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With these cash flows, the NPV of the project is:
b. To find the minimum number of cartons sold to still break even, we need to use the tax shield
approach to calculating OCF, and solve the problem similar to finding a bid price. Using the
initial cash flow and salvage value we already calculated, the equation for a zero NPV of the
project is:
NPV = 0 = –$2,100,000 – 325,000 + OCF(PVIFA11%,5) + [($325,000 + 118,500)/1.115]
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
Year
1
2
3
4
5
Sales
$2,424,189
$2,424,189
$2,424,189
$2,424,189
$2,424,189
Variable costs
1,145,429
1,145,429
1,145,429
1,145,429
1,145,429
Year
1
2
3
4
5
Operating CF
$584,920
$584,920
$584,920
$584,920
$584,920
Change in NWC
0
0
0
0
325,000
c. To find the highest level of fixed costs and still break even, we need to use the tax shield approach
to calculating OCF, and solve the problem similar to finding a bid price. Using the initial cash
flow and salvage value we already calculated, the equation for a zero NPV of the project is:
NPV = 0 = –$2,100,000 – 325,000 + OCF(PVIFA11%,5) + [($325,000 + 118,500)/1.115]
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
Year
1
2
3
4
5
Sales
$2,900,000
$2,900,000
$2,900,000
$2,900,000
$2,900,000
Variable costs
1,370,250
1,370,250
1,370,250
1,370,250
1,370,250
36. We need to find the bid price for a project, but the project has extra cash flows. Since we don’t already
produce the keyboard, the sales of the keyboard outside the contract are relevant cash flows. Since we
know the extra sales number and price, we can calculate the cash flows generated by these sales. The
cash flow generated from the sale of the keyboard outside the contract is:
Year 1
Year 2
Year 3
Year 4
we include these here. Remember that we are not only trying to determine the bid price, but we are
also determining whether or not the project is feasible. In other words, we are trying to calculate the
NPV of the project, not just the NPV of the bid price. We will include these cash flows in the bid price
calculation. Whether we include these costs in this initial calculation is irrelevant since you will come
up with the same bid price if you include these costs in this calculation, or if you include them in the
Solving for the OCF, we get:
OCF = $1,748,613.12/PVIFA13%,4
OCF = $587,873.59
Now we can solve for the bid price as follows:
37. a. Since the two computers have unequal lives, the correct method to analyze the decision is the
EAC. We will begin with the EAC of the new computer. Using the depreciation tax shield
approach, the OCF for the new computer system is:
OCF = ($85,000)(1 – .21) + ($580,000/5)(.21) = $91,510
Notice that the costs are positive, which represents a cash inflow. The costs are positive in this
OCF = $90,000(.21)
OCF = $18,900
The initial cost of the old computer is a little trickier. You might assume that since we already
own the old computer there is no initial cost, but we can sell the old computer, so there is an
opportunity cost. We need to account for this opportunity cost. To do so, we will calculate the
Aftertax salvage value = $60,000 + ($90,000 – 60,000)(.21)
Aftertax salvage value = $66,300
Now we can calculate the PV of costs of the old computer as:
PV of costs = –$238,400 + $18,900(PVIFA14%,2) + $66,300/1.142
PV of costs = –$156,262.42
b. If we are only concerned with whether or not to replace the machine now, and are not worrying
about what will happen in two years, the correct analysis is NPV. To calculate the NPV of the
decision on the computer system now, we need the difference in the total cash flows of the old
computer system and the new computer system. From our previous calculations, we can say the
cash flows for each computer system are:
t
New computer
Old computer
Difference
0
–$580,000
–$238,400
–$341,600
1
91,510
18,900
72,610
38. To answer this question, we need to compute the NPV of all three alternatives, specifically, continue
to rent the building, Project A, or Project B. We would choose the project with the highest NPV. If all
three of the projects have a positive NPV, the project that is more favorable is the one with the highest
NPV
There are several important cash flows we should not consider in the incremental cash flow analysis.
The remaining fraction of the value of the building and depreciation are not incremental and should
We will begin by calculating the NPV of the decision of continuing to rent the building first.
Continue to rent:
Rent
$75,000
Since there is no incremental depreciation, the operating cash flow is the net income. So, the NPV of
the decision to continue to rent is:
Product A:
Next, we will calculate the NPV of the decision to modify the building to produce Product A. The
income statement for this modification is the same for the first 14 years, and in Year 15, the company
will have an additional expense to convert the building back to its original form. This will be an
expense in Year 15, so the income statement for that year will be slightly different. The cash flow at
time zero will be the cost of the equipment, and the cost of the initial building modifications, both of
which are depreciable on a straight-line basis. So, the pro forma cash flows for Product A are:
Initial cash outlay:
Building modifications
–$115,000
Equipment
–340,000
Total cash flow
–$455,000
Years 1-14
Year 15
Revenue
$275,000
$275,000
Expenditures
115,000
115,000
The OCF each year is net income plus depreciation. So, the NPV for modifying the building to
manufacture Product A is:
Product B:
Now we will calculate the NPV of the decision to modify the building to produce Product B. The
income statement for this modification is the same for the first 14 years, and in Year 15, the company
will have an additional expense to convert the building back to its original form. This will be an
expense in Year 15, so the income statement for that year will be slightly different. The cash flow at
time zero will be the cost of the equipment, and the cost of the initial building modifications, both of
which are depreciable on a straight-line basis. So, the pro forma cash flows for Product B are:
Initial cash outlay:
Building modifications
–$160,000
Years 1-14
Year 15
Revenue
$295,000
$295,000
Expenditures
130,000
130,000
Depreciation
33,667
33,667
The OCF each year is net income plus depreciation. So, the NPV for modifying the building to
manufacture Product B is:
Since Product A has the highest NPV, the company should choose that option.
We could have also done the analysis as the incremental cash flows between Product A and continuing
to rent the building, and the incremental cash flows between Product B and continuing to rent the
building. The results of this type of analysis would be:
NPV of differential cash flows between Product A and continuing to rent:
NPV of differential cash flows between Product B and continuing to rent:
NPV = NPVProduct B – NPVRent
39. The discount rate is expressed in real terms, and the cash flows are expressed in nominal terms. We
can answer this question by converting all of the cash flows to real dollars. We can then use the real
interest rate. The real value of each cash flow is the present value of the Year 1 nominal cash flows,
discounted back to the present at the inflation rate. So, the real value of the revenue and costs will be:
Revenue in real terms = $415,000/1.06 = $391,509.43
rate. Therefore, the lease payments form a growing perpetuity with a negative growth rate. The real
present value of the lease payments is:
PVLease payments = $150,943.40/[.10 – (–.06)] = $943,396.23
Now we can use the tax shield approach to calculate the net present value. Since there is no investment
in equipment, there is no depreciation; therefore, no depreciation tax shield, so we will ignore this in
40. We are given the real revenue and costs, and the real growth rates, so the simplest way to solve this
problem is to calculate the NPV with real values. While we could calculate the NPV using nominal
values, we would need to find the nominal growth rates, and convert all values to nominal terms. The
real labor costs will increase at a real rate of 2 percent per year, and the real energy costs will increase
at a real rate of 3 percent per year, so the real costs each year will be:
Depreciation is a nominal cash flow, so to find the real value of depreciation each year, we discount
the real depreciation amount by the inflation rate. Doing so, we find the real depreciation each year
is:
Year 1 real depreciation = $28,750,000/1.05 = $27,380,952.38
Year 2 real depreciation = $28,750,000/1.052 = $26,077,097.51
Now we can calculate the pro forma income statement each year in real terms. We can then add back
depreciation to net income to find the operating cash flow each year. Doing so, we find the cash flow
of the project each year is:
Year 0
Year 1
Year 2
Year 3
Year 4
Revenues
$60,175,000.00
$68,475,000.00
$74,700,000.00
$64,325,000.00
EBT
$14,349,047.62
$22,230,927.49
$26,540,877.29
$18,271,024.51
Taxes
3,013,300.00
4,668,494.77
5,573,584.23
3,836,915.15
41. Here we have the sales price and production costs in real terms. The simplest method to calculate the
project cash flows is to use the real cash flows. In doing so, we must be sure to adjust the depreciation,
which is in nominal terms. We could analyze the cash flows using nominal values, which would
require calculating the nominal discount rate, nominal price, and nominal production costs. This
method would be more complicated, so we will use the real numbers. We will first calculate the NPV
EBT
$5,818,511
$6,082,438
$6,338,678
Tax
1,280,072
1,338,136
1,394,509
Net income
$4,538,439
$4,744,302
$4,944,169
OCF
$13,599,928
$13,541,864
$13,485,491
And the NPV of the headache only pill is:
year for the headache and arthritis pill will be:
Year 1
Year 2
Year 3
Sales
$40,425,000
$40,425,000
$40,425,000
Production costs
22,295,000
22,295,000
22,295,000
Depreciation
11,650,485
11,311,151
10,981,700
42. Since the project requires an initial investment in inventory as a percentage of sales, we will calculate
the sales figures for each year first. The incremental sales will include the sales of the new table, but
we also need to include the lost sales of the existing model. This is an erosion cost of the new table.
The lost sales of the existing table are constant for every year, but the sales of the new table change
every year. So, the total incremental sales figure for the five years of the project will be:
initial cash flow is the cost of the inventory. The company will have to spend money for inventory
with the new table, but will be able to reduce inventory of the existing table. So, the initial cash flow
today is:
New table
–$1,062,000
Old table
107,500
So, the aftertax salvage value of the equipment in five years will be:
Sell equipment
$6,800,000
Taxes
461,328
Salvage value
$5,261,328
Next, we need to calculate the variable costs each year. The variable costs of the lost sales are included
VC
3,499,400
4,263,450
5,245,800
4,700,050
4,372,600
Fixed costs
2,050,000
2,050,000
2,050,000
2,050,000
2,050,000
Dep.
0
0
2,286,400
3,918,400
2,798,400
EBT
$3,995,600
$5,296,550
$4,682,800
$2,121,550
$2,684,000
Tax
839,076
1,112,276
983,388
445,526
563,640
Old table
–107,500
Change
–$206,500
–$265,500
$147,500
$88,500
$1,190,500
Notice that we recover the remaining inventory at the end of the project. We must also spend $138,000
for inventory since the 250 units per year in sales of the oak table will begin again. The total cash
flows for the project will be the sum of the operating cash flow, the capital spending, and the inventory
The company should go ahead with the new table.
b. You can perform an IRR analysis, and would expect to find three IRRs since the cash flows
change signs three times.
c. The profitability index is intended as a “bang for the buck” measure; that is, it shows how much
shareholder wealth is created for every dollar of initial investment. This is usually a good measure
