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Chapter 9: Problem 22

Consider a three-year project with the following information: initial fixed asset investment \(=\$ 730,000 ;\) straight-line depreciation to zero over the five-year life; zero salvage value; price \(=\$ 31.75 ;\) variable costs \(=\) \(\$ 19.50 ;\) fixed costs \(=\$ 185,000 ;\) quantity sold \(=80,000\) 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 quantity sold is approximately \(8.085. This means that for each additional unit sold, the OCF will increase by approximately $8.085 when all other factors remain constant.

Step by step solution

01

Calculate the annual depreciation

In order to calculate the annual depreciation, we use the straight-line depreciation method. Since the asset is depreciated over 5 years, the annual depreciation is equal to the initial investment divided by 5. Initial_investment = $730,000 Depreciation = Initial_investment / 5 Depreciation = \(730,000 / 5 = \)146,000
02

Calculate Total Revenue, Variable Costs, and Fixed Costs

We have the price and the quantity sold, so it's easy to calculate the annual revenue, variable costs, and fixed costs. Price per unit = $31.75 Quantity_sold = 80,000 units Total_revenue = Price per unit * Quantity_sold Total_revenue = \(31.75 * 80,000 = \)2,540,000 Variable_cost per unit = $19.50 Total_variable_costs = Variable_cost per unit * Quantity_sold Total_variable_costs = \(19.50 * 80,000 = \)1,560,000 Total_fixed_costs = $185,000
03

Calculate OCF

Now we can use the OCF formula and the values calculated above: OCF = (Total_revenue - Total_variable_costs - Total_fixed_costs - Depreciation) * (1 - Tax_rate) + Depreciation Tax_rate = 34% OCF = (\(2,540,000 - \)1,560,000 - \(185,000 - \)146,000) * (1 - 0.34) + $146,000 OCF = \(649,000 * 0.66 + \)146,000 OCF = \(428,340 + \)146,000 OCF = $574,340
04

Calculate the sensitivity of OCF to changes in quantity sold

Now, we want to determine the sensitivity of OCF to changes in quantity sold. We achieve that by calculating the partial derivative of OCF with respect to the quantity sold: dOCF/dQuantity = d(Total_revenue - Total_variable_costs) / dQuantity * (1 - Tax_rate) Since Total_fixed_costs and Depreciation remain constant when the quantity changes, we can omit them in the partial derivative. Now, we calculate the partial derivative: dOCF/dQuantity = (Price - Variable_cost per unit) * (1 - Tax_rate) dOCF/dQuantity = (\(31.75 - \)19.50) * (1 - 0.34) dOCF/dQuantity = $12.25 * 0.66 dOCF/d_quantity = $8.085 So, the sensitivity of OCF to changes in quantity sold is \(8.085. This means that for each additional unit sold, the OCF will increase by approximately \)8.085 when all other factors remain constant.

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Key Concepts

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

Straight-Line Depreciation
Straight-line depreciation is a common method of allocating the cost of a fixed asset over its useful life. It's founded on the assumption that the benefit derived from the asset will be uniform over its lifespan. This is reflected in the calculation where the original cost of the asset is divided evenly over the depreciation period. For example, if a company invests in machinery costing \(730,000 with a fixed life of five years and anticipates no salvage value, the annual depreciation expense would be \)\frac{730,000}{5} = \(146,000\). This annual depreciation is factored into the Operating Cash Flow (OCF) calculations, becoming a non-cash expense that reduces the taxable income, effectively providing a tax shield.
Variable Costs
Variable costs are expenses that vary directly with the level of production or sales volume. They are typically correlated with the activities of a business; the more the company produces or sells, the higher the variable costs. In our exercise, the variable cost is \(19.50 per unit. This implies that for every unit produced and sold, the company incurs a cost of \)19.50. When considering the sensitivity of OCF, variable costs play a significant role because they have to be subtracted from total revenue to determine the profitability that's affected by the volume of sales.
Fixed Costs

Understanding Fixed Costs

Unlike variable costs, fixed costs remain unchanged regardless of the business's production or sales volumes. Fixed costs are the unavoidable expenses that a business must pay, such as rent, insurance, and salaries for employees on fixed contracts. In our exercise, the fixed cost is stipulated as $185,000 annually. This amount will stay constant regardless of how many units are sold, thus it does not affect the sensitivity of OCF to changes in quantity sold.
Tax Rate
The tax rate is a percentage at which income is taxed. The exercise applies a 34% tax rate to the company's income. This rate influences the Operating Cash Flow significantly due to its impact on net income after taxes. As we calculate OCF, which is a post-tax figure, the formula incorporates (1 - Tax_rate) to determine the actual cash flow available after taxes. The tax shield provided by depreciation and the effect of taxable income on OCF are essential considerations when analyzing financial performance and planning for tax liabilities.

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Most popular questions from this chapter

Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of \(\$ 2.7\) million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate \(\$ 2,450,000\) in annual sales, with costs of \(\$ 1,180,000\). If the tax rate is 35 percent, what is the OCF for this project?

CSM Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for \(\$ 510,000\) is estimated to result in \(\$ 218,000\) in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of \(\$ 64,000 .\) The press also requires an initial investment in spare parts inventory of \(\$ 21,000,\) along with an additional \(\$ 3,000\) in inventory for each succeeding year of the project. If the shop's tax rate is 34 percent and its discount rate is 11 percent, should the company buy and install the machine press?

Pappy's Potato has come up with a new product, the Potato Pet (they are freeze-dried to last longer). Pappy's paid \(\$ 120,000\) for a marketing survey to determine the viability of the product. It is felt that Potato Pet will generate sales of \(\$ 525,000\) per year. The fixed costs associated with this will be \(\$ 178,000\) per year, and variable costs will amount to 20 percent of sales. The equipment necessary for production of the Potato Pets will cost \(\$ 540,000\) and will be depreciated in a straight-line manner for the four years of the product life (as with all fads, it is felt the sales will end quickly). This is the only initial cost for the production. Pappy's is in a 40 percent tax bracket and has a required return of 13 percent. Calculate the payback period, NPV, and IRR.

Kenny, Inc., is looking at setting up a new manufacturing plant in South Park. The company bought some.land six years ago for \(\$ 8\) million in anticipation of using it as, a warehouse and distribution site, but the company has since decided to rent facilities elsewhere. The land would net \(\$ 10.2\) million if it were sold today. The company now wants to build its new manufacturing plant on this land; the plant will cost \(\$ 24\) million to build, and the site requires \(\$ 900,000\) worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project? Why?

McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell for \(\$ 675\) per set and have a variable cost of \(\$ 340\) per set. The company has spent \(\$ 150,000\) for a marketing study that determined the company will sell 70,000 sets per year for seven years. The marketing study also determined that the company will lose sales of 9,000 sets per year of its high-priced clubs. The high-priced clubs sell at \(\$ 1,100\) and have variable costs of \(\$ 550 .\) The company will also increase sales of its cheap clubs by 12,000 sets per year. The cheap clubs sell for \(\$ 300\) and have variable costs of \(\$ 100\) per set. The fixed costs each year will be \(\$ 10,800,000 .\) The company has also spent \(\$ 1,000,000\) on research and development for the new clubs. The plant and equipment required will cost \(\$ 19,800,000\) and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of \(\$ 1,500,000\) that will be returned at the end of the project. The tax rate is 40 percent, and the cost of capital is 14 percent. Calculate the payback period, the \(\mathrm{NPV}\), and the IRR.
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