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Chapter 10 Cash Flow Estimation LEARNING OBJECTIVES (Slide 10-‐2) 1. Understand the importance of cash flow and the distinction between cash flow and profits. 2. Identify incremental cash flow. 3. Calculate depreciation and cost recovery. 4. Understand the cash flow associated with the disposal of depreciable assets. 5. Estimate incremental cash flow for capital budgeting decisions. IN A NUTSHELL… In this chapter, the author examines how cash flow differs from profits. Since cash flow is the lifeline of business, it is very important to understand how to measure and forecast the various sources of cash flow that arise from the investment and disposal of assets. Accordingly, topics such as identifying and estimating incremental cash flow, calculating depreciation and cost recovery, and adjusting for salvage and terminal values are covered as part of the steps necessary prior to making capital budgeting decisions. LECTURE OUTLINE 10.1 The Importance of Cash Flow (Slides 10-‐3 to 10-‐4) Cash flow measures the actual inflow and outflow of cash, while profits represent merely an accounting measure of periodic performance. Figures 10.1 and 10.2 (shown below), help clarify the difference between net income and operating cash flow (OCF) of a firm. It is important to remind students that a firm can spend its operating cash flow but not its net income. Some firms have net losses (due to high depreciation write-offs) and yet can pay dividends from cash balances, while others show profits and may not have the cash available. 335 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 336 Brooks n Financial Management: Core Concepts, 2e Thus, cash flow is broader than net income as shown below. FIGURE 10.1 FIGURE 10.2 Figure 10.2 is a modified income statement in that it only considers the cash flow arising from operations. Accordingly, interest expense (which is a financing cash flow) is not included, and depreciation (which had been deducted in Figure 10.1, mainly for tax purposes ) is added back. Thus, OCF = EBIT –Taxes +Depreciation=Net Income + Interest +Depreciation $4,603 =$5,046 – $1,555 + $1,112 = $3313+$178+$1,112 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 337 10.2 Estimating Cash Flow for Projects: Incremental Cash Flow (Slides 10-‐5 to 10-‐13) When a firm is considering either expanding a current line of business, starting a new venture, or replacing an existing asset with a newer one, the changes in revenue and costs that occur will have an incremental effect on its operating cash flow. It is the timing and magnitude of these incremental cash flows that have to be carefully estimated and evaluated as part of any capital budgeting analysis. There are 7 important issues that have to be kept track of during a comprehensive cash flow estimation process. These issues include: sunk costs, opportunity cost, erosion, synergy gains, working capital, capital expenditures, and depreciation or cost recovery of assets. 10.2 (A) Sunk costs: are expenses that have already been incurred, or that will be incurred, regardless of the decision to accept or reject a project. For example, a marketing research study exploring business possibilities in a region would be a sunk cost, since its expenditure has been done prior to undertaking the project and will have to be paid whether or not the project is taken on. These costs although part of the income statement, should not be considered as part of the relevant cash flows when evaluating a capital budgeting proposal. 10.2 (B) Opportunity costs: include costs that may not be directly observable or obvious, but result from benefits being lost as a result of taking on a project. For example, if a firm decides to use an idle piece of equipment as part of a new business, the value of the equipment that could be realized by either selling or leasing it would be a relevant opportunity cost. 10.2 (C) Erosion costs: arise when a new product or service competes with revenue generated by a current product or service offered by a firm. For example, if a store offers two types of photo-copying services, a newer, more expensive choice and an older economical one, some of the revenues from the older repeat customers will be lost and should therefore be accounted for in the incremental cash flows. Example 1: Erosion costs Frosty Desserts currently sell 100,000 of its Strawberry-Shortcake Delight each year for $3.50 per serving. Its cost per serving is $1.75. Its chef has come up with a newer, richer concoction, “Extra-Creamy Strawberry Wonder,” which costs $2.00 per serving, will retail for $4.50 and should bring in 130,000 customers. It is estimated that after the launch the sales for the original variety will drop by 15%. Estimate the erosion cost associated with this venture. To calculate the erosion cost we must consider the amount of lost contribution margin (Selling price – unit cost) from SSD’s drop in sales. Erosion cost = (Unit sales of SSD before launch –Unit sales after launch) X (Selling Price – Unit Cost) èErosion cost = (100,000 – 85,000) × ($3.50-$1.75) = $26,250 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 338 Brooks n Financial Management: Core Concepts, 2e Margin contributed by ESW = ($4.50-$2.00) × 130,000= $325,000 Margin prior to new launch = 100,000 × ($3.50 – $1.75) = $175,000 Margin after launch = ($3.50 – $1.75) × 85,000 + $325,000 = $473,750 Net change in margin = $473, 750 – $175,000 = $298,750 Erosion cost = ESW’s contribution margin – net change in margin = $325,000 – $298,750 = $26,250 10.2 (D) Synergy gains: refer to the impulse purchases or sales increases for other existing products related to the introduction of a new product. For example, if a gas station with a convenience store attached, adds a line of fresh donuts and bagels, the sales of coffee and milk, would result in synergy gains. 10.2 (E) Working capital: investment refers to the additional cash flows arising from changes in current assets such as inventory and receivables (uses) and current liabilities such as accounts payables (sources) that occur as a result of a new project. Generally, at the end of the project, these additional cash flows are recovered and must be accordingly shown as cash inflows. Even though the net cash outflows—due to increase in net working capital at the start— may equal the net cash inflow arising from the liquidation of the assets at the end, the time value of money effects make these costs relevant. 10.3 Capital Spending and Depreciation (Slides 10-‐14 to 10-‐22) When a firm spends capital to acquire a productive (depreciable) asset, it is allowed to expense a portion of the cost of the asset each year, as a process of cost recovery via the reduced taxes that result from the write-off. The portion written off in the income statement, each year, is called the depreciation expense; and the accumulated total kept track of in the Balance sheet is known as Accumulated Depreciation. Thus, the book value of an asset equals its original cost less its accumulated depreciation. The two reasons we need to deal with depreciation when doing capital budgeting problems are: (1) the tax flow implications from the operating cash flow and (2) the gain or loss at disposal of a capital asset. Firms have a choice of using either straight line depreciation rates, or modified accelerated cost recovery system (MACRS) rates for allocating the annual depreciation expense, arising from an asset acquisition. 10.3 (A) Straight-‐line depreciation: rates are easy to apply since the annual depreciation expense is calculated by dividing the initial cost plus installation minus the expected residual value (at termination) equally over the expected productive life of the asset. The annual depreciation expenses are the same for each year. ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 339 10.3 (B) Modified Accelerated Cost Recovery System: rates are established by the federal government, since 1981, as a way to allow for firms to accelerate the depreciation write-off in early years of the asset’s life. These rates (shown below in Table 10.4) are set up based on various asset categories (class-lives), as shown in Table 10.3 in the text. Each column relating to an asset life has one additional year of depreciation than the class-life states, e.g. a 3-year class life asset is depreciated over 4 years. This is because the government assumes that the asset is put into use for only half a year at the start (halfyear convention), and thereby allowed ½ depreciation, with the last year (Year 4) being allowed the balance required to reach 100% (which amounts to ½ the prior year’s percentage. The depreciation rates in each column add up to 100%, i.e. no need to deduct residual value, with higher rates being allowed in earlier years and less in later years. With higher depreciation rates allowed in earlier years, the tax savings are higher due to the time value of money. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 340 Brooks n Financial Management: Core Concepts, 2e Example 2: MACRS depreciation The Grand Junction Furniture Company has just bought some specialty tools to be used in the manufacture of high-end furniture. The cost of the equipment is $400,000 with an additional $30,000 for installation. If the company has a marginal tax rate of 30%, compare its annual tax savings that would be realized from using MACRS depreciation rates. According to Table 10.3, specialty tools falls under a 3-year class asset with rates in Years 1-4 of 33.33%, 44.45%, 14.81%, and 7.41% respectively. Depreciable basis = Cost + Installation = $400,000 + $30,000 = $430,000 The annual depreciation expenses (i.e. annual rate × Dep. Basis)are shown below: Total MACRS rate Dep. Exp 33.33% $ 143,319 44.45% $ 191,135 14.81% $ 63,683 7.41% $ 31,863 100.00% $ 430,000 Two other specific depreciation-related issues, that affect capital budgeting analysis, include: 1. Dealing with assets which are sold off prior to being fully depreciated, would be true if we were replacing an asset with a newer model and salvaging some value from the old one prior to it being fully depreciated. 2. Selling a fully depreciated asset i.e. zero book value. 10.4 Cash Flow and the Disposal of Capital Equipment (Slides 10-‐23 to 10-‐26) When a depreciable asset is sold, the cash inflow that results can be higher than, equal to, or lower than the actual selling price of the asset, depending on whether it was sold above (taxable gain), at (zero-gain) or below (tax credit) book value. If the sale results in a taxable gain, then the cash inflow is reduced by the amount of the taxes (Tax rate × (Selling Price –Book Value). If the selling price is exactly equal to book value the cash inflow equals the sale price. If the asset is sold below its book value, a loss results, and can be written off taxes for the year, resulting effectively in an addition to cash inflows equal to (Book Value-Selling Price) × Tax rate. ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 341 Thus, the cash flow resulting from after-tax salvage value of a depreciable asset is calculated as follows: After-tax Salvage Value = Selling Price – Tax rate × (Selling price – Book Value) Or Selling Price + Tax rate × (Book Value – Selling Price) Example 3: Tax effects from disposal cash flow Let’s say that the manager of the Grand Junction Furniture Company decides to dispose of the specialty tools, acquired 2 years ago at a cost of $430,000 (including installation), to another firm for $125,000. How much of an after-tax cash flow will result, assuming that the tools were being depreciated based on the 3-year MACRS rates and the company’s marginal tax rate is 35% Depreciable basis = $430,000 Year 1 depreciation rate = 33.33% Year 2 depreciation rate = 44.45% Total depreciation taken so far = $430,000 × (33.33% + 44.45%) = $334, 454 Book Value = Depreciable basis – Accumulated depreciation Book Value = $430,000 – $334,454 = $95,546 Selling price = $125,000 > Book Value è Taxable gain on the sale è Taxable gain = $125,000-$95,546=$29,454 After-tax Salvage Value = Selling Price – (Tax rate × Taxable gain ) =$125,000 – .35 × ($29,454) =$125,000-$10,308.9=$114,691.1 After-tax Salvage Value = $114,691.1 Note: If Selling Price > BV è Cash Inflow = Selling Price less tax If Selling Price < BVè Cash Inflow = Selling Price + tax credit If Selling Price = BVè Cash Inflow = Selling Price 10.5 Projected Cash Flow for a New Product(Slides 10-‐27 to 10-‐34) A comprehensive capital budgeting analysis requires the estimation of initial and future incremental cash flows that are likely to result over the productive life of the project, followed by the application of one or more of the evaluation techniques that were covered in Chapter 9. In particular, the following 4 steps are typically involved: 1. Determination of the initial capital investment for the project Purchase cost + Installation + Initial Increase in net working capital – After-tax salvage value from disposal of old asset (if any) 2. Estimation of the annual operating cash flows (incremental) generated by the project, ignoring sunk costs and including erosion costs and side-effects. (Figure 10.3-10.5 in the text) OCF = EBIT – Taxes + Depreciation ©2013 Pearson Education, Inc. Publishing as Prentice Hall 342 Brooks n Financial Management: Core Concepts, 2e In the terminal year, besides the usual OCF we have to account for any salvage value that is received, which requires the calculation of Book value and taxes (or tax credits) on sale of the asset. (Table 10.7 in the text) Terminal Year Cash flow = OCF + After-tax Salvage Value 3. Determination of the change in net working capital which is usually an increase (outflow) at the beginning and a reduction (inflow) at the end. (Table 10.7 in the text) 4. Evaluation of the proposed project using an appropriate discount or hurdle rate and either the NPV or IRR approach. (See Figure 10.6 shown below.) Questions 1. How is cash flow different from profit or net income? Cash flow refers to the amount of cash received or spent in a specific period while profit or net income is an accounting measure of performance during a specific period of time. Cash flow can be spent; profits may not be available for spending. 2. Why is depreciation expense added back to the net income of a company to find the operating cash flow? Depreciation expense is a non cash flow item in the income statement. It represents a portion of the original cost (cash outflow) of a capital asset that occurred in a previous period. The expense reduces taxable income and thus taxes so it is included in the ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 343 income statement but must be added back to net income to find the operating cash flow. 3. Why are owners of a business only interested only in incremental cash flow for a project and not the total cash flow of a project? Only the incremental cash flow of a project adds value to the company as a whole and therefore value to the owners. When a project has revenue that is the result of lost revenue from another project owners do not see an increase in total revenue. 4. Why are sunk cost excluded from the incremental cash flow of a project? Does this mean that they were wasted expenses? Why or why not? Sunk costs are costs that would be spent regardless of the decision to accept or reject a project so they are not part of the cash flow that will be used to make the decision on a project. They are not wasted expenses as they may have been used to gather vital information for the decision. For example, a market study to determine the potential market of a new product may be critical in determining future sales and thus is important is estimating future cash flow. However, the cost of the study is a sunk cost. 5. Give an example of an erosion cost. Explain why this cost is part of the incremental cash flow of a project. Is there a case when a new product should get credit for additional revenue of another already existing product? Erosion cost is the lost profit of an existing product when a new product takes part of current sales of the existing product from a company’s current clients. For example, introducing bottled water by a beverage company may reduce its sale of carbonated beverages thus the lost profits from the carbonated beverages must be covered by the bottle water and therefore these erosion costs are part of the bottled water’s cash flow. However, if a competitor is also introducing bottled water and the beverage sales will be lost to a competitor if the company does not also introduce its bottled water into the market; these lost sales from the carbonated beverages are not part of the incremental costs of the bottled water. 6. Give an example of an opportunity cost and explain how you would estimate the cost as it applies to a particular project. An opportunity cost is a foregone benefit due to the selection of a project. An example of an opportunity cost is the potential lost revenue from selling land that is used in a plant expansion when there was a market for the vacant land. The opportunity cost is this case is the fair market value of the land, the amount that the company could have received if it had chosen to sell the land instead of expanding the plant. 7. Why must a company typically invest in working capital when starting a new project? Why is this investment in working capital recovered at the completion of the project? Working capital is necessary for making a project go. For example, if you are introducing a new product to the market such as a soft drink, you must bottle the drink for customers and this bottling process requires an investment in inventories such as bottles, labels, and caps. Increasing the working capital inventories at the start of a project is required but once the project is stopped (the product discontinued), there is no longer a need to keep these inventories and so they are reduced to zero. Reducing the inventories to zero is viewed as the recovered capital at the end of the project as it is a reduction in an asset account. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 344 Brooks n Financial Management: Core Concepts, 2e 8. How does depreciation spread the capital expenditure of a project over the life of the capital asset? Why is using MACRS usually beneficial to a company versus using straight-line depreciation? The original cost of new equipment or other large assets is not expensed on the income statement when it is purchased. However, each period a portion of this cash outlay is “expensed” to the income statement via depreciation. Over the life of the asset, these periodic depreciation expenses will add up to the original cost of the asset and thus spread this expense over the life of the asset. MACRS allows a greater percentage of the cost to be depreciated in the early years compared to straight-line depreciation. Because these expenses reduce taxes, the higher the expense the lower the taxes and the lower the cash outflow. Due to the time-value-of-money the earlier these expenses are recorded the sooner the tax reduction is received so MACRS is beneficial to the company based on the timing of the tax payments. 9. Why is there typically a tax gain or tax loss at the disposal of capital assets? There is typically a tax gain or tax loss at the disposal of capital assets because it is rare that the cash flow from the disposal is exactly equal to the current book value of the asset. The book value is the original cost minus the accumulated depreciation. 10. All six decision models from Chapter 9 rely on the appropriate timing and amount of cash flow. What are the potential errors a manager can make if this information is not accurate? If we use inappropriate amounts or an inappropriate timing of cash flow we can end up with one of two potential errors. We could reject good projects or we could accept bad projects. Both of these errors reduce the value of the company to the owners Prepping for Exams 1. a. 2. c. 3. d. 4. b. 5. a. 6. d. 7. a. 8. c. 9. c. 10. b. ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 345 Problems 1. Erosion costs. Fat Tire Bicycle Company currently sells 40,000 bicycles per year. The current bike is a standard balloon tire bike, selling for $90 with a production and shipping cost of $35. The company is thinking of introducing an off-road bike with a projected selling price of $410 and a production and shipping cost of $360. The projected annual sales for the off-road bike are 12,000. The company will lose sales in fat-tire bikes of 8,000 units per year if it introduces the new bike, however. What is the erosion cost from the new bike? Should Fat Tire start producing the off-road bike? ANSWER Erosion Cost = ($90 – $35) × 8,000 = $440,000 Net Annual Cash Flow with standard bike: ($90 – $35) × 40,000 = $2,200,000 Net Annual Cash Flow with standard and off-road bikes: ($90 – $35) × (40,000 – 8,000) = $1,760,000 ($410 – $360) × 12,000 = $600,000 Net Annual CF = $1,760,000 + $600,000 = $2,360,000 Increase of $160,000 per year so add new off-road bike to production. 2. Erosion costs. Heavenly Cookie Company has the following annual sales and costs for its current product line: Heavenly is thinking of adding Mississippi Mud brownies to the product line. The ultra-rich brownies would sell for $0.99 a piece and cost $0.81 to produce. The forecasted brownie volume is 250,000 per year. Introduction of brownies, however, will reduce cookie sales by 250,000 with the following drop in sales per cookie: 130,000 in chocolate chip, 60,000 in snickerdoodle, 40,000 in peanut butter, 10,000 in lemon drop, and 10,000 in cream-filled. What is the erosion cost of introducing the brownies? What is the net change in annual margin if Mississippi Mud brownies are added to the product line? ANSWER Erosion Cost for Chocolate Chip Erosion Cost for Snicker Doodle Erosion Cost for Peanut Butter Erosion Cost for Lemon Drop Erosion Cost for Cream Filled = ($0.49 – $0.19) × 130,000 = $39,000 = ($0.49 – $0.17) × 60,000 = $19,200 = ($0.49 – $0.15) × 40,000 = $13,600 = ($0.49 – $0.22) × 10,000 = $2,700 = ($0.59 – $0.31) × 10,000 = $2,800 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 346 Brooks n Financial Management: Core Concepts, 2e Total erosion cost: $39,000 + $19,200 + $13,600 + $2,700 + $2,800 = $77,300 Brownie Margin: ($0.99 – $0.81) × 250,000 = $45,000 Net Change in annual margin dollars is $45,000 – $77,300 = –$32,300 so do not add brownies to the product mix. 3. Opportunity costs. Revolution Records will build a new recording studio on a vacant lot next to the operations center. The land was purchased five years ago for $450,000. Today the value of the land has appreciated to $780,000. Revolutionary Records did not consider the value of the land (it had already spent the money to acquire the land long before this project was considered). The NPV of the recording studio was $600,000. Should Revolution Records consider the land as part of the cash flow of the recording studio? If yes, what value should be used, $450,000 or $780,000? How will the value affect the project? ANSWER The land needs to be included as part of the cash flow for the studio project because there is an opportunity cost here. If Revolution Records does not want to keep the land it can sell it for $780,000. So this current market value of $780,000 is the opportunity cost that the studio must cover. If the NPV without considering this cost is $600,000 for the studio then Revolution Records should just sell the land and have $780,000 as cash income (unless there are taxes that would reduce the net cash flow below $600,000). 4. Opportunity cost. Richards Tree Farm Inc. has branched into gardening over the years, and is now considering adding patio furniture to its product lineup. Currently, the area where the patio furniture is to be displayed is a vacant slab of concrete attached to the indoor shop. The company originally paid $8,500 to put in the slab of concrete three years ago. It would now cost $12,000 to put in the same slab of concrete. Should Richards consider the concrete slab when expanding its outdoor garden shop to include patio furniture? If yes, which value should it use? ANSWER The slab is a sunk cost unless there is another use for the slab that could provide cash flow to Richards Tree Farm. The additional cash flow that the slab could provide is the opportunity cost, not the current replacement cost or the original cost. 5. Working capital cash flow. Cool Water Inc. sells bottled water. The firm keeps in inventory plastic bottles at 10% of the monthly projected sales. These plastic bottles cost $0.005 each. The monthly sales for the coming year are as follows: ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 347 Show the anticipated cost of plastic bottles each month for these projected sales, the beginning inventory volume and ending inventory volume each month, and the monthly increase or decrease in cash flow for inventory given that an increase is a use of cash and a decrease is a source of cash. ANSWER COGS = Monthly Sales × $0.005 Beginning Inventory Balance = Current Month’s Sales Projection × 10% Ending Inventory Balance = Next Month’s Sales Projection × 10% Increase in Working Capital Cash = Ending Inventory – Beginning Inventory × $0.005 Month Exp. Sales (units) Ant. COGS Beg. Inv. Bal End. Inv. Bal. W. Cap. Increase January 2,000,000 $10,000 200,000 220,000 $100.00 February 2,200,000 $11,000 220,000 270,000 $250.00 March 2,700,000 $13,500 270,000 300,000 $150.00 April 3,000,000 $15,000 300,000 360,000 $300.00 May 3,600,000 $18,000 360,000 550,000 $950.00 June 5,500,000 $27,500 550,000 700,000 $750.00 July 7,000,000 $35,000 700,000 900,000 $1,000.00 August 9,000,000 $45,000 900,000 600,000 ($1,500.00) September 6,000,000 $30,000 600,000 400,000 ($1,000.00) October 4,000,000 $20,000 400,000 250,000 ($750.00) November 2,500,000 $12,500 250,000 130,000 ($600.00) December 1,300,000 $6,500 130,000 220,000 $450.00 TOTAL $244,000 $100.00 6. Working capital cash flow. Tires for Less is a franchise of tire stores throughout the greater Northwest. It has projected the following unit sales per tire and costs of tires for the coming year: ©2013 Pearson Education, Inc. Publishing as Prentice Hall 348 Brooks n Financial Management: Core Concepts, 2e The company policy is to have the next month’s anticipated sales for each tire type in the warehouse. Shipments are made to the various stores throughout the Northwest from the central warehouse. Show the anticipated cost of tires each month for these projected sales by tire type, the beginning inventory volume and ending inventory volume each month for each tire, and the monthly increase or decrease in cash flows for inventory given that an increase is a use of cash and a decrease is a source of cash. Find the total cost of goods sold and change in monthly working capital cash flows for all tires. What do you notice about the working capital change when you combine all four tires? ANSWER (Please note that there is an error in the data table…the amounts shown are actually units sold per type of tire, not dollars) COGS = Tire’s Monthly Volume × Tires Cost Beginning Inventory Balance = Current Month’s Sales Projection Ending Inventory Balance = Next Month’s Sales Projection Increase in Working Capital Cash = Ending Inventory – Beginning Inventory × cost of tire SNOW TIRES Month Anticipated COGS Beginning Inventory Balance Ending Inventory Balance ©2013 Pearson Education, Inc. Publishing as Prentice Hall Working Capital Increase Chapter 10 n Cash Flow Estimation 349 January $1,848,000 44,000 38,000 –$252,000 February $1,596,000 38,000 14,000 –$1,008,000 March $588,000 14,000 2,000 –$504,000 April $84,000 2,000 0 –$84,000 May $0 0 0 $0 June $0 0 0 $0 July $0 0 0 $0 August $0 0 0 $0 September $0 0 0 $0 October $0 0 16,000 $672,000 November $672,000 16,000 82,000 $2,772,000 December $3,444,000 82,000 48,000 –$1,428,000 TOTAL $8,232,000 $168,000 Rain Tire Working Capital and COGS Anticipated COGS Beginning Inventory Balance Ending Inventory Balance Working Capital Increase January $620,000 20,000 36,000 $496,000 February $1,116,000 36,000 46,000 $310,000 March $1,426,000 46,000 22,000 –$744,000 April $682,000 22,000 40,000 $558,000 May $1,240,000 40,000 20,000 –$620,000 June $620,000 20,000 2,000 –$558,000 July $62,000 2,000 2,000 $0 August $62,000 2,000 2,000 $0 September $62,000 2,000 14,000 $372,000 October $434,000 14,000 18,000 $124,000 November $558,000 18,000 20,000 $62,000 December $620,000 20,000 22,000 $62,000 Month TOTAL $7,502,000 $62,000 All-Terrain Tire Working Capital and COGS Month January Anticipated COGS Beginning Inventory Balance Ending Inventory Balance Working Capital Increase $192,000 4,000 5,000 $48,000 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 350 Brooks n Financial Management: Core Concepts, 2e February $240,000 5,000 7,000 $96,000 March $336,000 7,000 8,000 $48,000 April $384,000 8,000 12,000 $192,000 May $576,000 12,000 30,000 $864,000 June $1,440,000 30,000 39,000 $432,000 July $1,872,000 39,000 22,000 –$816,000 August $1,056,000 22,000 8,000 –$672,000 September $384,000 8,000 2,000 –$288,000 October $96,000 2,000 1,000 –$48,000 November $48,000 1,000 3,000 $96,000 December $144,000 3,000 5,000 $96,000 TOTAL $6,768,000 $48,000 All-Purpose Tire Working Capital and COGS Anticipated COGS Beginning Inventory Balance Ending Inventory Balance Working Capital Increase January $2,220,000 60,000 54,000 –$222,000 February $1,998,000 54,000 50,000 –$148,000 March $1,850,000 50,000 60,000 $370,000 April $2,220,000 60,000 65,000 $185,000 May $2,405,000 65,000 68,000 $111,000 June $2,516,000 68,000 75,000 $259,000 July $2,775,000 75,000 80,000 $185,000 August $2,960,000 80,000 70,000 –$370,000 September $2,590,000 70,000 70,000 $0 October $2,590,000 70,000 65,000 –$185,000 November $2,405,000 65,000 60,000 –$185,000 December $2,220,000 60,000 60,000 $0 TOTAL $28,749,000 Month $0 All Tires Working Capital and COGS COGS Beginning Inventory Balance Ending Inventory Balance Working Capital Increase January $4,880,000 128,000 133,000 $70,000 February $4,950,000 133,000 117,000 –$750,000 Anticipated Month ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 351 March $4,200,000 117,000 92,000 –$830,000 April $3,370,000 92,000 117,000 $851,000 May $4,221,000 117,000 118,000 $355,000 June $4,576,000 118,000 116,000 $133,000 July $4,709,000 116,000 104,000 –$631,000 August $4,078,000 104,000 80,000 –$1,042,000 September $3,036,000 80,000 86,000 $84,000 October $3,120,000 86,000 100,000 $563,000 November $3,683,000 100,000 165,000 $2,745,000 December $6,428,000 165,000 135,000 –$1,270,000 TOTAL $51,251000 $278,000 When you look across all the tires you see that the swings from month to month in inventory are reduced as some of the large swings in one type of tire are offset by the opposite swings of the other tires. This is one type of diversification effect from products that have seasonal sales variation when their individual sales variations across the seasons are offsetting. 7. Depreciation expense. Brock Florist Company buys a new delivery truck for $29,000. It is classified as a light-duty truck. a. Calculate the depreciation schedule using a five-year life, straight-line depreciation, and the half-year convention for the first and last years. b. Calculate the depreciation schedule using a five year life and MACRS depreciation. c. Compare the depreciation schedules from parts (a) and (b) before and after taxes with a 30% tax rate. What do you notice about the difference between these two methods? ANSWER a. Annual depreciation is cost of truck divided by five; $29,000/ 5 = $5,800 And for the first and last year we have $5,800 / 2 = $2,900. b. Depreciation schedule using MACRS; Year One Depreciation = $29,000 × 0.2000 = $5,800 Year Two Depreciation = $29,000 × 0.3200 = $9,280 Year Three Depreciation = $29,000 × 0.1920 = $5,568 Year Four Depreciation = $29,000 × 0.1152 = $3,340.80 Year Five Depreciation = $29,000 × 0.1152 = $3,340.80 Year Six Depreciation = $29,000 × 0.0576 = $1,670.40 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 352 Brooks n Financial Management: Core Concepts, 2e c. Comparing the two depreciation schedules before and after taxes (at 30%): Year Straight Line MACRS ∆ Before Tax ∆ After Tax One $2,900 $5,800 $2,900 $870 Two $5,800 $9,280 $3,480 $1,044 Three $5,800 $5,568 –$232 –$69.60 Four $5,800 $3,340.80 –$2,459.20 –$737.76 Five $5,800 $3,340.80 –$2,459.20 –$737.76 Six $2,900 $1,670.40 –$1,229.60 –$368.88 Total $29,000 $29,000 $0 $0 The difference is that the MACRS moves up the tax shield to the early years of depreciation yet the total tax shield is the same under both depreciation schedules. 8. Depreciation expense. Richards Tree Farm, Inc. has just purchased a new aerial tree trimmer for $91,000. Calculate the depreciation schedule using the property class category of a single-purpose agricultural and horticultural structure (from Table 10.3) for both straight line depreciation and MACRS. Use the half-year convention for both methods. Compare the depreciation schedules before and after taxes using a 40% tax rate. What do you notice about the difference between these two methods? ANSWER Annual straight line depreciation is cost of tree-trimmer divided by 7; $91,000/ 7 = $13,000 the first year would be $6,500 and the eighth year $6,500 (half year convention) and the other years $13,000. Depreciation schedule using MACRS; Year One Depreciation = $91,000 × 0.1429 = $13,003.90 Year Two Depreciation = $91,000 × 0.2449 = $22,285.90 Year Three Depreciation = $91,000 × 0.1749 = $15,915.90 Year Four Depreciation = $91,000 × 0.1249 = $11,365.90 Year Five Depreciation = $91,000 × 0.0893 = $8,126.30 Year Six Depreciation = $91,000 × 0.0893 = $8,126.30 Year Seven Depreciation = $91,000 × 0.0893 = $8,126.30 Year Eight Depreciation = $91,000 × 0.0445 = $4,049.50 Comparing the two depreciation schedules before and after taxes (at 40%): Year Straight Line MACRS ∆ Before Tax ∆ After Tax One $6,500 $13,003.90 $6,503.90 $2,601.56 Two $13,000 $22,285.90 $9,285.90 $3,714.36 Three $13,000 $15,915.90 $2,915.90 $1,166.36 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 353 Four $13,000 $11,365.90 –$1,634.10 –$653.64 Five $13,000 $8,126.30 –$4,873.70 –$1,949.48 Six $13,000 $8,126.30 –$4,873.70 –$1,949.48 Seven $13,000 $8,126.30 –$4,873.70 –$1,949.48 Eight $6,500 $4,049.50 –$2,450.50 –$980.20 Total $91,000 $91,000 $0 $0 The difference is that the MACRS moves up the tax shield to the early years of depreciation yet the total tax shield is the same under both depreciation schedules. 9. Cost recovery. Brock Florist Company sold their delivery truck in problem (see Problem 7) after three years of service. If MACRS was used for the depreciation schedule, what is the after tax cash flow from the sale of the truck (continue to use 30% tax rate) if a. the sales price was $15,000? b. the sales price was $10,000? c. the sales price was $5,000? ANSWER The accumulated depreciation after three years using MACRS is $29,000 × (0.20 + 0.32 + 0.192) = $20,648. The basis in the truck is therefore $29,000 – $20,648 = $8,352. a. If the sales price is $15,000 then the truck had a gain on sale of $15,000 – $8,352 = $6,648 and the tax liability is $6,648 × 0.30 = $1,994.40. The after tax cash flow is $15,000 – $1,994.40 = $13,005.60 b. If the sales price is $10,000 then the truck had a gain on sale of $10,000 – $8,352 = $1,648 and the tax liability is $1,648 × 0.30 = $494.40. The after tax cash flow is $10,000 – $494.40 = $9,505.60 c. If the sales price is $5,000 then the truck had a loss on sale of $5,000 – $8,352 = $3,352 and the tax credit is $3,352 × 0.30 = $1,005.90. The after tax cash flow is $5,000 + $1,005.90 = $6,005.90 10. Cost recovery. Jake Richards sold the tree trimmer (see Problem 8) after four years of service. If MACRS was used for the depreciation schedule, what is the after-tax cash flow from the sale of the trimmer (continue to use a 40% tax rate) if a. the sales price was $35,000? b. the sales price was $28,428.40? c. the sales price was $21,000? ©2013 Pearson Education, Inc. Publishing as Prentice Hall 354 Brooks n Financial Management: Core Concepts, 2e ANSWER The accumulated depreciation after four years using MACRS is $91,000 × (0.1429 + 0.2449 + 0.1749+ 0.1249) = $62,571.60. The basis in the trimmer is therefore $91,000 – $62,571.60 = $28,428.40. a. If the sales price is $35,000 then the trimmer had a gain on sale of $35,000 – $28,428.40 = $6,571.60 and the tax liability is $6,571.60 × 0.40 = $2,628.64. The after tax cash flow is $35,000 – $2,628.64 = $32,371.36 b. If the sales price is $28,428.40 then the truck had neither a gain nor loss on sale. There is no tax liability or tax credit on disposal so the after tax cash flow is $28,428.40 c. If the sales price is $21,000 then the truck had a loss on sale of $21,000 – $28,428.40 = $7,428.40 and the tax credit is $7,428.40 × 0.40 = $2,971.36. The after tax cash flow is $21,000 + $2,971.36 = $23,971.36 11. Operating cash flow. Grady Precision Measurement Tools has forecasted the following sales and costs for a new GPS system: annual sales of 48,000 units at $18 a unit, production costs at 37% of sales price, annual fixed costs for production at $180,000, and depreciation expense (straight-line) of $240,000 per year. The company tax rate is 35%. What is the annual operating cash flow of the new GPS system? ANSWER Revenue (48,000 × $18) $864,000 COGS (48,000 × $18 × 0.37) 319,680 Fixed Costs 180,000 Depreciation 240,000 EBIT $124,320 Taxes ($124,320 × 0.35) 43,512 Net Income $ 80,808 Add Back Depreciation 240,000 Operating Cash Flow (per year) $320,808 12. Operating cash flow. Huffman Systems has forecasted the following sales for home alarm systems to be 63,000 units per year at $38.50 per unit. The cost to produce each unit is expected to be about 42% of the sales price. The new product will have an additional $494,000 fixed costs each year, and the manufacturing equipment will have an initial cost of $2,400,000 and will be depreciated over eight years (straightline). The company tax rate is 40%. What is the annual operating cash flow for the alarm systems if the projected sales and price per unit are constant over the next eight years? ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 355 ANSWER Revenue (63,000 × $38.50) $2,425,500 COGS (63,000 × $38.50 × 0.42)1,018,710 Fixed Costs 494,000 Depreciation ($2,400,000 / 8) 300,000 EBIT $ 612,790 Taxes ($612,790 × 0.40) 245,116 Net Income $ 367,674 Add Back Depreciation 300,000 Operating Cash Flow (per year)$ 667,674 13. NPV. Using the operating cash flow information in Problem 11, determine whether Grady Precision Measurement Tools should add the GPS system to its set of products. The initial investment is $1,440,000 and is depreciated over six years (straight-line) and will be sold at the end of five years for $380,000. The cost of capital is 10% and the tax rate is still 35%. ANSWER Find the after-tax cash flow at disposal of the equipment: Book Value (Basis at end of five years) Original Cost $1,440,000 Depreciation expense per year is $1,440,000 / 6 = $240,000 Accumulated depreciation is 5 × $240,000 = $1,200,000 Basis = $1,440,000 – $1,200,000 = $240,000 Gain on Disposal = $380,000 – $240,000 = $140,000 Tax on Disposal = $140,000 × 0.35 = $49,000 After-tax cash flow at disposal = $380,000 – $49,000 = $331,000 1 5 (1.10) 1 NPV = −$1,440,000 + $320,808× + $331,000× 5 (1.10) (1.10) 1− NPV = -$1,440,000 + $320,808 × 3.7908 + $331,000 × 0.6209 NPV = -$1,440,000 + $1,216,114.72 + $205,524.96 = -$18,360.32 Reject the project. 14. NPV. Using the operating cash flow information in Problem 12, determine whether Huffman Systems add the home alarm system to their set of products. The manufacturing equipment will be sold off at the end of eight years for $210,000 and the cost of capital for this project is 14%. ANSWER Find the after-tax cash flow at disposal of the equipment: ©2013 Pearson Education, Inc. Publishing as Prentice Hall 356 Brooks n Financial Management: Core Concepts, 2e Book Value (Basis at end of five years) Original Cost $2,400,000 Depreciation expense per year is $2,400,000 / 8 = $300,000 Accumulated depreciation is 8 × $300,000 = $2,400,000 Basis = $2,400,000 – $2,400,000 = $0 Gain on Disposal = $210,000 – $0 = $210,000 Tax on Disposal = $210,000 × 0.40 = $84,000 After-tax cash flow at disposal = $210,000 – $84,000 = $126,000 1 8 (1.14) 1 NPV = −$2,400,000 + $667,674× + $126,000× 8 ( 0.14) (1.14) 1− NPV = -$2,400,000 + $667,674 × 4.6389 + $126,000 × 0.3506 NPV = -$2,400,000 + $3,097,248.81 + $44,170.44 = $741,419.25 Accept the project. 15. Operating cash flow (growing each year; MACRS). Mathews Mining Company is looking at a project that has the following forecasted sales: first-year sales are 6,800 units and will grow at 15% over the next four years (a five-year project). The price of the product will start at $124 per unit and increase each year at 5%. The production costs are expected to be 62% of the current year’s sales price. The manufacturing equipment to aid this project will have a total cost (including installation) of $1,400,000. It will be depreciated using MACRS and has a seven-year MACRS life classification. Fixed costs will be $50,000 per year. Mathews Mining has a tax rate of 30%.What is the operating cash flow for this project over these five years? Hint: Use a spreadsheet. ANSWER Set up in a spreadsheet Year 1 2 3 4 5 6,800 6,800 × 1.15 6,800 × 1.152 6,800 × 1.153 6,800 × 1.154 $124 $124 × 1.05 $124 × 1.052 $124 × 1.053 $124 × 1.054 Revenue $843,200 $1,018,164 $1,229,433 $1,484,540 $1,792,583 COGS $522,784 $631,262 $762,248 $920,415 $1,111,401 Fixed Costs $50,000 $50,000 $50,000 $50,000 $50,000 Depreciation $200,060 $342,860 $244,860 $174,860 $125,020 EBIT $70,356 -$5,958 $172,325 $339,265 $506,162 Taxes (30%) $21,107 -$1,787 $51,698 $101,780 $151,849 Unit Sales Price per unit ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 357 Net Income $49,249 -$4,171 $120,627 $237,485 $354,313 Add Back Depreciation $200,060 $342,860 $244,860 $174,860 $125,020 OCF $249,309 $338,689 $365,487 $412,345 $479,333 Revenue is Unit Sales × Price per Unit COGS is Revenue × 0.62 Depreciation is as follows: Year one $1,400,000 × 0.1429 Year two $1,400,000 × 0.2449 Year three $1,400,000 × 0.1749 Year four $1,400,000 × 0.1249 Year five $1,400,000 × 0.0893 = $200,060 = $342,860 = $244,860 = $174,860 = $125,020 Taxes are EBIT × 0.30 Net Income is EBIT – Taxes OCF is Net Income + Depreciation 16. Operating cash flow (growing each year; MACRS). Miglietti Restaurants is looking at a project with the following forecasted sales: first-year sales quantity of 31,000 with an annual growth rate of 3.5% over the next ten years. The sales price per unit is $42.00 and will grow at 2.25% per year. The production costs are expected to be 55% of the current year’s sales price. The manufacturing equipment to aid this project will have a total cost (including installation) of $2,400,000. It will be depreciated using MACRS and has a seven-year MACRS life classification. Fixed costs are $335,000 per year. Miglietti Restaurants has a tax rate of 30%.What is the operating cash flow for this project over these ten years? Hint: Use a spreadsheet. ANSWER Set up in a spreadsheet Year 1 2 3 4 5 31,000 31,000 × 1.035 31,000 × 1.0352 31,000 × 1.0353 31,000 × 1.0354 $42 $42 × 1.0225 $42 × 1.02252 $42 × 1.02253 $42 × 1.02254 $1,302,000 $1,377,890 $1,458,204 $1,543,187 $1,633,138 COGS $716,100 $757,840 $802,012 $848,753 $898,232 Fixed Costs $335,000 $335,000 $335,000 $335,000 $335,000 Depreciation $342,960 $587,760 $419,760 $299,760 $214,320 EBIT –$92,060 –$302,710 –$98,568 $59,674 $185,586 Taxes (30%) –$27,618 –$90,813 –$29,570 $17,902 $55,676 Net Income –$64,442 –$211,897 –$68,998 $41,772 $129,910 Add Back Depreciation $342,960 $587,760 $419,760 $299,760 $214,320 Unit Sales Price per unit Revenue ©2013 Pearson Education, Inc. Publishing as Prentice Hall 358 Brooks n Financial Management: Core Concepts, 2e OCF $375,863 $350,762 6 7 8 9 10 31,000 × 1.0355 31,000 × 1.0356 31,000 × 1.0357 31,000 × 1.0358 31,000 × 1.0359 $42 × 1.02255 $42 × 1.02256 $42 × 1.02257 $42 × 1.02258 $42 × 1.02259 $1,728,341 $1,829,081 $1,935,682 $2,048,508 $2,167,910 COGS $950,588 $1,005,995 $1,064,625 $1,126,679 $1,192,350 Fixed Costs $335,000 $335,000 $335,000 $335,000 $335,000 Depreciation $214,320 $214,320 $106,800 $0 $0 EBIT $228,433 $273,766 $429,257 $586,829 $640,560 Taxes (30%) $68,530 $82,130 $128,777 $176,049 $192,168 Net Income $159,903 $191,636 $300,480 $410,780 $448,392 Add Back Depreciation $214,320 $214,320 $106,800 $0 $0 OCF $374,223 $405,956 $407,280 $410,780 $448,392 Year Unit Sales Price per unit Revenue $278,518 $341,532 $344,230 Revenue is Unit Sales × Price per Unit COGS is Revenue × 0.55 Depreciation is as follows: Year one $2,400,000 × 0.1429 = $342,960 Year two $2,400,000 × 0.2449 = $587,760 Year three $2,400,000 × 0.1749 = $419,760 Year four $2,400,000 × 0.1249 = $299,760 Year five $2,400,000 × 0.0893 = $214,320 Year six $2,400,000 × 0.0893 = $214,320 Year seven $2,400,000 × 0.0893 = $214,320 Year eight $2,400,000 × 0.0445 = $106,800 Taxes are EBIT × 0.30 Net Income is EBIT – Taxes OCF is Net Income + Depreciation 17. NPV. Using the operating cash flow information from Problem 15, find the NPV of the project for Mathews Mining if the manufacturing equipment can be sold for $80,000 at the end of the five-year project and the cost of capital for this project is 12%. Hint: Use a spreadsheet. ANSWER Find the after-tax cash flow at disposal of the equipment: Book Value (Basis at end of five years) Original Cost $1,400,000 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 359 Depreciation is as follows: Year one $1,400,000 × 0.1429 = $200,060 Year two $1,400,000 × 0.2449 = $342,860 Year three $1,400,000 × 0.1749 = $244,860 Year four $1,400,000 × 0.1249 = $174,860 Year five $1,400,000 × 0.0893 = $125,020 Accumulated depreciation = $1,087,660 Basis = $1,400,000 – $1,087,660 = $312,340 Loss on Disposal = $80,000 – $312,340 = -$232,340 Tax Credit on Disposal = $232,340 × 0.30 = $69,702 After-tax cash flow at disposal = $80,000 + $69,702 = $149,702 NPV = -$1,400,000 + $249,309 / (1.12) + $338,689 / (1.12)2 + $365,487 / (1.12)3 + $412,345 / (1.12)4 + (479,333 + 149,702) / (1.12)5 = -$28,271.4 Reject the project. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 360 Brooks n Financial Management: Core Concepts, 2e 18. NPV. Using the operating cash flow information from Problem 16, find the NPV of the project for Miglietti Restaurants if the manufacturing equipment can be sold for $140,000 at the end of the ten-year project and the cost of capital for this project is 8%. Hint: Use a spreadsheet. ANSWER Find the after-cash flow at disposal of the equipment: Book Value (Basis at end of five years) Original Cost $2,400,000 Depreciation is as follows: Year one $2,400,000 × 0.1429 = $342,960 Year two $2,400,000 × 0.2449 = $587,760 Year three $2,400,000 × 0.1749 Year four $2,400,000 × 0.1249 = $299,760 Year five $2,400,000 × 0.0893 = $214,320 Year six $2,400,000 × 0.0893 = $214,320 Year seven $2,400,000 × 0.0893 Year eight $2,400,000 × 0.0445 Accumulated depreciation = $2,400,000 = $419,760 = $214,320 = $106,800 Basis = $2,400,000 – $2,400,000 = $0 Gain on Disposal = $140,000 – $0 = $140,000 Tax Credit on Disposal = $140,000 × 0.30 = $42,000 After-tax cash flow at disposal = $140,000 – $42,000 = $98,000 NPV = -$2,400,000 + 278,518 / (1.08) + 375,863 / (1.08)2 + $350,762 / (1.08)3 + $341,532 / (1.08)4 + $344,230 / (1.08)5 + $374,223 / (1.08)6 + $405,956 / (1.08)7 + $407,280 / (1.08)8 + $410,780 / (1.08)9 + ($448,392 + $98,000) / (1.08)10 = $95,202.13 Accept the project. 19. Project cash flows and NPV. The managers of Classic Autos Incorporated plan to manufacture classic Thunderbirds (1957 replicas). The necessary foundry equipment will cost a total of $4,000,000 and will be depreciated using a five-year MACRS life. Projected sales in annual units for the next five years are 300 per year. If sales price is $27,000 per car, variable costs are $18,000 per car, and fixed costs are $1,200,000 annually, what is the annual operating cash flow if the tax rate is 30%? The equipment is sold for salvage for $500,000 at the end of year five. What is the after tax cash flow of the salvage? Net working capital increases by $600,000 at the beginning of the project (Year 0) and is reduced back to its original level in the final year. What is the incremental cash flow of the project? Using a discount rate of 12% for the project, determine whether the project be accepted or rejected with the NPV decision model? ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 361 ANSWER Annual depreciation of foundry equipment is: Year One, $4,000,000 × 0.20 = $800,000 Year Two, $4,000,000 × 0.32 = $1,280,000 Year Three, $4,000,000 × 0.192 = $768,000 Year Four, $4,000,000 × 0.1152 = $460,800 Year Five, $4,000,000 × 0.1152 = $460,800 Operating Cash Flows are: Annual Sales, 300 × $27,000 = $8,100,000 Annual COGS, 300 × $18,000 = $5,400,000 In thousands (rounded) Year 1 Year 2 Year 3 Year 4 Sales Revenue $8,100 $8,100 $8,100 $8,100 -COGS $5,400 $5,400 $5,400 $5,400 -Fixed Costs $1,200 $1,200 $1,200 $1,200 - Depreciation $800 $1,280 $ 768 $ 461 EBIT $ 700 $ 220 $ 732 $1,039 -Taxes (30%) $ 210 $ 66 $ 220 $ 312 Net Income $ 490 $ 154 $ 512 $ 727 +Depreciation $ 800 $1,280 $ 768 $ 461 Operating Cash Flows $1,290 $1,434 $1,280 $1,188 Year 5 $8,100 $5,400 $1,200 $ 461 $1,039 $ 312 $ 727 $ 461 $1,188 The equipment is sold for salvage for $500,000 at the end of year five. It has a book value of $4,000,000 – $800,000 – $1,280,000 – $768,000 – $460,800 – $460,800 = $230,400 Gain on Sale is $500,000 – $230,400 = $269,600 Tax on Gain is $269,600 × 0.30 = $80,880 And after-tax cash flow on disposal is $500,000 – $80,880 = $419,120. Incremental Cash Flows for Project (Answer in Thousands, $000) Account/Activity Investment ΔNWC OCF Salvage Value Total Cash Flows (Incremental) Year 0 -$4,000 -$ 600 Year 1 Year 2 Year 3 Year 4 Year 5 $ 600 $1,290 $1,434 $1,280 $1,188 $1,188 $ 419 -$4,600 $1,290 $1,434 $1,280 $1,188 $2,207 NPV @ 12% = -$4,600 + $1,290/1.12 + $1,434/1.122 + $1,280/1.123 + $1,188/1.124 + $2,207/1.125 = -$4,600 + 1,152 + 1,143 + $911 + $755 + $1,252 = $613.345 Accept the project because NPV is positive $613,345 (with rounding to nearest thousand). 20. Project cash flows and NPV. The sales manager has a new estimate for the sale of the Classic Thunderbirds in Problem 19. The annual sales volume will be as follows: ©2013 Pearson Education, Inc. Publishing as Prentice Hall 362 Brooks n Financial Management: Core Concepts, 2e Year 1: 240 Year 2: 280 Year 3: 340 Year 4: 360 Year 5: 280. Rework the cash flows for operating cash flows with these new sales estimates and find the internal rate of return for the project using the incremental cash flows. ANSWER Operating Cash Flows are: Annual Sales, Year 1 Year 2 Year 3 Year 4 Year 5 Annual COGS, Year 1 Year 2 Year 3 Year 4 Year 5 Sales Revenue - COGS - Fixed Costs - Depreciation EBIT - Taxes Net Income + Depreciation Operating Cash Flows Year 1 $6,480 $4,320 $1,200 $ 800 $ 160 $ 48 $ 112 $ 800 $ 912 = 240 × $27,000 = $6,480,000 = 280 × $27,000 = $7,560,000 = 340 × $27,000 = $9,180,000 = 360 × $27,000 = $9,720,000 = 280 × $27,000 = $7,560,000 = 240 × $18,000 = $4,320,000 = 280 × $18,000 = $5,040,000 = 340 × $18,000 = $6,120,000 = 360 × $18,000 = $6,480,000 = 280 × $18,000 = $5,040,000 Operating Cash Flows In thousands (rounded) Year 2 Year 3 Year 4 $7,560 $ 9,180 $ 9,720 $ 5,040 $ 6,120 $ 6,480 $ 1,200 $ 1,200 $ 1,200 $ 1,280 $ 768 $ 461 $ 40 $ 1,092 $ 1,579 $ 12 $ 328 $ 474 $ 28 $ 764 $ 1,050 $ 1,280 $ 768 $ 461 $ 1,308 $ 1,532 $ 1,511 Year 5 $ 7,560 $ 5,040 $ 1,200 $ 461 $ 859 $ 258 $ 601 $ 461 $ 1,062 And the incremental cash flows are: Incremental Cash Flows for Project (Answer in Thousands, $000) Account/Activity Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Investment -$4,000 ΔNWC -$ 600 $ 600 OCF $ 912 $1,308 $1,532 $1,511 $1,062 Salvage Value $ 419 Total Cash Flows -$4,600 $ 912 $1,308 $1,532 $1,511 $2,081 (Incremental) The IRR is via calculator: ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 363 CF0 = – 4,600,000 C01 = $912,000 C02 = $1,308,000 C03 = $1,532,000 C04 = $1,511,000 C05 = $2,081,000 and Solving for IRR = 15.7115% and if the hurdle rate is still 12%, accept the project. Solutions to Advanced Problems for Spreadsheet Application 1. Erosion costs. 1 2 3 4 5 6 7 8 9 Eroded Revenue $ 136,893.75 $ 6,637.50 $ (159,442.50) $ (337,587.50) $ (441,970.00) $ (498,845.00) $ (514,900.00) $ (490,525.00) $ (493,075.00) Reduced Costs $ 62,537.50 $ 3,024.00 $ (72,297.50) $ (153,527.00) $ (199,038.00) $ (224,313.00) $ (231,160.00) $ (220,435.00) $ (221,180.00) Eroded CF $ 74,356.25 $ 3,613.50 $ (87,145.00) $ (184,060.50) $ (242,932.00) $ (274,532.00) $ (283,740.00) $ (270,090.00) $ (271,895.00) 2. Working capital impact on project. FIND OCF: Revenue Variable Fixed S,G & A Depreciation EBIT Taxes Net Income Add Depreciation OCF 1 $10,000,000.00 $ 4,000,000.00 $ 1,500,000.00 $ 1,250,000.00 $ 2,000,000.00 $ 1,250,000.00 $ 462,500.00 $ 787,500.00 $ 2,000,000.00 $ 2,787,500.00 2 $13,000,000.00 $ 5,200,000.00 $ 1,500,000.00 $ 1,400,000.00 $ 3,200,000.00 $ 1,700,000.00 $ 629,000.00 $ 1,071,000.00 $ 3,200,000.00 $ 4,271,000.00 3 $17,000,000.00 $ 6,800,000.00 $ 1,500,000.00 $ 1,750,000.00 $ 1,920,000.00 $ 5,030,000.00 $ 1,861,100.00 $ 3,168,900.00 $ 1,920,000.00 $ 5,088,900.00 4 $23,000,000.00 $ 9,200,000.00 $ 1,500,000.00 $ 2,000,000.00 $ 1,152,000.00 $ 9,148,000.00 $ 3,384,760.00 $ 5,763,240.00 $ 1,152,000.00 $ 6,915,240.00 5 $18,000,000.00 $ 7,200,000.00 $ 1,500,000.00 $ 2,000,000.00 $ 1,120,000.00 $ 6,180,000.00 $ 2,286,600.00 $ 3,893,400.00 $ 1,120,000.00 $ 5,013,400.00 6 $12,000,000.00 $ 4,800,000.00 $ 1,500,000.00 $ 1,500,000.00 $ 576,000.00 $ 3,624,000.00 $ 1,340,880.00 $ 2,283,120.00 $ 576,000.00 $ 2,859,120.00 Capital outlay $ 10,000,000.00 Working Capital CHG $ Incremental CF Capital Change in WC OCF Incremental CF IRR NPV 0 2,000,000.00 $ 1 600,000.00 $ 2 3 4 5 6 800,000.00 $ 1,200,000.00 $ (1,000,000.00) $ (1,200,000.00) $ (2,400,000.00) 0 1 2 3 4 5 6 $ (10,000,000.00) $ (2,000,000.00) $ (600,000.00) $ (800,000.00) $ (1,200,000.00) $ 1,000,000.00 $ 1,200,000.00 $ 2,400,000.00 $ 2,787,500.00 $ 4,271,000.00 $ 5,088,900.00 $ 6,915,240.00 $ 5,013,400.00 $ 2,859,120.00 $ (12,000,000.00) $ 2,187,500.00 $ 3,471,000.00 $ 3,888,900.00 $ 7,915,240.00 $ 6,213,400.00 $ 5,259,120.00 26.84% $5,524,065.25 Solutions to Mini-‐Case BioCom, Inc.: Part 2, Evaluating a New Product Line This case is designed to integrate the student’s understanding of incremental cash flows for capital budgeting decisions and touches on all major topics: investment, operating cash flows, working capital, and disposal cash flows. It also requires students to apply the NPV calculations and decision rules covered in the previous chapter. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 364 Brooks n Financial Management: Core Concepts, 2e 1. What is the total relevant initial investment for BioCom’s new product line? Would you include the designs and prototypes? Would you include the change in net working capital? Cost of new plant and equipment: $24,000,000 Increase in net working capital $ 480,000 $24,480,000 The cost of designs and prototypes is a sunk cost and should not be included. 2. What is the cash flow resulting from disposal of the equipment at the end of the project? Disposal price $2,400,000 Book Value $24,000,000.9424(24,000,000) 1,382,400 Gain on disposal 1,017,600 Tax 34% 345,984 Cash flow from disposal (disposal price – tax) $2,054,016 3. Compute a schedule of depreciation for the plant and equipment. Depreciation Schedule year 1 2 3 4 5 6 rate 20% 32% 19.20% 11.52% 11.52% 0.0576 4,800,00 0 7,680,00 0 4,608,00 0 2,764,80 0 2,764,80 0 1,382,40 0 depreciatio n ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 365 4. Compute a schedule of operating cash flows for BioCom’s new product. Operating Cash Flows Year 1 Revenue 2 $16,500,000 $17,490,000 COGS 3 4 5 $18,539,400 $19,651,764 $20,830,870 6,600,000 6,996,000 7,415,760 7,860,706 Fixed Costs 600,000 600,000 600,000 600,000 600,000 S,G, and A 825,000 699,600 926,970 982,588 1,041,543 Depreciation 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 EBIT 3,675,000 1,514,400 4,988,670 7,443,670 8,092,178 Taxes 1,249,500 Net Income 514,896 $2,425,500 $999,504 1,696,148 $3,292,522 8,332,348 2,530,848 $4,912,822 2,751,341 $5,340,838 Add back dep. 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 Less erosion costs 1,650,000 1,650,000 1,650,000 1,650,000 1,650,000 Operating cash flows $5,575,500 $7,029,504 $6,250,522 $6,027,622 $6,455,638 5. Compute a schedule of incremental cash flows for BioCom’s new product. Incremental cash flows T0 Capital Spending Change in NWC OCF Disposal cash flow Incremental Cash Flow T1 T2 T3 T4 T5 -24,000,000 -480,000 480,000 5,575,500 7,029,504 6,250,522 6,027,622 6,455,638 2,054,016 -24,480,000 5,575,500 7,029,504 6,250,522 6,027,622 8,989,654 6. Compute the project’s net present value. NPV (24,480,00 0) 5,575,000 1.09 7,029,504 1.092 6,250,522 1.093 6,027,622 1.094 8,989,654 1.095 Cash flows discounted at 9% (24,480,00 0) 5,114,678.9 0 5,916,592.8 8 4,826,549.8 3 4,270,119.3 9 5,842,658.2 9 Summing the discounted cash flows, NPVè $1,490,599.29 7. Does your answer to Question 6 indicate that management should accept or reject the product? The net present value is positive, so the project should be accepted. 8. Challenge question. A spreadsheet is recommended for this question. a. Recompute your answers to Questions 4 through 7 assuming sales grow at 12% per year. b. Recompute your answers to Questions 4 through 7 assuming sales grow at 0% per year. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 366 Brooks n Financial Management: Core Concepts, 2e c. Comment on the sensitivity of the NPV to the rate of growth in sales. Spreadsheet solution is on next page. Operating Cash Flows (with sales growth rate = 12% per year) Year 1 2 3 4 5 $16,500,00 0 $18,480,00 0 $20,697,60 0 $23,181,3 12 $25,963,069 6,600,000 7,392,000 8,279,040 9,272,525 10,385,228 Fixed Costs 600,000 600,000 600,000 600,000 600,000 S,G, and A 825,000 924,000 1,034,880 1,159,066 1,298,153 Depreciation 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 EBIT 3,675,000 1,884,000 6,175,680 9,384,922 10,914,888 Taxes 1,249,500 640,560 2,099,731 3,190,873 3,711,062 $2,425,500 $1,243,440 $4,075,949 $6,194,04 8 $7,203,826 Add back dep. 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 Less erosion costs 1,650,000 1,650,000 1,650,000 1,650,000 1,650,000 $5,575,500 $7,273,440 $7,033,949 $7,308,84 8 $8,318,626 T1 T2 T3 T4 Revenue COGS Net Income Operating cash flows Incremental cash flows T0 Capital Spending -24,000,000 Change in NWC -480,000 OCF T5 480,000 5,575,500 7,273,440 7,033,949 7,308,848 Disposal cash flow 8,318,626 2,054,016 Incremental Cash Flow -24,480,000 NPV @ 9% $ 4,419,790.77 5,575,500 7,273,440 7,033,949 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 7,308,848 10,852,642 Chapter 10 n Cash Flow Estimation 367 Operating Cash Flows(sales growth rate= 0%) Year 1 2 3 4 5 $16,500,000 $16,500,000 $16,500,000 $16,500,000 $16,500,000 6,600,000 6,600,000 6,600,000 6,600,000 6,600,000 Fixed Costs 600,000 600,000 600,000 600,000 600,000 S,G, and A 825,000 825,000 825,000 825,000 825,000 Depreciation 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 EBIT 3,675,000 795,000 3,867,000 5,710,200 5,710,200 Taxes 1,249,500 270,300 1,314,780 1,941,468 1,941,468 $2,425,500 $524,700 $2,552,220 $3,768,732 $3,768,732 Add back dep. 4,800,000 7,680,000 4,608,000 2,764,800 2,764,800 Less erosion costs 1,650,000 1,650,000 1,650,000 1,650,000 1,650,000 $5,575,500 $6,554,700 $5,510,220 $4,883,532 $4,883,532 T1 T2 T3 T4 T5 Revenue COGS Net Income Operating cash flows Incremental cash flows T0 Capital Spending Change in NWC –24,000,000 –480,000 OCF 480,000 5,575,500 6,554,700 5,510,220 4,883,532 Disposal cash flow 4,883,532 2,054,016 Incremental Cash Flow –24,480,000 NPV @ 9% $(1,312,487.24) 5,575,500 6,554,700 5,510,220 4,883,532 7,417,548 NPV is quite sensitive to the growth rate of sales. Doubling the growth rate almost triples the NPV, while a flat growth rate leads to a negative NPV and the project would be rejected. This sensitivity suggests that the project may be riskier than it seemed from the most likely scenario of 6% growth. ©2013 Pearson Education, Inc. Publishing as Prentice Hall 368 Brooks n Financial Management: Core Concepts, 2e Additional Problems with Solutions 1. Erosion cost. Volvo is looking to introduce a new “hybrid” car in the US. Their analysts estimate that they will sell 20,000 of these new cars per year. The unit cost per car is $18,000 and they plan on selling the vehicle for $22,000. If the current sales of Volvo’s sedan, which costs $15,000 to produce and sells for $20,000, go down from 25,000 units per year to 18,000 units, is this a worthwhile move for Volvo? Calculate the amount of the erosion cost and the incremental cash flow that will result if they go ahead with the launch. ANSWER (Slides 10-‐35 to 10-‐36) OLD SEDAN Current EBIT = # of cars sold × (Price – Cost)=25,000 × ($20,000-$15,000) = $125,000,000 EBIT (after launch) = 18,000 × ($5000) = $90,000,000 Lost EBIT = $125,000,000 – $90,000,000 = $35,000,000= Erosion Cost HYBRID EBIT = 20,000 × ($22,000-$18,000) = $80,000,000 COMBINED EBIT = $80,000,000 + $90,000,000 = $170,000,000 Since the Combined EBIT is higher than the current EBIT by $45,000, 000 it would be a worthwhile move for Volvo. 2. Depreciation rates. R.K. Boats Inc. has just installed a new hydraulic lift system which is being categorized as a 5-year class-life asset under MACRS. The total purchase cost plus installation amounted to $750,000. RKB has always used straightline depreciation in the past, but their accountant is pushing the owner to use the MACRS rates this time around. The owner seems to think that it really doesn’t matter since the total depreciation under each method will still sum up to $750,000 and be spread over 6 years with the application of the “half-year” convention. Do you agree with the owner? Please explain by making the appropriate calculations. RKB’s hurdle rate is 10% and its marginal tax rate is 30%. ANSWER (Slides 10-‐37 to 10-‐38) Under straight-line depreciation: Annual dep.exp. = Cost + Installation / Life = $750,000/5 = $150,000 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 369 Using “half-year” convention the comparison of yearly depreciation under the 2 methods is as follows: MACRS rate MACRS Dep. St. Line Dep Diff. Tax Gain 1 20% 150000 75,000 75,000 22500 2 32% 240000 150000 90,000 27000 3 19.20% 144000 150000 -6,000 -1800 4 11.52% 86400 150000 -63,600 -19080 5 11.52% 86400 150000 -63,600 -19080 6 5.76% 43200 75000 -31,800 -9540 750000 750000 0 0 Year Total 100% NPV @10% $2,265.82 So clearly, with the tax advantages coming in earlier i.e. in the first two years, the time value of money advantages makes it a positive NPV move. 3. Disposal Cash Flow. Reddy Laboratories had purchased some manufacturing equipment five years ago for a total cost of $3,000,000, and has been depreciating it using the MACRS – 7 year class-life rates. Currently, newer, more efficient equipment is available and Reddy has found a buyer who is willing to pay $$500,000 for the old equipment. If the firm, which has a marginal tax rate of 35%, disposes of the system to the buyer, how much will the after-tax cash flows add up to? ANSWER (Slides 10-‐39 to 10-‐40) The 7-year MACRS rates are as follows: After 5 years, the book value would be (0893+.0893+.0445) × $3,000,000 Book value = 0.2231 × $3,000,000 = $669, 300 Loss on sale = Selling Price – Book value = $500,000 – $669,300 = -$169,300 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 370 Brooks n Financial Management: Core Concepts, 2e Tax credit = Tax rate × Loss = 0.35 × $169,300 = $59,255 After-tax cash inflow = Selling price + Tax credit = $500,000 + $59,255 = $559,255 4. Operating cash flow (growing each year; MACRS). Balik Ventures is looking at a project with the following forecasted sales: first-year sales quantity of 20,000 with an annual growth rate of 4% over the next 5 years. The sales price per unit is $35.00 and will grow at 5% per year. The production costs are expected to be 45% of the current year’s sales price. The manufacturing equipment to aid this project will have a total cost (including installation) of $2,200,000. It will be depreciated using MACRS and has a five-year MACRS life classification. Fixed costs are $285,000 per year. The firm has a tax rate of 35%.What is the operating cash flow for this project over these 5 years? Hint: Use a spreadsheet and round units to the nearest whole number. ANSWER (Slides 10-‐41 to 10-‐43) Based on 5-year MACRS rates, the annual depreciation expense is as follows: Dep. Basis è 2,200,000 Year Rate Depreciation 1 0.2 440000 2 0.32 704000 3 0.192 422400 4 0.1152 253440 5 0.1152 253440 6 0.0576 126720 The operating cash flow over the 5-year period is calculated as follows: Rate Year 1 Year 2 Year 3 Year 4 Year 5 Unit sales 4% 30,000 31,200 32,448 33,746 35,096 Sales price 5% $35.00 $36.75 $38.59 $40.52 $42.54 Revenues Prod. Costs $1,050,000 $1,146,600 $1,252,087 $1,367,279 $1,493,069 45% $472,500 $515,970 $563,439 $615,276 $671,881 Fixed costs $ 285,000 $ 285,000 $ 285,000 $ 285,000 $ 285,000 Depreciation $440,000 $704,000 $422,400 $253,440 $253,440 ($147,500) ($358,370) ($18,752) $213,564 $282,748 ($51,625) ($125,430) ($6,563) $74,747 $98,962 Net Income ($95,875) ($232,941) ($12,189) $138,816 $183,786 Add Dep $440,000 $422,400 $253,440 $253,440 EBIT Taxes 35% $704,000 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 371 Op. Cash Flow $344,125 $471,060 $410,211 $392,256 $437,226 5. Comprehensive Capital Budgeting. Let’s say that Balik Ventures has forecasted the operating cash flows over the 5 year project life as shown in Problem 4 above. The project will entail an investment of 10% of the first year’s forecasted production costs for working capital, which will be recovered at the end of the 5-year life. In addition, the equipment will be sold for 20% of its initial cost when the project is terminated. If the firm uses a hurdle rate of 14% for similar risk projects, should they go ahead with this venture? Why or why not? ANSWER (Slides 10-‐44 to 10-‐47) In addition to the operating cash flow for years 1-5, we need to calculate the initial year and terminal year cash flow and add them in. Initial Year Cash Flow (Year 0) Cost of Equipment = $2,200,000 Increase in NWC = .10 × (Year 1 production cost) = 0.1 × $472,500 = $47,250 Total cost at start up = -2, 247,250 Terminal Year Cash Flow Recovery of NWC = +$47, 250 After-tax Salvage Value of Equipment = Selling Price –Tax on Gain Where; Tax on gain = Tax rate × (Selling Price – Book Value) Selling Price = 20% of Cost = .2 × (2,200,000) = $440,000 Book Value = Year 6 MACRS Dep. Rate × Dep. Basis=.0576 × 2200000=$126,720 Tax on Gain = 0.35 × ($440,000-$126.720) = $109,648 After-tax Salvage Value = $440,000-$109,648= $330,352 Total Terminal Year Cash Flow (not including OCF) = 47, 250 + 330,352 = 377,602 Year Cash Flow 0 –$2,247,250 1 $344,125 2 $471,060 3 $410,211 4 $392,256 5 $437,226+377,602=$814,828 NPV @10% = -$463,045.5 REJECT THE PROJECT! ©2013 Pearson Education, Inc. Publishing as Prentice Hall