Week 6 | Depreciation | Book Value

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    CHAPTER 9 Answers to critical thinking and concepts review questions 1.  In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 4.  Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any one particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure remains unchanged, financing costs are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone  principle. 5.  Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus depreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield T C D. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental after-tax cash flows. 6.  There are two particularly important considerations. The first is erosion. Will the essentialised  book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other  publishers step in and produce such a product? If so, then any erosion is much less relevant. A  particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s  perspective) or new books (not good). The concern arises any time that there is an active market for used product. 11.  It is true that if average revenue is less than average cost, the firm is losing money. This much of the statement is therefore correct. At the margin, however, accepting a project with a marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow. At the margin, even if a firm is losing money, as long as marginal revenue exceeds marginal cost, the firm will lose less than it would without the new project. Solutions to questions and problems 1.  The $7.5 million acquisition cost of the land six years ago is a sunk cost. The $10.3 million current after-tax value of the land is an opportunity cost if the land is used rather than sold off. The $24 million cash outlay and $975   000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is: Cash flow = $10   300   000 + 24   000   000 + 975   000 Cash flow = $35   275   000 2.  Sales due solely to the new product line are: 29   000($18   500) = $536   500   000   Increased sales of the caravan line occur because of the new product line introduction; thus: 2500($73   000) = $182   500   000 in new sales is relevant. Erosion of luxury caravan sales is also due to the new portable campers; thus: 750($115   000) = $86   250   000 loss in sales is relevant. The net sales figure to use in evaluating the new line is thus:  Net sales = $536   500   000 + 182   500   000 – 86   250   000  Net sales = $632   750   000 3.  We need to construct an income statement. The income statement is: Sales $ 750   000 Variable costs 412   500 Fixed costs 182   500 Depreciation 86   000 EBIT $ 69   000 Taxes@35% 20   700  Net income $ 48   300 4. To find the OCF, we need to complete the income statement as follows: Sales $ 657   900 Variable costs 352   900 Depreciation 97   500 EBIT $ 207   500 Taxes@35% 72   625  Net income $ 134   875 The OCF for the company is: OCF = EBIT + Depreciation – Taxes   OCF = $207   500 + 97   500 – 72   625 OCF = $232   375 The depreciation tax shield is the depreciation times the tax rate, so: Depreciation tax shield = Depreciation( T  C  ) Depreciation tax shield = 0.35($97   500) Depreciation tax shield = $34   125 The depreciation tax shield shows us the increase in OCF by being able to expense depreciation. 5. The diminishing value method of depreciation is twice the rate of straight line. A seven-year asset is 14.286%pa so the DV rate is 28.571%. Remember, to find the amount of depreciation for any year, you multiply the written down value of the asset times the DV percentage for the year. The depreciation schedule for this asset is: Beginning Year Beginning Book Value DepreciationDepreciationAllowance Ending Book Value 1 $870 000.00 28.571% $248 571.43 $621 428.57   2 $621 428.57 28.571% $177 551.02 $443 877.55 3 $443 877.55 28.571% $126 822.16 $317 055.39 4 $317 055.39 28.571% $90 587.26 $226 468.14 5 $226 468.14 28.571% $64 705.18 $161 762.96 6 $161 762.96 28.571% $46 217.99 $115 544.97 7 $115 544.97 28.571% $33 012.85 $82 532.12 6.  The asset has a useful life of 8 years and we want to find the book value of the asset after 5 years. With straight-line depreciation, the depreciation each year will be: Annual depreciation = $635   000 / 8 Annual depreciation = $79   375 So, after five years, the accumulated depreciation will be: Accumulated depreciation = 5($79   375) Accumulated depreciation = $396   875 The book value at the end of Year Five is thus: BV 5  = $635   000 – 396   875 BV 5  = $238   125 The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured. After-tax salvage value = $125   000 + ($238   125 – 125   000)(0.3) After-tax salvage value = $158   937.50 To find the taxes on salvage value, remember to use the equation: Taxes on salvage value = (BV – MV) T  C   This equation will always give the correct sign for a tax inflow (refund) or outflow (payment). 7.  To find the book value at the end of four years, we need to find the accumulated depreciation for the first four years. We use a table as in Problem 5, the DV depreciation rate is 40%. The depreciation schedule for this asset is: Year Beginning Book Value Dep. % Depreciation  Allowance Ending Book Value 1 $6   400   000.00 40.00% $ 2   560   000.00 $3   840   000.00 2 3   840   000.00 40.00% $ 1   536   000.00 2   304   000.00 3 2   304   000.00 40.00% $ 921   600.00 1   382   400.00 4 1   382   400.00 40.00% $ 552   960.00 829   440.00 The asset is sold at a gain to book value, so this gain is taxable.   After-tax salvage value = $1   530   000 + ($829   440 – 1   530   000)(.3) After-tax salvage value = $1   319   832.00 8.  We need to calculate the OCF, so we need an income statement. The lost sales of the current sound board sold by the company will be a negative since it will lose the sales. Sales of new $39   600   000 Lost sales of old –7   359   000 Variable costs 17   732   550 Fixed costs 2   400   000 Depreciation 1   975   000 EBT $10   133   450 Tax 3   040   035  Net income $7   093   415 The OCF for the company is: OCF = EBIT + Depreciation – Taxes   OCF = $10   133   450 + 1   975   000 – 3   040   035 OCF = $9   068   415 11.  The cash outflow at the beginning of the project will increase because of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we must also account for the taxes that will  be paid on this sale. So, the cash flows for each year of the project will be: Year Cash Flow 0 – $2   010   000 = –$1   860   000 – 150   000 1 809   000 2 809   000 3 1   081   500 = $809   000 + 150   000 + 175   000 + (0 – 175   000)(.30) And the NPV of the project is:  NPV = –$2   010   000 + $809   000(PVIFA 14%,2 ) + ($1   081   500 / 1.14 3 )  NPV = $52   130.05 13.  First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation = $735   000/5 Annual depreciation = $147   000  Now, we calculate the after-tax salvage value. The after-tax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so: After-tax salvage value = MV + (BV – MV) T  C   
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