Answer:
a) expected revenue = 20,000 tons x $600 = $12,000,000 per year
initial investment = $3,000,000 + $300,000 = $3,300,000
contribution margin per unit = $600 - $450 = $150
total contribution margin = $150 x 20,000 = $3,000,000
annual fixed costs = $850,000
depreciation expense per year = $750,000
tax rate = 38%
required return rate = 18%
after tax salvage value = $280,000 x (1 - 38%) = $173,600
NCF₀ = -$3,300,000
NCF₁ = [($3,000,000 - $850,000 - $750,000) x 0.62] + $750,000 = $1,618,000
NCF₂ = $1,618,000
NCF₃ = $1,618,000
NCF₄ = $1,618,000 + $300,000 + $173,600 = $2,091,600
NPV = $1,296,797.61
IRR = 36.36%
b) our best case scenario:
expected revenue = 20,000 tons x $660 = $13,200,000 per year
initial investment = $2,550,000 + $285,000 = $2,835,000
contribution margin per unit = $660 - $450 = $210
total contribution margin = $210 x 20,000 = $4,200,000
annual fixed costs = $850,000
depreciation expense per year = $637,500
tax rate = 38%
required return rate = 18%
after tax salvage value = $322,000 x (1 - 38%) = $199,640
NCF₀ = -$2,835,000
NCF₁ = [($4,200,000 - $850,000 - $637,500) x 0.62] + $637,500 = $2,319,250
NCF₂ = $2,319,250
NCF₃ = $2,319,250
NCF₄ = $2,319,250 + $285,000 + $199,640 = $2,803,890
NPV = $3,655,445.13
IRR = 74.34%
our worst case scenario:
expected revenue = 20,000 tons x $540 = $10,800,000 per year
initial investment = $3,450,000 + $315,000 = $3,765,000
contribution margin per unit = $540 - $450 = $90
total contribution margin = $90 x 20,000 = $1,800,000
annual fixed costs = $850,000
depreciation expense per year = $862,500
tax rate = 38%
required return rate = 18%
after tax salvage value = $238,000 x (1 - 38%) = $147,560
NCF₀ = -$3,765,000
NCF₁ = [($1,800,000 - $850,000 - $862,500) x 0.62] + $862,500 = $916,750
NCF₂ = $916,750
NCF₃ = $916,750
NCF₄ = $916,750 + $315,000 + $147,560 = $1,379,310
NPV = -$1,060,302.54
IRR = 3.56%
