Marketing Mathematics -Exercises 1

Objectives of the Exercise

Generally in accounting problems, the focus is on a "classification" of expenses.

In the exercises that follow, you are given some expenses and information; however, the objective here is to arrive at a per unit cost estimate that can be the basis of setting a price. Some expenses are not given to you 'directly' in the exercise - they have to be anticipated by you, and estimated based on the data.

Prices, of course, may be determined as a percentage above costs, or a markup on selling price may be decided upon. Specifically, the exercises become a reminder and review to better understand the following:

What is profit and what are some concepts of returns that are used - eg. return on cost, sales or investment?Ask yourselves, when would each of the concepts be more useful.

How are inventories treated in the context of estimating profits.

What is the impact on marketing costs of holding inventories and giving credit. These factors are very important in taking decisions in the field of channel management and marketing strategy.

This exercises serve as a review of the basics of the concepts of break even analysis, and fixed versus variable costs. Students are reminded that in marketing the break even concept is central to many decisions - eg. a sales person is not recruited unless the additional profits cover the costs of employing him; alternatively, a branch may not be opened unless the additional sales justify the expenses of running a new branch office.

Finally we review the concept of elasticity and its application. Elasticity estimates are frequently used and made in market research reports. Students should be familiar with the types of calculations that can be made based on the simple concept of elasticity.

Quantitative Assignment

PART A

In this assignment explain and show the details of all your calculations (typing them). If the details are not shown you will not receive any marks. Handwritten responses will not be accepted. Wherever you feel an interest calculation is required, assume the rate of interest to be 10%.

Information:

A young college student John, decides to make computers in a small workshop. A single computer consists of the following components, that cost the amounts given:

ComponentsCost in $ per computer

Picture tube for monitor:

20

Bare chassis

15

Passive resistors

25

Active IC's

70

Cabinet

40

Speakers /accessories

20

Other Costs and Expenses:

In addition to the above part and component costs: John has one engineer (whom he cannot do without), and pays $ 24,000 a year for his services. This engineer has been employed on a five year contract, that cannot be breached. John also has rented the workshop with a 'lease' that cannot be broken, paying $6,000 a year as rent. Assume John's venture has no other annual costs. As initial investment, John has also spent $ 100,000 on manufacturing plant and equipment that should be usable for a period of five years.

Q 1

(a): Considering the 'Information' given, what is John's profit or loss, if he manufactures and sells 300 computers a year and prices each at $ 250.

(b): John buys materials for 320 computers in the year 2004. However, he sells only 300 computers at a price of $ 280 each.

(b - 1)Now what is his profit or loss?

(b - 2) Calculate the following ratios: Profits as a percentage of sales, Profits as a percentage of costs, and if John has invested $ 100,000 as his initial capital investment, then calculate the return on initial investment.

Q2: If John wishes to 'break even' .i.e. make neither a profit or a loss, then what should he price the computer at, if he is selling 300 computers in a year?

Q3: What should John price the computer at if he wishes to make a profit of 10%, as a percentage of cost. [This is also known as a markup on cost]. John is selling 300 computers in a year.

Q4: What should John price the computer at if he wishes to make a profit of 10%, as a percentage of sales. [ This is also simply referred to as markup or markup on sales]. John is selling 300 computers in a year.

Q5: Suppose, John prices a computer at $ 230. Then at what level of sales will John make neither a profit or a loss .i.e., at what level of sales will John break even?

Q6: Suppose John finds demand to be 1400 computers per year, so he makes this number of computers annually. Now what is his break even price?

Q7: Assume the production level of 1400 computers per year. John finds that he has to maintain an average component inventory equal to 2 month's production, finished goods in warehouses amount to three month's production, payments are made by dealers and distributors two and a half months after purchase. The annual rate of interest relevant to John's business is 10%. Now what is the break even price for John?

Q8: John plans to introduce a product in the Florida market - to he expects to invest $ 300,000 on a building that has a resale value of $ 200,000 after five years, his revenues are expected to be $ 100,000 per year and costs are $40,000 by the end of the first year, $ 45,000 for the next year, and $30,000 per year for the remaining three years. Calculate the NPV of the Florida project, if the discount rate or rate of interest is 10% annually.

Q9: John sells 1500 computers in one month; the present price is $ 900. He raises price of the computer to $ 1000. What will be his monthly sales after the price increase, if a market research study finds the price elasticity to be (-)0.7.

Q10: Describe and analyze the following data, calculating elasticities. For a product, when price increases from $10 to $12, the demand increases from 200 to 225 [Calculate elasticity]; On the other hand when price increases from $ 16 to $ 18, the demand decreases from 230 to 225 [Calculate elasticity]. Explain what seems to be happening.