27. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 41,000. The
OCF at this level of sale is: OCF = [($230 – 210)(41,000) – $450,000](0.62) + 0.38($1,700,000M/5) OCF = $358,600 The sensitivity of changes in the OCF to quantity sold is: ?OCF/?Q = ($358,600 – 346,200)/(41,000 – 40,000) ?OCF/?Q = +$12.40 The NPV at this level of sales is: NPV = –$1.7M – $450,000 + $358,600(PVIFA13%,5) + [$450K + $500K(1 – .38)]/1.135 NPV = –$476,223.32 And the sensitivity of NPV to changes in the quantity sold is: ?NPV/?Q = (–$476,223.32 – (–519,836.99))/(41,000 – 40,000) ?NPV/?Q = +$43.61 You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV
changes $43.61 for every unit sale, so we can divide the NPV for 40,000 units by the sensitivity to get a change in quantity. Doing so, we get: –$519,836.99 = $43.61(?Q) ?Q = –11,919 For a zero NPV, we need to increase sales by 11,919 units, so the minimum quantity is: QMin = 40,000 + 11,919 QMin = 51,919
28. We will use the bottom up approach to calculate the operating cash flow. Assuming we operate the
project for all four years, the cash flows are:
Year 0 1 2 3 4 Sales ?7,000,000 ?7,000,000 ?7,000,000 ?7,000,000 Operating costs 3,000,000 3,000,000 3,000,000 3,000,000 Depreciation 2,000,000 2,000,000 2,000,000 2,000,000 EBT ?2,000,000 ?2,000,000 ?2,000,000 ?2,000,000 Tax 760,000 760,000 760,000 760,000 Net income ?1,240,000 ?1,240,000 ?1,240,000 ?1,240,000 +Depreciation 2,000,000 2,000,000 2,000,000 2,000,000 Operating CF ?3,240,000 ?3,240,000 ?3,240,000 ?3,240,000 Change in NWC –?2,000,000 0 0 0 ?2,000,000 Capital spending –8,000,000 0 0 0 0 Total cash flow –?10,000,000 ?3,240,000 ?3,240,000 ?3,240,000 ?5,240,000 There is no salvage value for the equipment. The NPV is: NPV = –?10,000,000 + ?3,240,000(PVIFA16%,4) + ?5,2400,000/1.164 NPV = ?170,687.46 The cash flows if we abandon the project after one year are:
Year 0 1 Sales ?7,000,000 Operating costs 3,000,000 Depreciation 2,000,000 EBT ?2,000,000 Tax 760,000 Net income ?1,240,000 +Depreciation 2,000,000 Operating CF ?3,240,000 Change in NWC –?2,000,000 ?2,000,000 Capital spending –8,000,000 6,310,000 Total cash flow –?10,000,000 ?11,550,000 The book value of the equipment is: Book value = ?8,000,000 – (1)(?8,000,000/4) Book value = ?6,000,000
So the taxes on the salvage value will be: Taxes = (?6,000,000 – 6,500,000)(.38) Taxes = –?190,000
This makes the aftertax salvage value: Aftertax salvage value = ?6,500,000 – 190,000 Aftertax salvage value = ?6,310,000
The NPV if we abandon the project after one year is: NPV = –?10,000,000 + ?11,550,000/1.16 NPV = –?43,103.45
If we abandon the project after two years, the cash flows are: Year Sales
Operating costs Depreciation EBT Tax
Net income +Depreciation Operating CF
Change in NWC Capital spending Total cash flow
0
–?2,000,000 –8,000,000 –?10,000,000 1
?7,000,000 3,000,000 2,000,000 ?2,000,000 760,000 ?1,240,000 2,000,000 ?3,240,000
0 0
?3,240,000 2
?7,000,000 3,000,000 2,000,000 ?2,000,000 760,000 ?1,240,000 2,000,000 ?3,240,000
?2,000,000 5,240,000 ?10,480,000
The book value of the equipment is: Book value = ?8,000,000 – (2)(?8,000,000/4) Book value = ?4,000,000
So the taxes on the salvage value will be: Taxes = (?4,000,000 – 6,000,000)(.38) Taxes = –?760,000
This makes the aftertax salvage value: Aftertax salvage value = ?6,000,000 – 760,000 Aftertax salvage value = ?5,240,000
The NPV if we abandon the project after two years is: NPV = –?10,000,000 + ?3,240,000/1.16 + ?10,480,000/1.162 NPV = ?581,450.65
If we abandon the project after three years, the cash flows are: Year Sales
Operating costs Depreciation EBT Tax
Net income +Depreciation Operating CF
Change in NWC Capital spending Total cash flow
0
–?2,000,000 –8,000,000 –?10,000,000 1
?7,000,000 3,000,000 2,000,000 ?2,000,000 760,000 ?1,240,000 2,000,000 ?3,240,000
0 0
?3,240,000 2
?7,000,000 3,000,000 2,000,000 ?2,000,000 760,000 ?1,240,000 2,000,000 ?3,240,000
0 0
?3,240,000 3 ?7,000,000 3,000,000 2,000,000 ?2,000,000 760,000 ?1,240,000 2,000,000 ?3,240,000
?2,000,000 2,620,000 ?7,860,000
The book value of the equipment is: Book value = ?8,000,000 – (3)(?8,000,000/4) Book value = ?2,000,000
So the taxes on the salvage value will be: Taxes = (?2,000,000 – 3,000,000)(.38) Taxes = –?380,000
This makes the aftertax salvage value: Aftertax salvage value = ?3,000,000 – 380,000 Aftertax salvage value = ?2,620,000
The NPV if we abandon the project after two years is:
NPV = –?10,000,000 + ?3,240,000(PVIFA16%,2) + ?7,860,000/1.163 NPV = ?236,520.56
We should abandon the equipment after two years since the NPV of abandoning the project after two years has the highest NPV.
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