## Problem No. 1

## How to calculate raw materials to produce finished product/goods?

A factory uses a particular raw material. There are three processes A, B and C. The data relating to inputs, outputs and rejections during the month of April are given below:

Inputs (in pieces) (Including opening W.I.P) | Rejections (in Pieces) | Output (in pieces) | |

A | 18,000 | 6,000 | 12,000 |

B | 19,800 | 1,800 | 18,000 |

C | 20,400 | 3,400 | 17,000 |

Determining what should be inputs and Process A when final product transferred from process C is 1,000 pieces.

#### Required:

Calculate the cost of raw materials to produce one piece of the finished product when:

(a) the weight of the finished product is 10 gram.

(b) the price of the raw material is $1 per kg.

### Solution

**(a). Process**

No. of Pieces | Rejected Pieces | |||

Input | Output | No. | % of output | |

A | 18,000 | 12,000 | 6,000 | 50% |

B | 19,800 | 18,000 | 1,800 | 10% |

C | 20,400 | 17,000 | 3,400 | 20% |

If 1,000 good pieces should be the output of Process C the input should be 1,000 plus 20%, i.e., 1,200 pieces. This input of 1,200 units of Process C should be the output of process B. The percentage of rejection being 10% in process B, the input in process B should be 1,200 pieces plus, i.e., 1,320 pcs. Similarly, 1,320 pcs. should be should be the output of Process A. The rejection being 50%, the input of process A should be 1,320 plus 50%, i.e., 1,980 pcs. It can be tabulated as follows:

Process | Input | Rejection | % Rejection of output | Output |

A | 1,980 | 660 | 50% | 1,320 |

B | 1,320 | 120 | 10% | 1,200 |

C | 1,200 | 200 | 20% | 1,000 |

**(b) Given: **

weight of the finished product = 10 grams per pc.

Assuming that there is no other loss of material, the total material required for 1,980 pcs. of input of Process A shall be:

1,980 pcs. X 10 gms. = 19,800 gms.

Rate of Material = $1 per kg.

Cost of raw material = (19,800X1) / 1,000 = $19.80

Cost o fraw material per pc.= 19.80 / 1,000 = $0.0198

## Problem No. 2

## Calculation of Maximum, Minimum and reorder stock levels.

**(1).** Discuss the consideration that influences the setting of maximum, minimum and reorder stock levels. Illustrate their computation by using the following information for a component ‘ZYP’.

Normal usage | 50 per week |

Minimum usage | 25 per week |

Maximum usage | 75 per week |

Re-order quantity | 300 units |

Re-order period | 4 to 6 weeks |

### Solution

(Note: For consideration influencing the stock levels, read the discussion in the previous pages)

**Re-order level = Max. consumption per day / per week etc. X Max. Re-order period**

= 75 units X 6 weeks = 450 Units.

**Maximum Level = Re-order Level + Re-order Quantity – (Minimum consumption per day/per week etc. X Minimum time required to obtain supplies)**

= 450 units + 300 units – (25 units x 4 weeks)

= 750 units – 100 units = 650 units

**Minimum Level = Re-Order level – (Normal consumption per day/per week etc. X Average Re-order period)**

= 450 units – (50 units x 5 weeks)

= 450 units – 250 units = 200 units

(2). Two Components, A and B are used as follows:

Normal usage = 50 units per week each

Minimum usage = 25 units per week each

Maximum usage = 75 units per week each

Reorder quantity **A:** 400 units

Reorder quantity **B:** 600 units

Reorder period **A:** 4 to 6 weeks

Reorder period **B:** 2 to 4 weeks

#### Required:

Calculate for each component

(i) Reorder Level

(ii) Minimum level

(iii) Maximum level

(iv) Average stock level

### Solution

**(i) Reorder Level** = Maximum consumption per day/per week etc. X Maximum Re-Order Period

Component A = 75 units X 6 weeks = 450 units

Component B = 75 units X 4 weeks = 300 units

**(ii) Minimum Level** = Reorder Level – (Normal consumption per day/per week etc. X Average Re-order period)

Component A = 450 units – (50 units x 5 weeks) = 200 units

Component B = 300 units – (50 units x 3 weeks) = 150 units

**(iii) Maximum Level** = Reorder level – Reorder Quantity – (Minimum consumption per day/per week, etc. X Minimum Time Required to get supplies)

Component A = 450 units + 400 units – (25 units x 4 weeks)

= 850 units – 100 units = 750 units

Component B = 300 units + 600 units – (25 units x 2 weeks)

= 900 units – 50 units = 850 units

**Average Stock Level** = Minimum Level + 1/2 (Reorder Quantity)

Component A = 200 units + (1 / 2 X 400 units) = 400 units

Component B = 150 units + (1/2 X 600 units) = 450 units

## Problem 3

## Calculation of Material Turnover Ratio

Following figures were taken from the records of John and Co. for the year 31st March 2019. The valuation of inventory is $1 per kg:

Material ‘X’ | Material ‘Y’ | |

$ | $ | |

Opening Stock | 1,700 | 1,200 |

Purchases | 51,000 | 32,000 |

Closing Stock | 1,200 | 1,000 |

**Required:**

Calculate the material turnover ratio and express in number of days the average inventory is held.

### Solution

**Working notes:**

**1. Material consumed**

Material ‘X’(kgs.) | Material ‘Y’(kgs.) | |

Opening stock Add: Purchases | 1,700 51,000 | 1,200 32,000 |

52,700 | 33,200 | |

Less: Closing Stock | 1,200 | 1,000 |

51,500 | 32,200 |

**2. Average Inventory**

Average inventory = (Opening Stock + Closing Stock) / 2

Material X = (1,700 + 1,200) / 2 = 1,450 kgs.

Material Y = (1,200 + 1,000) / 2 = 1,100 kgs.

**3. Material Turnover Ratio**

= Material consumed during the period / Average Inventory

Material X = 51,500 / 1,450 = 35.5 times (approx.)

Material Y = 32,200 / 1,100 = 29.3 times (approx.)

**4. Number of days Average Inventory is held**

= Total No. of days in the period / Material Turnover

Material X = 365 / 35.5 = 10.3 days (approx.)

Material Y = 365 / 29.3 = 12.5 days (approx.)

## Problem 4

## Calculation of Economic Order Quantity

**(1).** Do as directed:

Annual consumption: 40,00,000 kgs.

Cost of placing one order: $100

Cost of carrying one kg. of raw material for one year: $0.5

Required:

Calculate the Economic Order Quantity (EOQ)

Solution:

**(2).** The annual demand for a product is 6,400 units. The unit cost is $6 and inventory carrying cost is 25% per annum. If the cost of one procurement is $75 determine:

(i) Economic order quantity

(ii) No. of orders per year

(iii) Time between two consecutive orders.

### Solution

(i) Economic Order Quantity

(ii) No. of orders per year = Annual consumption / Size of one order

= 6,400 units / 800 units

= 8 orders

(iii) Time gap between two consecutive orders = 12 months / No. of orders

= 12 months / 8 orders

= 1.5 months