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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?

Short Answer

Expert verified
The operating cash flow (OCF) is sensitive to changes in quantity sold with a factor of 8. This means that any increase or decrease in quantity sold will affect the OCF by 8 times that change.

Step by step solution

01

Calculate annual depreciation

The total investment is given as \(420,000\), and the asset depreciates to zero over three years. We will use straight-line depreciation, so we can find the annual depreciation by dividing the total investment by the number of years. Annual depreciation \(= \frac{Initial~Investment}{Number~of~Years}\) Annual depreciation \(= \frac{420,000}{3} = 140,000\) The annual depreciation cost is \(140,000\).
02

Calculate total revenues

The annual revenue can be computed using the price and quantity sold: Total Revenues \(= Price \times Quantity~Sold\) Total Revenues \(= 26 \times 110,000 = 2,860,000\) The total revenues amount to \(2,860,000\).
03

Calculate total costs

To find the total costs, we will sum the fixed costs, variable costs, and depreciation expenses: Total Costs \(= Fixed~Costs + (Variable~Costs \times Quantity) + Depreciation\) Total Costs \(= 185,000 + (18 \times 110,000) + 140,000 = 2,805,000\) The total costs are \(2,805,000\).
04

Calculate earnings before tax (EBT)

Compute the earnings before tax by subtracting the total costs from the total revenues. Earnings Before Tax (EBT) \(= Total~Revenues - Total~Costs\) EBT \(= 2,860,000 - 2,805,000 = 55,000\) The earnings before tax are \(55,000\).
05

Calculate taxes

Calculate the total taxes using the tax rate of 34%: Taxes \(= EBT \times Tax~Rate\) Taxes \(= 55,000 \times 0.34 = 18,700\) The total taxes are \(18,700\).
06

Calculate net income

Compute the net income by subtracting the taxes from the EBT: Net Income \(= EBT - Taxes\) Net Income \(= 55,000 - 18,700 = 36,300\) The net income is \(36,300\).
07

Calculate operating cash flow (OCF)

Determine the OCF by adding the net income and depreciation: Operating Cash Flow (OCF) \(= Net~Income + Depreciation\) OCF \(= 36,300 + 140,000 = 176,300\) The operating cash flow is \(176,300\).
08

Analyze sensitivity

To find out how sensitive the OCF is to changes in quantity sold, express the OCF as a function of the quantity sold and analyze its sensitivity. Let 'Q' denote the quantity sold. We have: OCF\(= (Price - Variable~Cost) \times Q - Fixed~Costs - Taxes + Depreciation\) Differentiate the OCF with respect to the quantity sold (Q): \(\frac{d(OCF)}{dQ} = (Price - Variable~Cost)\) The sensitivity of OCF to changes in quantity sold is determined by the difference between the price and variable cost. In this case, it is: \(\frac{d(OCF)}{dQ} = 26 - 18 = 8\) The OCF is sensitive to changes in quantity sold with a factor of 8. Any increase or decrease in quantity sold will affect the OCF by \(8\) times that change.

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Key Concepts

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

Depreciation
Depreciation is a critical concept in accounting, especially when dealing with long-term projects. It is the method by which a company allocates the cost of a tangible asset over its useful life. This allocation allows firms to spread out the expenditure, making their financial statements reflect a more accurate picture of their operations.
For the exercise at hand, we use straight-line depreciation, one of the simplest methods. The asset's value decreases by the same amount each year. Given an initial investment of $420,000 and a project life of three years, the annual depreciation is calculated by dividing the initial cost by the number of years: \[\text{Annual Depreciation} = \frac{420,000}{3} = 140,000\]
This straight-line approach helps ease the impact of depreciation on financial outcomes, providing a steady deduction each year rather than fluctuating charges.
Fixed and Variable Costs
Understanding the distinction between fixed and variable costs is crucial for managing and predicting cash flow in any business operation.
**Fixed Costs** remain constant regardless of the production volume or sales level. In the scenario provided, the fixed costs are \(185,000 annually. This is a necessary cost for running the project, independent of how much is produced or sold.
**Variable Costs**, on the other hand, change in direct relation to the quantity of goods produced. In our case, the variable cost is \)18 per unit. For the sale of 110,000 units, the total variable costs sum up to:\[\text{Total Variable Costs} = 18 \times 110,000 = 1,980,000\]
These costs will fluctuate with changes in production levels, significantly affecting the project's cash flow sensitivity.
Earnings Before Tax
Earnings Before Tax (EBT) is an important measure of a company's profitability before tax expenses are deducted. It gives a clearer picture of operational efficiency by isolating income from taxes.
To calculate EBT, we subtract total costs—which are the sum of fixed costs, variable costs, and depreciation—from the total revenues:\[\text{EBT} = \text{Total Revenues} - \text{Total Costs} = 2,860,000 - 2,805,000 = 55,000\]
This figure, $55,000 in our example, reveals the earnings generated purely from operating activities before accounting for taxes. EBT helps in comparative analysis across companies with different tax situations, highlighting potential operational strengths or weaknesses.
Net Income
Net Income refers to the profit remaining after all deductions, including taxes, have been subtracted from total earnings. It is the final measure of profitability and an important indicator for stakeholders.
To find Net Income, use the Earnings Before Tax (EBT) figure and apply the tax expense using the tax rate given. For this exercise, taxes are calculated at a rate of 34%:\[\text{Taxes} = 55,000 \times 0.34 = 18,700\]Subtracting the tax amount from the EBT gives the net income:\[\text{Net Income} = 55,000 - 18,700 = 36,300\]
This value, $36,300, represents the actual profit available for the business after settling tax obligations. Monitoring net income helps evaluate the true financial health and performance outcomes over time.

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Most popular questions from this chapter

Covington Transmissions, Inc., has the following estimates for its new gear assembly project: price \(=\$ 1,850\) per unit; variable costs \(=\) \(\$ 160\) per unit; fixed costs \(=\$ 7\) million; quantity \(=90,000\) units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?

Consider a project with the following data: accounting break-even quantity \(=18,000\) units; cash break-even quantity \(=\) 12,000 units; life \(=\) five years; fixed costs \(=\$ 110,000 ;\) variable costs \(=\$ 20\) per unit; required return \(=18\) percent. Ignoring the effect of taxes, find the financial break- even quantity.

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.

At an output level of 30,000 units, you calculate that the degree of operating leverage is \(3 .\) If output rises to 36,000 units, what will the percentage change in operating cash flow be? Will the new level of operating leverage be higher or lower? Explain.

Everest Everwear Corporation can manufacture mountain climbing shoes for \(\$ 10.94\) per pair in variable raw material costs and \(\$ 32\) per pair in variable labor expense. The shoes sell for \(\$ 95\) per pair. Last year, production was 140,000 pairs. Fixed costs were \(\$ 800,000 .\) What were total production costs? What is the marginal cost per pair? What is the average cost? If the company is considering a one-time order for an extra 10,000 pairs, what is the minimum acceptable total revenue from the order? Explain.

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