Question

Niece Equipment Rentals of Del​ Valle, Texas, has recently been approached about the prospect of purchasing a large construction crane. The crane rents for ​$480 an hour but​ operator, fuel, insurance and miscellaneous expenses run ​$195 an hour when the crane is in use. The company owner estimates that it will cost ​$1010 a month to store and maintain the crane and the annual depreciation expense is ​$51,000

a. Calculate the accounting​ break-even number of annual rental hours needed to produce zero operating earnings from the crane​ (before taxes).
b. Calculate the cash​ break-even point. If we ignore​ non-cash expenses such as depreciation in the​ break-even calculation, how many hours must the crane be rented in order to break even on a cash​ basis?
c. Why do we have two different​ break-even points? What does each one tell​ you?

Answer 1

The accounting break-even number of annual rental hours needed is approximately 183 hours, and the cash break-even point is also around 183 hours. The two different break-even points consider different financial aspects, with accounting break-even considering all expenses and cash break-even focusing on cash flows excluding non-cash costs.

Step-by-step explanation:

a. Accounting Break-even Analysis

To calculate the accounting break-even number of annual rental hours, we need to find the point where the operating earnings from the crane are zero. The formula for accounting break-even is:

Accounting Break-even = Fixed Costs / (Rental Revenue per Hour - Variable Costs per Hour)

Using the given information, we can calculate:

Fixed Costs = Storage and Maintenance Costs + Depreciation Expenses = $1,010 + $51,000 = $52,010

Rental Revenue per Hour = Rental Income - Variable Costs per Hour = $480 - $195 = $285

Now, substituting the values into the formula, we get:

Accounting Break-even = $52,010 / $285 ≈ 182.8 hours

Therefore, the accounting break-even number of annual rental hours needed to produce zero operating earnings is approximately 183 hours.

b. Cash Break-even Analysis

To calculate the cash break-even point, we need to ignore non-cash expenses like depreciation. The formula for cash break-even is:

Cash Break-even = Fixed Costs / (Rental Revenue per Hour - Variable Costs per Hour excluding Depreciation)

Substituting the values from part a, we get:

Cash Break-even ≈ $52,010 / $285 ≈ 182.8 hours

Therefore, the cash break-even point is approximately 183 hours.

c. Explanation

We have two different break-even points because accounting break-even takes into account all expenses, including non-cash expenses like depreciation, while the cash break-even focuses only on cash flows and excludes non-cash expenses. Accounting break-even gives a more comprehensive view of overall profitability, while cash break-even helps in assessing the ability to cover cash expenses.

Answer 2

To produce zero operating earnings before taxes, Niece Equipment Rentals needs to rent the crane for approximately 222 hours annually. On a cash basis, they need to rent it for around 43 hours to break-even. These two break-even points are important as they distinguish between covering all costs including non-cash items like depreciation and ensuring the company does not run out of cash respectively.

Step-by-step explanation:

Break-even Analysis for Niece Equipment Rentals

For Niece Equipment Rentals to determine the accounting break-even point for the rental of a construction crane, we need to calculate the number of rental hours required to cover all operating costs and depreciation, resulting in zero operating earnings before taxes. The calculation is as follows:

1. Calculate total annual fixed costs which include storage and maintenance cost as well as annual depreciation: $1010 (monthly maintenance and storage) * 12 (months) + $51,000 (annual depreciation) = $63,120.
2. Calculate the difference between the rental charge per hour ($480) and variable costs per hour ($195), which is the contribution margin per hour: $480 - $195 = $285.
3. Divide the total fixed costs by the contribution margin per hour to determine the number of rental hours needed to break-even: $63,120 / $285 = 221.47 hours. Therefore, approximately 222 hours of rental are needed to break-even on an accounting basis (since we cannot rent a crane for a fraction of an hour).

To calculate the cash break-even point, we exclude the non-cash expense of depreciation:

1. Calculate total annual cash fixed costs by excluding depreciation: $1010 * 12 = $12,120.
2. Use the previously calculated contribution margin per hour ($285).
3. Divide the cash fixed costs by the contribution margin per hour: $12,120 / $285 = 42.53 hours. Therefore, approximately 43 hours of rental are needed to break-even on a cash basis.

We have two different break-even points because one considers all expenses including non-cash items like depreciation (accounting break-even), while the other considers only the cash outflows (cash break-even). The accounting break-even tells us how many hours the crane needs to be rented to cover all costs on paper, whereas the cash break-even shows us how many hours it needs to be rented to ensure that the company does not run out of cash.