Question

Say you own a​ 500-unit apartment complex. When the apartments are​ 90% occupied, monthly operating costs total​ $200,000. When occupancy dips to​ 80%, monthly operating costs fall to​ $197,000. A nearby manufacturing plant has just announced that it will close in three months. Since many residents will lose their jobs and move​ away, you fear occupancy may drop to 50​%. If this​ happens, what do you expect your monthly operating costs to​ be?

Answer 1

Answer:

$188,000

Explanation:

To solve this exercise we will use the "High Low Method" which is a technique that allows to determine the costs associated with a certain level of activity, identifying its fixed and variable elements. This is done by taking the two most "extreme" data (the highest and the lowest) from a data set.

We will follow these steps:

1. Identify the data set:

                                  Cost            Units

90% occupancy $ 200,000        450

80% occupancy   $ 197,000         400

Because it is a 500-unit apartament complex, with an occupancy level of 90%, it means that there are 450 units in operation, and with an occupancy level of 80%, 400.

A 50% occupancy level implies that there are 250 units in operation. Therefore, we want to find the total cost associated with the maintenance of these units.

2. Identify the extreme data.

According to the data set, the most extreme are:

The highest cost is $ 200,000 and the highest number of units is 450.

The lowest cost is $ 197,000 and the lowest number of units is 400.

3. Calculate the variable cost per unit.

For this we follow the following formula :

$VCU = \frac{HC - LC}{HU - LU}$

Where HC = Highest Cost, LU= Lowest Cost, HU = Highest number of Units, LU = Lowest number of Units.

We replace :

$VCU = \frac{200,000 - 197,000}{450 - 400}$

$VCU = \frac{3000}{50}$

VCU = $ 60 per unit.

4. Calculate the fixed cost

Any level of activity is chosen. Here we will choose the highest: 450 units that operate at a cost of $ 200,000. Although we could choose the 400 units that operate at $ 197,000. It does not matter which one.

Now what we do is apply the following formula:

$FC = HC - (VCU * HU)$

Where HC = Highest Cost, VCU = Variable Cost per Unit, HU = Highest number of Units.

We replace:

FC = 200,000 - ($ 60 * 450)

FC= 200,000 - (27,000)

FC = 173,000

5. Calculate the total variable cost of the new activity

We multiply the Variable Cost per Unit ($ 60) by the number of units that will operate at a 50% occupancy level (250)

Variable cost of the new activity = $ 60 * 250

Variable cost of the new activity = $ 15,000

6. Calculate the total cost

The fixed cost ($ 173,000) and the total variable cost of the new activity ($ 15,000) are added

Total cost = $ 173,000 + $ 15,000 = $ 188,000

This is the final answer.