## Introduction to Quantitative Methods

Task 1 of 1: Numeracy Assessment and Exercise

Question 1:

Given are the revenue and expenses of DYI Stores Ltd., a high street chain selling DYI goods.

Year Revenue Expenses Actual profits budgeted profits

2013 £ 316,449,668.60 £ 313,395,191.59 £ 3,046,000.00

2014 £ 354,423,628.83 £ 344,734,710.74 £ 9,561,000.00

2015 £ 396,954,464.29 £ 379,208,181.82 £ 18,115,000.00

a. The above table requires computation of Actual Profits.

Actual Profits for each year = Revenue of the year – Expenses of the year.

Year Revenue Expenses Actual profits budgeted profits

2013 £ 316,449,668.60 £ 313,395,191.59 = £ 316,449,668.60 – £ 313,395,191.59

= £ 3,054,477.01 £ 3,046,000.00

2014 £ 354,423,628.83 £ 344,734,710.74 = £ 354,423,628.83 – £ 344,734,710.74

= £ 9,688,918.09 £ 9,561,000.00

2015 £ 396,954,464.29 £ 379,208,181.82 = £ 396,954,464.29 – £ 37,9,208,181.82

= £ 1,77,46,282.47 £ 18,115,000.00

b. Computation of likely profit of 2016:

Annual Revenue Increase Rate = (Revenue of Year 2 – Revenue of Year 1) / Revenue of Year 1

Year Revenue Annual Revenue Increase rate

2013 £ 316,449,668.60

2014 £ 354,423,628.83 = (£ 354,423,628.83 – £ 316,449,668.60) / £ 316,449,668.60

= 12.00%

2015 £ 396,954,464.29 = (£ 396,954,464.29 – £ 354,423,628.83) / £ 354,423,628.83

= 12.00%

Similarly,

Annual Expense Increase Rate = (Expense of Year 2 – Expense of Year 1) / Expense of Year 1

Year Expenses Annual Expense Increase rate

2013 £ 313,395,191.59

2014 £ 344,734,710.74 = (£ 344,734,710.7 – £ 313,395,191.59) / £ 313,395,191.59

= 10.00%

2015 £ 379,208,181.82 = (£379,208,181.82 – £ 344,734,710.74) / £ 344,734,710.74

= 10.00%

Budgeted figures for 2016:

Budgeted Revenue of 2016 = Revenue of 2015 + 12% of Revenue of 2015

Budgeted Expense of 2016 = Expense of 2015 + 10% of Expense of 2015

Budgeted Profit = Budgeted Revenue of 2016 – Budgeted Expense of 2016

Year Revenue Expenses budgeted profits

2016 = £ 396,954,464.29 + (12% * £ 396,954,464.29)

= £ 444,589,000.00 = £ 379,208,181.82 + (10% * £ 379,208,181.82)

= £ 417,129,000.00 = £ 444,589,000.00 – £ 417,129,000.00

= £ 27,460,000.00

c. Law of Probability and likelihood of actual profits being higher than the budgeted profits:

Probability is a computed estimation of the accruing of an event. In normal business, the law of probability can be applied to compute several possible outcomes in various arenas of business. Investments, client services and competitive strategies are examples of such fields. In case of investments, the entity should predict how many products they should sell to be able to invest the appropriate quantum of resources into the production. In case of Customer behaviour, prediction is needed for companies to be able to know how they can promote their services.

In the given case, the total number of years for which the profit data is available is 3.

Of the 3 years given, Number of years where Actual Profit is greater than Budgeted Profit = 2

Number of years where Actual Profit is less than Budgeted Profit = 1

Ratio of Actual profit being higher than budgeted profit over actual profit being lower than budgeted profit = 2:1

In terms of percentage, it is 66.67% : 33.33%

Thus, the probability that the actual profit shall be greater than budgeted profit is 66.67%.

Question 2:

Part 1:

a. Given,

Purchase price = £ 350

Reselling price = £ 450

Garage space rent = £ 800 per month

Let the number of units sold in a month be x

Total sales = 450x

Total purchases = 350x

Gross profit = 450x – 350x = 100x

Net profit = Gross Profit – Other expenses

= 100x – 800

Therefore, equation to calculate profit = 100x -800

b. In order to attain Breakeven,

Breakeven units = Fixed Costs / Contribution per unit

Breakeven units = 800 / 100

= 8 units.

c. If John sells 23 pushchairs, his profit shall be :

Equation: 100x – 800

= (100 * 23) – 800

= 2300 – 800

= £ 1500

Part 2:

a. Given,

Purchase Price = £ 0.90

Sales price = £ 1

Store Rent = £ 2000 per month.

Let the number of units sold in a month be x

Total sales = 1x

Total purchases = 0.90x

Gross profit = 1x – 0.90x = 0.10x

Net profit = Gross Profit – Other expenses

= 0.10x – 2000

Therefore, equation to calculate profit = 0.10x – 2000

b. In order to attain Breakeven,

Breakeven units = Fixed Costs / Contribution per unit

Breakeven units = 2000 / 0.10

= 20,000 units.

c. If Hector sells 15000 products, his loss shall be :

Equation: 0.10x – 2000

= (0.10 * 15000) – 2000

= 1500 – 2000

= £ 500 loss

Question 3:

Part 1:

a. Equation for computation of Maximum Profit:

Relationship between sales and Price:

First, we need to write the equation to represent the calculation

Profit = Revenue – Cost

Revenue = Quantity sold * Price

R = Revenue

Using the High-Low method,

At price 15, quantity = 0

At price 14, quantity = 15

Quantity change per change in price = (15-0) / (15-14)

= 15

Now, at price = 14, quantity = 1

Quantity Per Day)*( = (225 – 15P) * 10

Revenue Per Day = P * (225 – 15P) * 10

= 2250P – 150P2

Cost Per Day = 10*4.5 * (225 – 15P) + 130

= 10125 – 675P + 130

= 10255 – 675P

Profit Per Day = Revenue Per Day – Cost Per Day

= 2250P – 150P2 – 10255 + 675P

= 2925P – 150P2 – 10255

This equation can be used to create a table for price range from £15 to £3

b. Table presenting price and profit:

Price Quantity per hour Revenue per day(£) Cost (£) Profit (£)

3 180 5400 8230 -2830

4 165 6600 7555 -955

5 150 7500 6880 620

6 135 8100 6205 1895

7 120 8400 5530 2870

8 105 8400 4855 3545

9 90 8100 4180 3920

10 75 7500 3505 3995

11 60 6600 2830 3770

12 45 5400 2155 3245

13 30 3900 1480 2420

14 15 2100 805 1295

15 0 0 130 -130

Note: The cost also includes the fixed cost of rent space.

c. Graph presentation:

d. The maximum possible profit is £ 3,995 per day.

The selling price to achieve this profit is £ 10 per unit.

Part 2:

a. Tabular Presentation of Price and Profit:

In order to derive a relationship between price and quantity, the quantity sold = 180 – 40P.

This has been computed using the high low method.

At price 4, quantity = 20

At price 1, quantity = 140

quantity change per change in price = (140 -20) / (4 – 1) = 40

Say for Price = 1, Quantity is 140.

Quantity = 180 – (40*price)

Quantity sold = 180 – 40P

Revenue = P * (180 – 40P)

= 180P – 40P2

Cost = (Quantity * 0.65) + 60

= (180 – 40P) * 0.65 + 60

= 117 – 26P + 60

= 177 – 26P

Profit = Revenue – Cost

= 180P – 40P2 – (177 – 26 P)

= 206P – 40P2 – 177

Price Quantity Revenue Cost Profit/(Loss)

4 20 80 73 7

3.5 40 140 86 54

3 60 180 99 81

2.5 80 200 112 88

2 100 200 125 75

1.5 120 180 138 42

1 140 140 151 -11

0.5 160 80 164 -84

b. Diagrammatic presentation of the above:

c. Optimal Selling Price = £ 2.5 as it yields the maximum profit of £ 88.