【文章內(nèi)容簡介】 FC + Depreciation)(1 – tC)] / [(P – VC)(1 – tC)] QA = [($340,000 + $20,000) (1 – )] / [($ – ) (1 – )] QA = 281, b. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the in initial investment by the sevenyear annuity factor, discounted at 15 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA15%,7 EAC = $140,000 / EAC = $33, 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) $140,000 = C{[1 – (1/)7 ] / .15} C = $33, Now we can calculate the financial breakeven point. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = [$33, + $340,000(.65) – $20,000(.35)] / [($2 – ) (.65)] QF = 297, or about 297,657 units10. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the in initial investment by the fiveyear annuity factor, discounted at 8 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA8%,5 EAC = 165。300,000 / EAC = 165。75, 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) 165。300,000 = C{[1 – (1/)5 ] / .08} C = 165。75, The annual depreciation is the cost of the equipment divided by the economic life, or: Annual depreciation = 165。300,000 / 5 Annual depreciation = 165。60,000 Now we can calculate the financial breakeven point. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = [165。75, + 165。100,000(.66) – 165。60,000()] / [(165。60 – 8) (.34)] QF = 3, or about 3,518 units Intermediate11. a. At the accounting breakeven, the IRR is zero percent since the project recovers the initial investment. The payback period is N years, the length of the project since the initial investment is exactly recovered over the project life. The NPV at the accounting breakeven is: NPV = I [(1/N)(PVIFAR%,N) – 1] b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and the NPV is negative and equal to the initial cash outlay. c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true, then the IRR of the project is equal to the required return. It is impossible to state the payback period, except to say that the payback period must be less than the length of the project. Since the discounted cash flows are equal to the initial investment, the undiscounted cash flows are greater than the initial investment, so the payback must be less than the project life. 12. Using the tax shield approach, the OCF at 110,000 units will be: OCF = [(P – v)Q – FC](1 – tC) + tC(D) OCF = [($28 – 19)(110,000) – 150,000]() + ($420,000/4) OCF = $590,100 We will calculate the OCF at 111,000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is: OCF = [($28 – 19)(111,000) – 150,000]() + ($420,000/4) OCF = $596,040 The sensitivity of the OCF to changes in the quantity sold is: Sensitivity = DOCF/DQ = ($596,040 – 590,100)/(111,000 – 110,000) DOCF/DQ = +$ OCF will increase by $ for every additional unit sold. 13. a. The basecase, bestcase, and worstcase values are shown below. Remember that in the bestcase, sales and price increase, while costs decrease. In the worstcase, sales and price decrease, and costs increase. Scenario Unit sales Variable cost Fixed costs Base 190 元15,000 元225,000 Best 209 元13,500 元202,500 Worst 171 元16,500 元247,500 Using the tax shield approach, the OCF and NPV for the base case estimate is: OCFbase = [(元21,000 – 15,000)(190) – 元225,000]() + (元720,000/4) OCFbase = 元657,750 NPVbase = –元720,000 + 元657,750(PVIFA15%,4) NPVbase = 元1,157, The OCF and NPV for the worst case estimate are: OCFworst = [(元21,000 – 16,500)(171) – 元247,500]() + (元720,000/4) OCFworst = 元402,300 NPVworst = –元720,000 + 元402,300(PVIFA15%,4) NPVworst = +元428, And the OCF and NPV for the best case estimate are: OCFbest = [(元21,000 – 13,500)(209) – 元202,500]() + (元720,000/4) OCFbest = 元950,250 NPVbest = –元720,000 + 元950,250(PVIFA15%,4) NPVbest = 元1,992, b. To calculate the sensitivity of the NPV to changes in fixed costs we choose another level of fixed costs. We will use fixed costs of 元230,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get: OCF = [(元21,000 – 15,000)(190) – 元230,000]() + (元720,000/4) OCF = 元654,500 And the NPV is: NPV = –元720,000 + 元654,500(PVIFA15%,4) NPV = 元1,148, The sensitivity of NPV to changes in fixed costs is: DNPV/DFC = (元1,157, – 1,148,)/(元225,000 – 230,000) DNPV/DFC = – For every dollar FC increase, NPV falls by . c. The accounting breakeven is: QA = (FC + D)/(P – v) QA = [元225,000 + (元720,000/4)]/(元21,000 – 15,000) QA = 68 At the accounting breakeven, the DOL is: DOL = 1 + FC/OCF DOL = 1 + (元225,000/元180,000) = For each 1% increase in unit sales, OCF will increase by %.14. The marketing study and the research and development are both sunk costs and should be ignored. 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。 55,000 = €38,500,000E