Question

We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.

Answer 1

Answer:

base scenario:

initial outlay = $786,000

depreciation expense per year = $786,000 / 8 = $98,250

contribution margin per unit = $48 - $25 = $23

total units sold per year = 65,000

fixed costs per year = $725,000

tax rate = 22%

NCF year 0 = -$786,000

NCF year 1-8 = {[($23 x 65,000) - $98,250 - $725,000] x 0.78} + $98,250 = $622,215

NPV = $2,533,471.10

IRR = 78%

best case scenario:

initial outlay = $786,000

depreciation expense per year = $786,000 / 8 = $98,250

contribution margin per unit = ($48 x 110%) - ($25 x 90%) = $30.30

total units sold per year = 65,000 x 110% = 71,500

fixed costs per year = $725,000 x 90% = $625,500

tax rate = 22%

NCF year 0 = -$786,000

NCF year 1-8 = {[($30.30 x 71,500) - $98,250 - $625,500] x 0.78} + $98,250 = $1,223,556  

NPV = $5,741,580.96

IRR = 156%

worst case scenario:

initial outlay = $786,000

depreciation expense per year = $786,000 / 8 = $98,250

contribution margin per unit = ($48 x 90%) - ($25 x 110%) = $15.70

total units sold per year = 65,000 x 90% = 58,500

fixed costs per year = $725,000 x 110% = $797,500

tax rate = 22%

NCF year 0 = -$786,000

NCF year 1-8 = {[($15.70 x 58,500) - $98,250 - $797,500] x 0.78} + $98,250 = $172,116

NPV = $132,226.16

IRR = 14%