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Sensitivity Analysis Consider a four-year project with the following information: Initial fixed asset investment \(=\mathbf{\$ 3 8 0 , 0 0 0}\); straight-line depreciation to zero over the four-year life; zero salvage value; price \(=\$ 54\); variable costs \(=\$ 42 ;\) fixed costs \(=\$ 185,000\); quantity sold \(=90,000\) units; tax rate \(=34\) percent. How sensitive is OCF to changes in quantity sold?

Short Answer

Expert verified
The sensitivity of OCF to changes in the quantity_sold is determined by calculating the partial derivative of OCF with respect to Quantity_sold. Using the chain rule, we find the partial derivative as: d(OCF)/d(Quantity_sold) = Price_per_unit - Variable_cost_per_unit + Tax_rate * (Variable_cost_per_unit - Price_per_unit) The higher the value of this derivative, the more sensitive the OCF is to changes in the quantity_sold.

Step by step solution

01

Calculate Revenue

To calculate revenue, multiply the price per unit by the quantity sold. Revenue = Price_per_unit * Quantity_sold
02

Calculate Variable Costs

To calculate the variable costs, multiply the variable cost per unit by the quantity sold. Variable_costs = Variable_cost_per_unit * Quantity_sold
03

Calculate Total Costs

Total costs are the sum of the variable_costs and fixed costs. Total_costs = Variable_costs + Fixed_costs
04

Calculate Depreciation

Using straight-line depreciation to zero over the four-year life, we need to take the initial fixed asset investment and divide it by the project life (4 years). Depreciation = Initial_fixed_asset_investment / Project_life
05

Calculate Taxable Income

Subtract total costs and depreciation from revenue to get the taxable income. Taxable_Income = Revenue - Total_costs - Depreciation
06

Calculate Taxes

Taxes can be calculated by multiplying the taxable income by the tax rate. Taxes = Taxable_Income * Tax_rate
07

Calculate Net Income

Net income is calculated by subtracting taxes from taxable income. Net_Income = Taxable_Income - Taxes
08

Calculate Operating Cash Flow (OCF)

Finally, to calculate the operating cash flow (OCF), add back depreciation to the net income. Operating_Cash_Flow = Net_Income + Depreciation Now that we have the OCF calculated, we can analyze the sensitivity of the OCF to changes in the quantity_sold.
09

Calculate the Sensitivity of OCF to Changes in Quantity Sold

To determine the sensitivity of the OCF to changes in the quantity_sold, find the derivative of the OCF with respect to quantity_allowed. Let's find the partial derivative of the OCF with respect to Quantity_sold. By utilizing the chain rule, we will determine the derivative of each element of the OCF. For Revenue, Variable_costs, and Total_costs (other variables will remain constant): d(Revenue)/d(Quantity_sold) = Price_per_unit d(Variable_costs)/d(Quantity_sold) = Variable_cost_per_unit d(Total_costs)/d(Quantity_sold) = d(Variable_costs)/d(Quantity_sold) Now, we can find the partial derivative of OCF with respect to Quantity_sold: d(OCF)/d(Quantity_sold) = Price_per_unit - Variable_cost_per_unit + Tax_rate * (Variable_cost_per_unit - Price_per_unit) After calculating the partial derivative, we can now understand the sensitivity of OCF changes to changes in the quantity sold. The higher the value of this derivative, the more sensitive the OCF is to changes in the quantity_sold.

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Key Concepts

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

Operating Cash Flow (OCF)
Understanding Operating Cash Flow (OCF) is essential for business and financial analysis. It represents the amount of cash generated by a company's regular business operations. OCF is calculated by starting with net income, adding back non-cash expenses such as depreciation, and adjusting for changes in working capital.

For example, in the textbook exercise, the OCF is determined after calculating net income and then adding back the straight-line depreciation. The reason depreciation is added back is because it's a non-cash charge, meaning it doesn't affect the company's cash balance. This makes OCF a more accurate measure of cash earned as it removes the effects of accounting decisions and shows only the cash aspect of revenues and costs.

When evaluating sensitivity, the change in OCF in response to variations in quantity sold is crucial. It provides insights into how fluctuations in sales can impact the liquidity and financial planning of the business. In other words, if the quantity sold increases or decreases, it's important to determine how significantly that affects the cash available to the business for its operational needs and obligations.
Straight-line Depreciation
Straight-line depreciation is an accounting method used to allocate the cost of a tangible asset over its useful life. This method assumes that the asset will provide value evenly over its life, resulting in an equal expense charge each year.

In the context of the exercise, the initial investment in fixed assets is depreciated to zero over four years, meaning that each year, one-fourth of the asset's cost is accounted for as an expense. Though it doesn't involve actual cash outflow, depreciation affects the taxable income calculation and, ultimately, the OCF.

Recognizing the importance of depreciation is also critical when considering the sensitivity of OCF to changes—while it remains constant regardless of sales volume, it still plays a role in annual tax reduction and needs to be factored into any analysis of operating cash.
Taxable Income Calculation
Taxable income for a company is important because it determines the tax liability the business has to the government. It's calculated by taking the gross revenue and subtracting both the cost of goods sold (including variable costs) and operating expenses (including fixed costs and depreciation).

For instance, in the exercise, the taxable income is found by subtracting both the total variable and fixed costs, as well as the straight-line depreciation from the revenue. Remember that depreciation, while non-cash, reduces taxable income and therefore lowers taxes.

When considering sensitivity analysis in corporate finance, understanding how taxable income reacts to variations in components like sold quantity can shed light on tax strategies and potential cash flow scenarios. If quantities sold fluctuate, how much would the resulting taxable income—and therefore the generated cash flows—change?
Revenue and Cost Analysis
Revenue and cost analysis forms the backbone of financial planning and management. It's about comprehending how a company's revenues are built up and how its costs are structured. Revenue is simply the total income received from sales of goods or services. Costs, on the other hand, are divided into variable costs, which change with sales volume, and fixed costs, which remain the same regardless of sales.

As illustrated by the textbook problem, calculating both revenue and total costs is a straightforward process but highly relevant for predicting business performance. The sensitivity analysis then becomes a tool to examine how changes in the quantity sold directly influence the revenue and, after costs are deducted, the OCF.

By closely analyzing these figures, companies can predict potential outcomes of changing sales volumes, helping in making informed decisions about production levels, pricing strategies, and market demands.

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Most popular questions from this chapter

Decision Trees The manager for a growing firm is considering the launch of a new product. If the product goes directly to market, there is a \(\mathbf{5 0}\) percent chance of success. For \(\$ 135,000\) the manager can conduct a focus group that will increase the product's chance of success to 65 percent. Alternatively, the manager has the option to pay a consulting firm \(\$ 400,000\) to research the market and refine the product. The consulting firm successfully launches new products 85 percent of the time. If the firm successfully launches the product, the payoff will be \(\$ 1.5\) million. If the product is a failure, the NPV is zero. Which action will result in the highest expected payoff to the firm?

Financial Break-Even Analysis You are considering investing in a company that cultivates abalone for sale to local restaurants. Use the following information: The discount rate for the company is 15 percent, the initial investment in equipment is \(\$ 360,000\), and the project's economic life is seven years. Assume the equipment is depreciated on a straight-line basis over the project's life. 1\. What is the accounting break-even level for the project? 2\. What is the financial break-even level for the project?

Financial Breakeven The Cornchopper Company is considering the purchase of a new harvester. Cornchopper has hired you to determine the break-even purchase price in terms of present value of the harvester. This break-even purchase price is the price at which the project's NPV is zero. Base your analysis on the following facts: \- The new harvester is not expected to affect revenues, but pretax operating expenses will be reduced by \(\$ 12,000\) per year for 10 years. \- The old harvester is now 5 years old, with 10 years of its scheduled life remaining. It was originally purchased for \(\$ 50,000\) and has been depreciated by the straight-line method. \- The old harvester can be sold for \(\$ 18,000\) today. \- The new harvester will be depreciated by the straight-line method over its 10-year life. \- The corporate tax rate is 34 percent. \- The firm's required rate of return is 15 percent. \- The initial investment, the proceeds from selling the old harvester, and any resulting tax effects occur immediately. \- All other cash flows occur at year-end. \- The market value of each harvester at the end of its economic life is zero.

Decision Trees Young screenwriter Carl Draper has just finished his first script. It has action, drama, and humor, and he thinks it will be a blockbuster. He takes the script to every motion picture studio in town and tries to sell it but to no avail. Finally, ACME studios offers to buy the script for either (a) \(\$ 12,000\) or (b) 1 percent of the movie's profits. There are two decisions the studio will have to make. First is to decide if the script is good or bad, and second if the movie is good or bad. First, there is a 90 percent chance that the script is bad. If it is bad, the studio does nothing more and throws the script out. If the script is good, they will shoot the movie. After the movie is shot, the studio will review it, and there is a 70 percent chance that the movie is bad. If the movie is bad, the movie will not be promoted and will not turn a profit. If the movie is good, the studio will promote heavily; the average profit for this type of movie is \(\$ 20\) million. Carl rejects the \(\$ 12,000\) and says he wants the 1 percent of profits. Was this a good decision by Carl?

Option to Wait Hickock Mining is evaluating when to open a gold mine. The mine has 60,000 ounces of gold left that can be mined, and mining operations will produce 7,500 ounces per year. The required return on the gold mine is 12 percent, and it will cost \(\$ 14\) million to open the mine. When the mine is opened, the company will sign a contract that will guarantee the price of gold for the remaining life of the mine. If the mine is opened today, each ounce of gold will generate an aftertax cash flow of \(\$ \mathbf{4 5 0}\) per ounce. If the company waits one year, there is a 60 percent probability that the contract price will generate an aftertax cash flow of \(\$ 500\) per ounce and a 40 percent probability that the aftertax cash flow will be \(\$ 410\) per ounce. What is the value of the option to wait?

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