Hoi Chong Transport, Ltd., operates a fleet of delivery trucks in Singapore. The company has determined that if a truck is driven 165,000 kilometers during a year, the average operating cost is 12.9 cents per kilometer. If a truck is driven only 110,000 kilometers during a year, the average operating cost increases to 16.2 cents per kilometer. Express the variable and fixed costs in the form Y=a+bx

Y = 1,089,000 + 6.30X

Explanation:

To get the answer, we use high and low cost estimation method. The method is used to separate fixed and variable costs. The formula for the high and low method is as follows:

VC = (HAC - LAC

) : (HAU - LAU)

Where:

HAU = High Activity Units = 165,000

HAC = High Activity Cost = 165,000 * 12.9 = 2,128,500.00 cents

LAU = Low Activity Units = 110,000

LAC = Lowe Activity Cost = 110,000 * 16.2 = 1,782,000.00 cents

VC = Variable cost is per unit

Substituting the values into equation 1, we have:

VC = (2,128,500.00 - 1,782,000.00) : (165,000 - 110,000)

= 346,500.00 : 55,000

VC = 6.30 cents per unit

To calculate the fixed cost, we use the equation:

Y = a + b. X

Where

Y = Total Cost

a = Fixed Cost

b = VC = 6.3 cents

X = Units Produced

We can use either of the high or low figures to calculate the fixed cost. That is, either of the high or low figures will give us the same answer. If we use the high cost and the high activity, then:

Y = Total Cost = 2,128,500.00

X = 165,000

Therefore,

Y = a + b. X becomes:

2,128,500.00 = a + (6.30 * 165,000)

2,128,500.00 = a + 1,039,500.00

Making "a" the subject of the formula, we have

a = 2,128,500.00 - 1,039,500.00

= 1,089,000.00

Since b = 6.30 and a = 1,089,000.00, we can now express the variable and fixed costs in the following form:

Y = 1,089,000 + 6.30X