Question

Beetroots (Pty) Ltd is a company that buys fresh veggies in bulk and sell it direct to the public after packaging it in smaller quantities.

The following cost data is available for six months:

Month	Kg Veggies	Total cost
January	200 kg	$3 800
February	500 kg	$8 600
March	900 kg	$14 300
April	350 kg	$5 950
May	780 kg	$12 800
June	800 kg	$13 200

The financial manager is of the opinion that the total cost for the month is related t the quantity of veggies that is packaged (measured in kilograms).

Required:

1.1 Compile a cost formula (cost function) by making use of the High-Low method.

1.2 Compile a cost formula (cost function) by making use of the Least-Square method (Simple Regression Analysis). SHOW ALL CALCULATIONS

1.3 Explain why there is a difference between the cost formula according to the High-Low method and the cost formula according to the Least-Square method, and advise the best method to use.

1.4 Calculate the budgeted cost for July and August according to both cost formulas if the expected quantity of veggies that will be packaged is 950kg and 1 020kg respectively.

Answer 1

Answer 1.1:

As per high low method

Variable Cost per unit = (Highest Activity cost – Lowest activity cost)/ (Highest activity units- Lowest activity units)

So Variable cost per unit = ($ 14,300 - $ 3,800)/ (900 kg – 200 kg) = $ 10,500 / 700 kg = 15 per kg

And fixed cost = total cost at a fixed activity – variable cost at a fixed activity

So fixed cost = $ 14,300 – ($ 15 per kg * 900 kgs) = $ 14,300 - $ 13,500 = $ 800

Answer 1.2:

Least Squares Method (Linear Regression):

In this method we follows a simple cost function i.e. y = a + mx

Where

y = total cost

a = total fixed cost

m = slope or level of activity

x = variable cost per unit

So in order to find out variable cost per unit (x) = nΣxy − (Σx) (Σy)

       nΣx² − (Σx)²

Month	Units in kg (x)	Total cost (y)	xy	x2
Jan	200	3800	760000	40000
Feb	500	8600	4300000	250000
March	900	14300	12870000	810000
April	350	5950	2082500	122500
May	780	12800	9984000	608400
June	800	13200	10560000	640000
Total	3530	58650	40556500	2470900

So let’s put all this in the equation:

Variable cost per units (x) = (6)( 40556500) – (3530)(58650) / (6)( 2470900) – (3530)²

                                              = 243339000 – 207034500 / 14825400 – 12460900

                                              = 36304500 / 2364500

                                              = 15.35   

Fixed cost = ∑y – b∑x / n = 58650 – (15.35)(3530) / 6 = 4464.5/6 = 744

Answer 1.3:

Difference between high low method and least square method comes in existence because of data they used. In high low method, we consider only two data that is most active and least active data series while least square consider all the data despite of their weight.

I will advise to use least square method as it would consider all months cost despite of most active and least active which tends to ignorance of all other series of data. However this method not easy to use and needs a lot of data.

Answer 1.4:

Month	Units in kg	Variable cost		Fixed Cost		Total cost
		High Low	Least Square	High Low	Least Square	High Low	Least Square
July	950	14250	14582.5	800	744	15050	15326.5
August	1020	15300	15657	800	744	16100	16401