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\(A\) proposed project has fixed costs of \(\$ 30,000\) per year. The operating cash flow at 7,000 units is \(\$ 63,000 .\) Ignoring the effect of taxes, what is the degree of operating leverage? If units sold rises from 7,000 to \(7,300,\) what will be the increase in operating cash flow? What is the new degree of operating leverage?

Short Answer

Expert verified
The degree of operating leverage (DOL) for the given project is approximately 0.910. When the units sold rise from 7,000 to 7,300, the increase in operating cash flow is -\$31,683, indicating a decrease in operating cash flow. The new degree of operating leverage is approximately 24.05.

Step by step solution

01

Calculate the Operating Income for 7000 units

To find the operating income for 7000 units, we need to subtract the fixed costs from the operating cash flow. Operating Income = Operating Cash Flow - Fixed Costs Operating Income = \$63,000 - \$30,000 = \$33,000
02

Calculate the Variable Cost per Unit for 7000 units

Since total variable costs = Operating cash flow - Operating income, we can calculate the total variable cost and then find the variable cost per unit by dividing it by the number of units sold. Total Variable Cost = \$63,000 - \$33,000 = \$30,000 Variable cost per unit = \(\frac{\$30,000}{7,000}\) = \$4.29 (approximately)
03

Calculate the Degree of Operating Leverage (DOL)

Now we can calculate the DOL using the formula: \(DOL = \frac{\% \Delta Operating \, Income}{\% \Delta Units \, Sold}\) Since we don't have the percentage changes, we can use an alternative formula: \(DOL = \frac{(Units \, Sold)(Variable \, Cost \, per \, Unit)}{Operating \, Income}\) DOL = \(\frac{(7,000)(\$ 4.29)}{\$33,000}\) ≈ 0.910 (approximately)
04

Calculate the New Operating Income for 7300 units

First, find the new total variable cost by multiplying the new number of units sold (7300) by the variable cost per unit (\$4.29). New Total Variable Cost = (7300)(\$4.29) ≈ \$31,317 Now, calculate the new operating income: New Operating Income = New Total Variable Cost - Fixed Costs New Operating Income = \$31,317 - \$30,000 = \$1,317
05

Calculate the Increase in Operating Cash Flow

Since operating cash flow = Operating income + Fixed Costs, we can find the new operating cash flow for 7300 units and then calculate the increase in operating cash flow. New Operating Cash Flow = New Operating Income + Fixed Costs New Operating Cash Flow = \$1,317 + \$30,000 = \$31,317 Increase in Operating Cash Flow = New Operating Cash Flow - Old Operating Cash Flow Increase in Operating Cash Flow = \$31,317 - \$63,000 = -\$31,683
06

Calculate the New Degree of Operating Leverage (DOL)

Now we can calculate the new DOL using the formula: \(DOL_{new} = \frac{(Units \, Sold_{new})(Variable \, Cost \, per \, Unit)}{Operating \, Income_{new}}\) DOL_{new} = \(\frac{(7,300)(\$ 4.29)}{\$1,317}\) ≈ 24.05 (approximately) The new degree of operating leverage is 24.05. The increase in operating cash flow is -\$31,683, indicating a decrease in operating cash flow when units sold rise from 7000 to 7300.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Operating Leverage
Operating leverage is a key concept in financial management that measures how sensitive a company's operating income is to changes in sales volume. It reflects the fixed versus variable cost structure of a business. When a company has high operating leverage, a small change in sales can lead to larger changes in operating income. This is due to the fixed costs that must be covered before any profit is made.
In our exercise, the degree of operating leverage (DOL) was calculated using the formula:
  • \[DOL = \frac{(\text{Units Sold})(\text{Variable Cost per Unit})}{\text{Operating Income}}\]
The calculated DOL for 7,000 units was approximately 0.910, indicating how operating income would change in response to sales volume changes. A new sales volume of 7,300 units significantly changed the DOL to 24.05, showcasing how small increases in sales can drastically impact the leverage when costs and income are recalculated.
Operating Cash Flow
Operating cash flow is a measure of the cash generated by a company's normal business operations. It indicates the ability of a firm to generate sufficient cash to maintain and grow operations, without relying on external financing sources.
In the given problem, the operating cash flow at 7,000 units was $63,000. This was derived from subtracting fixed costs from the total cash flow. As the units increased to 7,300, the new operating cash flow was calculated as $31,317. The change here was negative ($-31,683), reflecting that the increase in units sold did not equate to a proportional increase in cash flow, largely due to the structure of fixed and variable costs.
Variable Costs
Variable costs are costs that change in proportion to the level of goods or services that a business produces. Unlike fixed costs, these costs increase with more production and sales.
To determine the variable cost per unit, the total variable cost was calculated by subtracting the operating income from the operating cash flow. Here, it was \(30,000 for 7,000 units, leading to a variable cost per unit of approximately \)4.29.
  • Formula used: \[\text{Variable cost per unit} = \frac{\text{Total Variable Costs}}{\text{Units Sold}}\]
As the number of units increased to 7,300, the total variable costs adjusted proportionally, demonstrating the nature of variable expenses.
Fixed Costs
Fixed costs are business expenses that are not dependent on the level of goods or services produced by the business. They remain constant regardless of the company's output.
In this exercise, the fixed costs were given as $30,000 annually. These costs play a significant role in calculating both operating income and cash flow, as they must be deducted before earnings are calculated. Regardless of whether the company produces 7,000 or 7,300 units, these fixed costs stay the same, influencing the operating leverage and the business's overall financial health. Understanding fixed costs is crucial for assessing how changes in sales volume impact profit.

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Most popular questions from this chapter

Consider a project to supply Detroit with 35,000 tons of machine screws annually for automobile production. You will need an initial \(\$ 1,500,000\) investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be \(\$ 300,000\) and that variable costs should be \(\$ 200\) per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the fiveyear project life. It also estimates a salvage value of \(\$ 500,000\) after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of \(\$ 230\) per ton. The engineering department estimates you will need an initial net working capital investment of \(\$ 450,000 .\) You require a 13 percent return and face a marginal tax rate of 38 percent on this project. a. What is the estimated OCF for this project? The NPV? Should you pursue this project? b. Suppose you believe that the accounting department's initial cost and salvage value projections are accurate only to within ±15 percent; the marketing department's price estimate is accurate only to within ±10 percent; and the engineering department's net working capital estimate is accurate only to within ±5 percent. What is your worst-case scenario for this project? Your best-case scenario? Do you still want to pursue the project?

A project has the following estimated data: price = \(\$ 65\) per unit; variable costs \(=\$ 33\) per unit; fixed costs \(=\$ 4,000 ;\) required return \(=16\) percent; initial investment \(=\$ 9,000 ;\) life \(=\) three years. Ignoring the effect of taxes, what is the accounting break-even quantity? The cash break- even quantity? The financial break-even quantity? What is the degree of operating leverage at the financial break-even level of output?

Calculating costs and Break-Even Bob's Bikes Inc. (BBI) manufactures biotech sunglasses. The variable materials cost is \(\$ .74\) per unit and the variable labor cost is \(\$ 2.61\) per unit. a. What is the variable cost per unit? b. Suppose BBI incurs fixed costs of \(\$ 610,000\) during a year in which total production is 300,000 units. What are the total costs for the year? c. If the selling price is \(\$ 7.00\) per unit, does \(B B I\) break even on a cash basis? If depreciation is \(\$ 150,000\) per year, what is the accounting break-even point?

We are evaluating a project that costs \(\$ 924,000,\) has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 130,000 units per year. Price per unit is \(\$ 34.00\), variable cost per unit is \(\$ 19,\) and fixed costs are \(\$ 800,000\) per year. The tax rate is 35 percent, and we require a 15 percent return on this project. a. Calculate the accounting break-even point. What is the degree of operating leverage at the accounting break-even point? b. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500 unit decrease in projected sales. c. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a \(\$ 1\) decrease in estimated variable costs.

Consider a three-year project with the following information: initial fixed asset investment \(=\$ 420,000 ;\) straight-line depreciation to zero over the three-year life; zero salvage value; price \(=\$ 26 ;\) variable costs \(=\) \(\$ 18 ;\) fixed costs \(=\$ 185,000 ;\) quantity sold \(=110,000\) units; tax rate \(=34\) percent. How sensitive is OCF to changes in quantity sold?

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