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Using the provided information and the required rate of return of
12%, let's calculate the NPV for the new strip mine project:
1.
Calculate the initial investment:
Land purchase cost: $5 million
Equipment cost: $85 million
Initial Investment = $5 million + $85 million = $90 million
2.
Calculate the annual cash flows from the project:
Year 1:
Revenue from the contract: 500,000 tonnes/year * $82/tonne =
$41 million
Revenue from excess production: 620,000 tonnes * $76/tonne
= $47.12 million
Variable costs: 620,000 tonnes * $31/tonne = $19.22 million
Fixed costs: $4.1 million
Working capital investment: 5% of total sales = 5% * ($41
million + $47.12 million) = $4.42 million
Cash Flow at Year 1 = $41 million + $47.12 million - $19.22
million - $4.1 million - $4.42 million = $60.38 million
Year 2:
Revenue from the contract: 500,000 tonnes/year * $82/tonne =
$41 million
Revenue from excess production: 680,000 tonnes * $76/tonne
= $51.68 million
Variable costs: 680,000 tonnes * $31/tonne = $21.08 million
Fixed costs: $4.1 million
Working capital investment: 5% of total sales = 5% * ($41
million + $51.68 million) = $4.63 million
Cash Flow at Year 2 = $41 million + $51.68 million - $21.08
million - $4.1 million - $4.63 million = $62.87 million
Year 3:
Revenue from the contract: 500,000 tonnes/year * $82/tonne =
$41 million
Revenue from excess production: 730,000 tonnes * $76/tonne
= $55.28 million
Variable costs: 730,000 tonnes * $31/tonne = $22.63 million
Fixed costs: $4.1 million
Working capital investment: 5% of total sales = 5% * ($41
million + $55.28 million) = $4.82 million
Cash Flow at Year 3 = $41 million + $55.28 million - $22.63
million - $4.1 million - $4.82 million = $64.73 million
Year 4:
Revenue from the contract: 500,000 tonnes/year * $82/tonne =
$41 million
Revenue from excess production: 590,000 tonnes * $76/tonne
= $44.84 million
Variable costs: 590,000 tonnes * $31/tonne = $18.29 million
Fixed costs: $4.1 million
Working capital investment: 5% of total sales = 5% * ($41
million + $44.84 million) = $4.29 million
Cash Flow at Year 4 = $41 million + $44.84 million - $18.29
million - $4.1 million - $4.29 million = $58.25 million
3.
Determine the salvage value of the equipment at the end of
the project:
Salvage Value = Equipment cost * 60% = $85 million * 60% =
$51 million
4.
Calculate the cash flow at the end of year 5 for land
reclamation cost:
Cash Flow at Year 5 = Cost of reclamation = $2.7 million
5.
Calculate the cash flow at the end of year 6 for the charitable
expense deduction:
Cash Flow at Year 6 = Charitable expense deduction = $6
million
6.
Calculate the present value factor for each year using the
company's required return rate of 12%:
PV Factor = 1 / (1 + Required Return Rate)^Year
Year 1: PV Factor = 1 / (1 + 12%)^1 = 0.8929
Year 2: PV Factor = 1 / (1 + 12%)^2 = 0.7972
Year 3: PV Factor = 1 / (1 + 12%)^3 = 0.7118
Year 4: PV Factor = 1 / (1 + 12%)^4 = 0.6355
Year 5: PV Factor = 1 / (1 + 12%)^5 = 0.5674
Year 6: PV Factor = 1 / (1 + 12%)^6 = 0.5066
7.Discount each cash flow to its present value using the respective
PV factor:
Present Value = Cash Flow * PV Factor
Year 1: Present Value = $60.38 million * 0.8929 = $53.92 million
Year 2: Present Value = $62.87 million * 0.7972 = $50.09 million
Year 3: Present Value = $64.73 million * 0.7118 = $46.14 million
Year 4: Present Value = $58.25 million * 0.6355 = $37.00 million
Year 5: Present Value = $2.7 million * 0.5674 = $1.53 million
Year 6: Present Value = -$6 million * 0.5066 = -$3.04 million
(negative because it's a charitable expense deduction)
8.
Sum up all the present values to calculate the NPV:
NPV = Sum of Present Values - Initial Investment
NPV = $53.92 million + $50.09 million + $46.14 million +
$37.00 million + $1.53 million - $3.04 million - $90 million
NPV = $96.54 million - $90 million
NPV = $6.54 million
The calculated NPV for the new strip mine project is $6.54 million.
Since the NPV is positive, it indicates that the project is expected to
generate a positive return and may be considered favorable. Beaver
Mining should take the contract and open the mine. However, it's
important to note that the NPV calculation is based on the given
assumptions and estimates, and any changes to those factors can
affect the project's profitability.
Certainly! I will perform the calculations to determine the NPV of the
SuperTread project.
Step 1: Initial Investment
Initial Investment = $10 million (Research and development costs) +
$160 million (Production equipment cost) + $9 million (Working
capital requirement)
Initial Investment = $179 million
Step 2: Cash Flows from the OEM Market
Year 1:
Cash Flow at Year 1 (OEM Market) = -$10.264 million
Years 2-4:
Cash Flow at Year 2 (OEM Market) = -$10.264 million * (1 + 3.25%)
= -$10.616 million
Cash Flow at Year 3 (OEM Market) = -$10.264 million * (1 +
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3.25%)^2 = -$10.978 million
Cash Flow at Year 4 (OEM Market) = -$10.264 million * (1 +
3.25%)^3 = -$11.351 million
Step 3: Cash Flows from the Replacement Market
Year 1:
Cash Flow at Year 1 (Replacement Market) = $84.48 million
Years 2-4:
Cash Flow at Year 2 (Replacement Market) = $84.48 million * (1 +
3.25%) = $87.31 million
Cash Flow at Year 3 (Replacement Market) = $84.48 million * (1 +
3.25%)^2 = $90.26 million
Cash Flow at Year 4 (Replacement Market) = $84.48 million * (1 +
3.25%)^3 = $93.33 million
Step 4: Salvage Value of Production Equipment
Salvage Value = $65 million * (1 + 3.25%)^4 = $71.31 million
Step 5: Present Value Factors
PV Factor Year 1 = 1 / (1 + 13.4%)^1 = 0.8817
PV Factor Year 2 = 1 / (1 + 13.4%)^2 = 0.779
PV Factor Year 3 = 1 / (1 + 13.4%)^3 = 0.686
PV Factor Year 4 = 1 / (1 + 13.4%)^4 = 0.6055
Step 6: Discounted Cash Flows
Discounted Cash Flow Year 1 = Cash Flow at Year 1 (OEM Market) *
PV Factor Year 1 + Cash Flow at Year 1 (Replacement Market) * PV
Factor Year 1
Discounted Cash Flow Year 1 = (-$10.264 million) * 0.8817 + $84.48
million * 0.8817 = $69.94 million
Discounted Cash Flow Year 2 = Cash Flow at Year 2 (OEM Market) *
PV Factor Year 2 + Cash Flow at Year 2 (Replacement Market) * PV
Factor Year 2
Discounted Cash Flow Year 2 = (-$10.616 million) * 0.779 + $87.31
million * 0.779 = $66.49 million
Discounted Cash Flow Year 3 = Cash Flow at Year 3 (OEM Market) *
PV Factor Year 3 + Cash Flow at Year 3 (Replacement Market) * PV
Factor Year 3
Discounted Cash Flow Year 3 = (-$10.978 million) * 0.686 + $90.26
million * 0.686 = $58.88 million
Discounted Cash Flow Year 4 = Cash Flow at Year 4 (OEM Market) *
PV Factor Year 4 + Cash Flow at Year 4 (Replacement Market) * PV
Factor Year 4 + Salvage Value * PV Factor Year 4
Discounted Cash Flow Year 4 = (-$11.351 million) * 0.6055 + $93.33
million * 0.6055 + $71.31 million * 0.6055 = $84.90 million
Step 7: Net Present Value (NPV)
NPV = Sum of Discounted Cash Flows - Initial Investment
NPV = $69.94 million + $66.49 million + $58.88 million + $84.90
million - $179 million
NPV = $80.21 million
Therefore, the NPV of the SuperTread project is $80.21 million.
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