Question

2. Given the following data for Smith Coffee Shop, use the high-low method to determine the variable cost per unit (cup of coffee), total fixed costs, and the estimated total cost formula or total cost equation. Units (8) Costs (7) January 1.500 2.750 February 2.000 3,000 March 1,400 2.700 April 1,200 2,600

Answer 1

Answer :

Using high-low method,

Variable Cost per unit = (Highest Activity Cost - Lowest Activity Cost) / (Highest Activity Units - Lowest Activity Units)

In this case, the highest activity is in the month of February when the highest units i.e. 2,000 are produced. Whereas, the lowest activity is in the month of April when the lowest units i.e. 1,200 units are produced.

Which means,

Highest Activity Cost = 3,000

Lowest Activity Cost = 2,600

Highest Activity Units = 2,000

Lowest Activity Units = 1,200

Therefore,

Variable Cost per unit = (3,000 - 2,600) / (2,000 - 1,200)

Variable Cost per unit = 400/800

Variable Cost per unit = 0.50

Total Cost = (Variable Cost per unit * Units Produced) + Total Fixed Cost

Using highest level activity,

3,000 = (0.50 * 2,000) + Total Fixed Cost

3,000 = 1,000 + Total Fixed Cost

Total Fixed Cost = 3,000 - 1,000

Total Fixed Cost = 2,000

Note : Total Fixed Cost can also be calculated using the lowest level activity :

2,600 = (0.50 * 1,200) + Total Fixed Cost

2,600 = 600 + Total Fixed Cost

Total Fixed Cost = 2,600 - 600

Total Fixed Cost = 2,000

Total Cost Equation :

y = a + bx

where,

y is the total cost

a is the fixed cost

​​​​​b is the variable cost per unit

x is the number of units produced

So, the equation is

y = 2,000 + 0.50x

We can check this equation using data of any month.

Equation using the data of January

y = 2,750

a = 2,000

b = 0.50

x = 1,500

y = a + bx

2,750 = 2,000 + (0.50 * 1,500)

2,750 = 2,000 + 750

2,750 = 2,750

Hence the equation is proved.

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