The pro forma income statement will be: Sales
Variable costs Costs
Depreciation EBT Taxes
Net income
�38,115,000 12,384,000 6,750,000 2,600,000 16,381,000 6,552,400 �9,828,600 Using the bottom up OCF calculation, we get:
OCF = Net income + Depreciation = �9,828,600 + 2,600,000 OCF = �12,428,600 And the best-case NPV is:
NPV = –�18.2M – .95M + �12,428,600(PVIFA14%,7) + .95M/1.147 NPV = �34,527,280.98
Worst-case 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: Sales New clubs Exp. clubs Cheap clubs
�630 ? 49,500 = �31,185,000 �1,100 ? (– 14,300) = – 15,730,000
�400 ? 9,000 = 3,600,000 �19,055,000
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. costs New clubs Exp. clubs Cheap clubs
�352 ? 49,500 = �17,424,000 �600 ? (– 14,300) = – 8,580,000 �180 ? 9,000 = 1,620,000 �10,464,000
16.
The pro forma income statement will be: Sales
Variable costs Costs
Depreciation EBT Taxes
Net income
�19,055,000 10,464,000 8,250,000 2,600,000 – 2,259,000
903,600 *assumes a tax credit –�1,355,400
Using the bottom up OCF calculation, we get: OCF = NI + Depreciation = –�1,355,400 + 2,600,000 OCF = �1,244,600 And the worst-case NPV is:
NPV = –�18.2M – .95M + �1,244,600(PVIFA14%,7) + .95M/1.147 NPV = –�13,433,120.34
To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need to change the price of the new club. We will choose �750, but the choice is irrelevant as the sensitivity will be the same no matter what price 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: Sales New clubs Exp. clubs Cheap clubs
�750 ? 55,000 = �41,250,000 �1,100 ? (– 13,000) = –14,300,000
�400 ? 10,000 = 4,000,000 �30,950,000
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. costs New clubs Exp. clubs Cheap clubs
�320 ? 55,000 = �17,600,000 �600 ? (–13,000) = –7,800,000 �180 ? 10,000 = 1,800,000 �11,600,000
The pro forma income statement will be: Sales
Variable costs Costs
Depreciation EBT Taxes
Net income
�30,950,000 11,600,000 7,500,000 2,600,000 9,250,000 3,700,000 � 5,550,000 Using the bottom up OCF calculation, we get: OCF = NI + Depreciation = �5,550,000 + 2,600,000 OCF = �8,150,000 And the NPV is:
NPV = –�18.2M – 0.95M + �8.15M(PVIFA14%,7) + .95M/1.147 NPV = �16,179,339.89
So, the sensitivity of the NPV to changes in the price of the new club is: ?NPV/?P = (�16,179,339.89 – 9,103,636.91)/(�750 – 700) ?NPV/?P = �141,514.06
For every euro increase (decrease) in the price of the clubs, the NPV increases (decreases) by �141,514.06.
To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply need to change the quantity sold. We will choose 60,000 units, but the choice is irrelevant 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: Sales New clubs Exp. clubs Cheap clubs
�700 ? 60,000 = �42,000,000 �1,100 ? (– 13,000) = –14,300,000
�400 ? 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. costs New clubs Exp. clubs Cheap clubs
�320 ? 60,000 = �19,200,000 �600 ? (–13,000) = –7,800,000 �180 ? 10,000 = 1,800,000 �13,200,000
The pro forma income statement will be: Sales
Variable costs Costs
Depreciation EBT Taxes
Net income
�31,700,000 13,200,000 7,500,000 2,600,000 8,400,000 3,360,000 � 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 = –�18.2M – �0.95M + �7.64(PVIFA14%,7) + �0.95M/1.147 NPV = �13,992,304.43
So, the sensitivity of the NPV to changes in the quantity sold is: ?NPV/?Q = (�13,992,304.43 – 9,103,636.91)/(60,000 – 55,000) ?NPV/?Q = �977.73
For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by �977.73.
The base-case NPV is:
NPV = –￡1,750,000 + ￡420,000(PVIFA16%,10) NPV = ￡279,955.54
17. a.
18.
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:
￡1,500,000 = (￡60)Q(PVIFA16%,9) Q = ￡1,500,000/[￡60(4.6065)] Q = 5,427.11
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.
The ￡1,500,000 is the market value of the project. If you continue with the project in one year, you forego the ￡1,500,000 that could have been used for something else. If the project is a success, present value of the future cash flows will be: PV future CFs = ￡60(9,000)(PVIFA16%,9) PV future CFs = ￡2,487,533.69
From the previous question, if the quantity sold is 4,000, we would abandon the project, and the cash flow would be ￡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 = [(￡2,487,533.69 + ￡1,500,000)/2] + ￡420,000 Expected value of project at year 1 = ￡2,413,766.85
The NPV is the present value of the expected value in one year plus the cost of the equipment, so:
NPV = –￡1,750,000 + (￡2,413,766.85)/1.16 NPV = ￡330,833.49
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 = ￡60(4,000)(PVIFA16%,9) PV future CFs = ￡1,105,570.53
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 = ￡1,500,000 – 1,105,570.53 Gain from option to abandon = ￡394,429.47
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)(￡394,429.47)/1.16 Option value = ￡170,012.70
c. a.
b.
英文版罗斯公司理财习题答案chap009.doc
