds, International bonds are the bonds issued in a country ...

International bonds are the bonds issued in a country by a non-domestic entity. In fact, it is a collective term used for Eurobonds, foreign bonds and global bonds.

#### 91-day t-bills, 91-Day T-Bills Starting from July, 1965, 91-day T-bills...

91-Day T-Bills Starting from July, 1965, 91-day T-bills were issued at a discount rate ranging from 2.5-4.6 percent per annum. Till July, 1974, the discount rate was 4.6 percen

#### Management, . Why do some organizations seem to have a new CEO every year o...

. Why do some organizations seem to have a new CEO every year or two, whereas others have top leaders who stay with the company for many years (e.g., John Chambers at Cisco)? What

#### Exchange rate changes decrease risk of foreign investment, Would exchange r...

Would exchange rate changes all time increase the risk of foreign investment? Discuss the condition within which exchange rate changes may actually decrease the risk of foreign inv

#### Inflation and exchange rates, Inflation and Exchange Rates To understan...

Inflation and Exchange Rates To understand the impact of inflation, several terms should be understood. For example, inflation from the investors' standpoint must be clearly de

#### What is the basic approach of the financial management, Q. What is the basi...

Q. What is the basic Approach of the financial management ? 1) The first approach view finance as to providing the funds needed by a business on the most suitable terms. This ap

#### Determine the calculation of materiality, Determine the calculation of mate...

Determine the calculation of materiality For example: Turnover 1% -1.5% Net assets 1% -2% Net profit 2% -6% Whatever numbers are selected they would be based on r

#### Limitations of traditional approach in financial management, Q. Limitations...

Q. Limitations of Traditional Approach in financial management? Limitations of Traditional Approach: - The traditional approach continued till mid 1950's. It has at the prese

#### Show the analysis of credit information, Q. Show the Analysis of Credit Inf...

Q. Show the Analysis of Credit Information? Analysis of Credit Information: - Subsequent to obtaining the desired information from various sources the information is examined t