BASIC FORMULAS FOR BUSINESS MATHEMATICS AND …...MAXI’19 | A Greater COHSS BASIC FORMULAS FOR BUSINESS MATHEMATICS AND SAMPLE QUESTIONS 1. Commission = sales × rate 2. Commission

MAXI’19 | A Greater COHSS

BASIC FORMULAS FOR BUSINESS

MATHEMATICS AND SAMPLE

QUESTIONS

1. Commission = sales × rate

2. Commission =commission amount × rate (where quota exist)

3. But commission amount = sales – Quota (- return where it exit)

To find sales

Let c = commission

S = sales

R = rate

If C = S * R

Then s = C/R

Also R = C/S

4. Gross earning= Monthly salary + commission

If there is a bonus Gross Earning = Monthly salary + commission +

Bonus

NB: If you don’t see Gross earning and you see total earning, they

are the same

5. Bonus = bonus amount * bonus rate

Bonus amount = sales – Commission limit

NB: Commission limit is the quota.

6. Total earning = Salary + personal commission + Override (where

override exist)

7. Override = (Store sales - Store quota) * override rate.

8. Rebate = Rebate amount * rebate rate.

But Rebate amount = total purchases – minimum requirement

9. Total earning – Draws

Trade discount


The discount method is used when we are interested in knowing both the net

price and the actual amount of the discount. There are 2 methods I.E

Discount and complement method.

Complement method is used when we are interested in knowing the net

price.

Discount method

1. Discount amount = List price * Discount Rate

2. Net price = List price – Discount amount

3. Price to pay = list price – discount Amount

4. Total discount amount = total amount to pay before discount – Amount to

pay after discount.

Complement Method

1. Complement = 100 – discount rate

2. Net price = compliment rate * list price

3. Discount rate = 100 – (product of complement rate)

Series Discount.

This where both the discount and complement method can be used.

Cash discount for fully paid invoices

1. Net purchase amount = invoice amount – merchandised returns – Freight

(Handing and order cost)

2. Cash discount = discount rate * net purchase amount

3. Cost of merchandised = net purchases – cash discount.

4. Remittance = cost of merchandised + freight {If any.}

Cash discount for partially paid invoices

1. Amount credited = Total amount paid + Amount of cash discount.

2. Unpaid balance = Invoice amount – Amount credited

a) complement rate = 100% - Discount rate.

B) Amount credited = Amount paid or Remittance/ compliment rate

Dealing with sales and purchases for principal.

1. Total proceeds = net proceed from A + net proceed from B

2. Net proceeds = gross proceeds – total charges

But Total charges = Commission + freight


NB:

a. For price, the last two (2) digits should be in pesewas

b. For food, all digits are valid

Inventory and turn over

a. Average cost or weighted method

1. Inventory valuation = average cost * number of items in inventory at the

time of valuation

2. But average cost = Total cost / Quantity produced.

3. Total cost = Number of item * cost of item

4. Total cost = Fixed cost + Variable cost

5. Total revenue = price ×quantity

b. Gross profit method

value of inventory= Merchandise available for sale (at cost) – cost of

goods sold

where merchandise available for sale=opening stock+ purchases (at

cost)

cost of goods sold+mark up=net sales

mark up=mark up rate × net sales

c. Retail method

value of inventory at retail=merchandise available for sale (at retail)-net

sales

NB: WITH LOWER OF COST OR MARKET VALUE METHOD,

THE COST IS USED WHEN MARKET VALUE EXCEED THE

COST AND MARKET VALUE IS USED WHEN COST EXCEED

THE MARKET VALUE.

TAXES

1.Sales Taxes=Amount of Sales × Sales Tax Rate

2.Amount to Pay =Cost + Sales Tax

NB: All overtime income and allowances are taxed at a flat rate of 10%

3.Amount paid as tax = Sum of tax from all levels taxable

NB: Incomes are earned monthly so if the salary is given yearly, divide

by 12 to get what the individual will pay as tax per month


PAYROLL

1.Gross Earnings = (Hours worked x Hourly rate) + Overtime pay + Allowances

2. Gross Pay = Salary + Overtime Pay + Allowances

NB Gross earnings is the same as gross pay

3. Overtime Pay = 1.5 x Hourly rate

4. Regular income = 8hrs/40hrs per week x Hourly Rate

5. Overtime Income= Overtime hours x Overtime Rate

COMPUTING INVENTORY TURNOVER

Before turnover can be determined, average inventory must be calculated.

When circulating for average inventory, consider the following

INVENTORY IS TAKEN

AVERAGE INVENTORY (at cost

and retail

Annually (once a year) (BI + EI) ÷ 2

Semi annually (Every six month) (BI + end of 6 months + EI) ÷ 3

Quarterly (every three months). (BI + 3 quarterly+ EI) ÷ 5

Monthly (every month) ( BI + 11 Monthly + EI) ÷ 13

INVENTORY TURNOVER AT RETAIL= Net Sales /Average turnover

INVENTORY TURNOVER AT COST = Cost of goods sold/Average

inventory

COST OF GOODS SOLD = Goods available for sale – Closing inventory

BREAKEVEN ANALYSIS

Breakeven Point = TR=TC


Contribution per unit = Price per unit – variable cost per unit

Margin of safety= budgeted volume of sales/qty – breakeven sales/qty

Breakeven quantity= fixed cost/ contribution per unit

Breakeven sales = fixed cost/ 1-contribution per unit

NB:

When fixed cost increase, BEP will increase

ANYTIME YOUR B.E.PPOINT GOES UP, YOUR BUSINESS

BECOMES MISERABLE BECAUSE YOU NEED TO LOOK FOR

MANY WAYS TO SELL MORE.

TO SHOW AN INCREASE IN REVENUE, YOU READF ON THE Y-

AXIS

IF A COMPANY MAKES ABNORMAL PROFIT, THE

GOVERNMENT WILL TAX THE COMPANY, WINDFOX TAX.

SAMPLE QUESTIONS AND ANSWERS

Break Even

MCQ: Fixed cost is divided by break-even revenues to calculate

A. cost margin

B. fixed margin

C. revenue margin

D. contribution margin

Answer D

MCQ: If break-even number of units are 120 units and fixed cost is GHC62000,

then contribution margin per unit will be

A. GHC74,400


B. GHC7,440,000

C. GHC516.67

D. GHC51,667

Answer C

MCQ: If break-even number of units are 200 units and fixed cost is GHC80000,

then contribution margin per unit will be

A. GHC400

B. GHC600

C. GHC800

D. GHC1,000

Answer A

MCQ: At break-even point, an operating income must be equal to

A. GHC3,000

B. GHC2,000

C. GHC1,000

D. zero

Answer D

MCQ: If contribution margin per unit is GHC700 per unit and break-even per

unit is $40, then fixed cost would be

A. GHC35,000

B. GHC28,000

C. GHC17,500

D. GHC82,000

Answer B


INVENTORY

1. An increase in the firm’s receivable turnover ratio means that:

A) it is collecting credit sales more quickly than before.

B) cash sales have decreased.

C) it has initiated more liberal credit terms.

D) inventories have increased.

Ans: A

2. A firm’s inventory turnover (IT) is 8 times on a cost of goods sold (COGS) of

GHC800,000. If the ITchanges to 5 times while the COGS remains the same, a

substantial amount of funds is either releasedfrom or additionally invested in

inventory. In fact, __________.

A) GHC160,000 is released

B) GHC100,000 is additionally invested

C) GHC60,000 is additionally invested

D) GHC60,000 is released

Ans: C)

3. Reorder point is divided by number of sold units for per unit of time to

calculate

a) relevant carrying cost

b) relevant ordering cost

c) purchase order lease time

d) number of purchase orders

Ans: C

4. Purchase order lead time is multiplied to number of units is sold per unit of

time to calculate

a) carrying costs

b) relevant total costs


c) economic order quantity

d) reorder point

Ans: D

5. If purchase order lead time is 35 minutes and number of units sold per time is

400 units, then reorder point will be

a) 14000 units

b) 14500 units

c) 15000 units

d) 15500 units

Ans: A

6. A firm’s inventory turnover (IT) is 5 times on a cost of goods sold (COGS) of

GHC800,000. If the IT isimproved to 8 times while the COGS remains the

same, a substantial amount of funds is released fromor additionally invested in

inventory. In fact,

A) GHC160,000 is released

B) GHC100,000 is additionally invested.

C) GHC60,000 is additionally invested.

D) GHC60,000 is released.

Ans: D

7. Ninety-percent of Vogel Bird Seed’s total sales of GHC600,000 is on credit.

If its year-end receivablesturnover is 5, the average collection period (based on

a 365-day year) and the year-end receivablesare, respectively:

A) 365 days and GHC108,000.

B) 73 days and GHC120,000.

C) 73 days and GHC108,000.

D) 81 days and GHC108,000.

Ans: C

8. If EOQ = 360 units, order costs are GHC5 per order, and carrying costs are

GHC.20 per unit, what is theusage in units?

A) 129,600 units


B) 2,592 units

C) 25,920 units

D) 18,720 units

Ans: B

9. Costs of not carrying enough inventory include:

A) lost sales.

B) customer disappointment.

C) possible worker layoffs.

D) all of these.

Ans: D

BREAK EVEN ANALYSIS

31A

34B

35D

36A

37B

38B

39B

46D

31. With regard to break –even charts and break-even analysis, which of the

following is true ?

a. It is assumed that variable cost fluctuates in direct proportion to output

b. The break the break-even point is at the intersection of the sales line and the

variable cost line

c. A break-even chart shown the maximum profit possible


d. A break-even chart is capable of dealing with any change of product mix

34. Break-even analysis assumes that over the relevant range:

a. Total costs are unchanged

b. Unit variable costs are unchanged

c. Variable costs are non-linear

d. Unit fixed costs are unchanged

35. ABC Ltd. Has fixed costs of GHC60,000 p.a.. It manufactures a single

product, which it sells for

GHC20 per unit. Its contribution to sales ratio is 40%. ABC Ltd‘s break-even

point in units is : sts of `

b. 3,000

c. 5,000

d. 7,500

36. Sun Ltd. Makes a single product which it sells for GHC10 per unit. Fixed

costs are GHC48,000 per

month and the product has a contribution to sales ratio of 40%. In a period when

actual sales were

GHC1, 40,000. Sun Ltd.‘s margin of safety in units was :

a. 2,000

b. 6,000

c. 8,000

d. 12,000

37. A company produced 500 units of a product and incurred the following

costs: `

Direct materials 8,000

Direct wages 10,000


Overheads (20% fixed) 45,000

If the sales value of 500 units was GHC1,02,000, what is contribution margin ?

a. 44%

b. 47%

c. 53%

d. 74%

Use the following data for questions 38 and 39:

Budget data for the Happy Ltd.

Sales (1,00,000 units) GHC10,00,000

Costs : Variable GHC7,00,000

Fixed GHC2,10,000 9,10,000

Operating profit GHC90,000

38. If fixed costs increased by GHC31,500 with no other cost or revenue factors

changing, the

break-even sales in units would be :

a. GHC34,500

b. GHC80,500

c. GHC69,000

d. GHC94,500

39. If Happy Ltd. Is subject to an effective income tax rate of 40%, the number

of units Happy

Ltd. Would have to sell to earn an after-tax profit of GHC90,000 is :

a. 100,000 units

b. 1,20,000 units

c. 1,12,000 units

d. 1,45,000 units


46. The firms monthly cost of production is GHC1,46,000 at an output level of

8,000 units. If it

achieves an output level of 12,000 units it will incur production cost of `

GHC1,94,000 cost of

production for 15,000 units is

a. GHC1,80,000

b. GHC2,00,000

c. GHC50,000

d. GHC2,30,000

TAXES AND PAYROLL

14. The tax base is GHC9,000.00 for unemployment taxes and an employee has

accumulated

earnings of GHC8,200.00 on March 30. On April 15 the employee’s gross

earnings are

GHC1,300.00. How much of his April 15 earnings are subject to unemployment

taxes?

a. GHC1,300.00

b. GHC8,200.00

c. GHC800.00

d. None, he has exceeded the tax base

Answer C

“The is only one thing that makes a dream

impossible to achieve: The fear of failure”


– Paulo Coelho

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BASIC FORMULAS FOR BUSINESS MATHEMATICS AND …...MAXI’19 | A Greater COHSS BASIC FORMULAS FOR BUSINESS MATHEMATICS AND SAMPLE QUESTIONS 1. Commission = sales × rate 2. Commission