【正文】 ant as the sensitivity will be the same no matter what quantity we choose. We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs€700 180。 60,000 = €42,000,000Exp. clubs€1,100 180。 (– 13,000) = –14,300,000Cheap clubs€400 180。 10,000 = 4,000,000€31,700,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs€320 180。 60,000 = €19,200,000Exp. clubs€600 180。 (–13,000) = –7,800,000Cheap clubs€180 180。 10,000 = 1,800,000€13,200,000 The pro forma ine statement will be:Sales€31,700,000Variable costs13,200,000Costs7,500,000Depreciation 2,600,000EBT8,400,000Taxes 3,360,000Net ine€ 5,040,000 Using the bottom up OCF calculation, we get: OCF = NI + Depreciation = €5,040,000 + 2,600,000 OCF = €7,640,000 The NPV at this quantity is: NPV = –€ – € + €(PVIFA14%,7) + € NPV = €13,992, So, the sensitivity of the NPV to changes in the quantity sold is: DNPV/DQ = (€13,992, – 9,103,)/(60,000 – 55,000) DNPV/DQ = € For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by €.17. a. The basecase NPV is: NPV = –163。1,750,000 + 163。420,000(PVIFA16%,10) NPV = 163。279, b. We would abandon the project if the cash flow from selling the equipment is greater than the present value of the future cash flows. We need to find the sale quantity where the two are equal, so: 163。1,500,000 = (163。60)Q(PVIFA16%,9) Q = 163。1,500,000/[163。60()] Q = 5, Abandon the project if Q 5,428 units, because the NPV of abandoning the project is greater than the NPV of the future cash flows. c. The 163。1,500,000 is the market value of the project. If you continue with the project in one year, you forego the 163。1,500,000 that could have been used for something else.18. a. If the project is a success, present value of the future cash flows will be: PV future CFs = 163。60(9,000)(PVIFA16%,9) PV future CFs = 163。2,487, From the previous question, if the quantity sold is 4,000, we would abandon the project, and the cash flow would be 163。1,500,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so: Expected value of project at year 1 = [(163。2,487, + 163。1,500,000)/2] + 163。420,000 Expected value of project at year 1 = 163。2,413, The NPV is the present value of the expected value in one year plus the cost of the equipment, so: NPV = –163。1,750,000 + (163。2,413,)/ NPV = 163。330, b. If we couldn’t abandon the project, the present value of the future cash flows when the quantity is 4,000 will be: PV future CFs = 163。60(4,000)(PVIFA16%,9) PV future CFs = 163。1,105, The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project, so: Gain from option to abandon = 163。1,500,000 – 1,105, Gain from option to abandon = 163。394, We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is: Option value = (.50)(163。394,)/ Option value = 163。170,19. If the project is a success, present value of the future cash flows will be: PV future CFs = 163。60(18,000)(PVIFA16%,9) PV future CFs = 163。4,975, If the sales are only 4,000 units, from Problem 18, we know we will abandon the project, with a value of 163。1,500,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so: Expected value of project at year 1 = [(163。4,975, + 163。1,500,000)/2] + 163。420,000 Expected value of project at year 1 = 163。3,657, The NPV is the present value of the expected value in one year plus the cost of the equipment, so: NPV = –163。1,750,000 + 163。3,657, NPV = 163。1,403, The gain from the option to expand is the present value of the cash flows from the additional units sold, so: Gain from option to expand = 163。60(9,000)(PVIFA16%,9) Gain from option to expand = 163。2,487, We need to find the value of the option to expand times the likelihood of expansion. We also need to find the value of the option to expand today, so: Option value = (.50)(163。2,487,)/ Option value = 163。1,072,20. a. The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge divided by the contribution margin (selling price minus variable cost). In this case, there are no fixed costs, and the depreciation is the entire price of the press in the first year. So, the accounting breakeven level of sales is: QA = [(FC + Depreciation)(1 – tC)] / [(P – VC)(1 – tC)] QA = [($0 + 2,000) (1 – )] / [($10 – 8) (1 – )] QA = 1,000 b. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). The initial investment is the $10,000 in licensing fees. Dividing the in initial investment by the threeyear annuity factor, discounted at 12 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA12%,3 EAC = $10,000 / EAC = $4, Note, this calculation solves for the annuity payment with the initial investment as the present value of the annuity, in other words: PVA = C({1 – [1/(1 + R)]t } / R) $10,000