Question

We are evaluating a project that costs $744,000, has a six-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 45,000 units per year. Price per unit is $60, variable cost per unit is $20, and fixed costs are $740,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.

  

Calculate the best-case and worst-case NPV figures.

Answer 1

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. The last row highlighted in yellow is your answer. Figures, if any, in parenthesis mean negative values. All financials are in $. Calculations are sequential and the two cases *best case and worst case" have been placed side by side in the table below.

Parameter	Linkage	Best Case	Worst Case
Quantity	Q; Best case = 45,000 x (1 + 10%); Worst case = 45,000 x (1 - 10%)	49,500	40,500
Sale price per unit	SP; Best case = 60 x (1 + 10%); Worst case = 60 x (1 - 10%)	66.00	54.00
Variable cost per unit	VC; Best case = 20 x (1 - 10%); Worst case = 20 x (1 + 10%)	18.00	22.00
Fixed costs	FC; Best case = 740,000 x (1 - 10%); Worst case = 740,000 x (1 + 10%)	666,000	814,000
Initial investment	C0	744,000	744,000
Life (years)	N	6	6
Annual depreciation	D =C0 / N	124,000	124,000
Tax rate	T	35%	35%
Annual Cash flows	C = [(SP - VC) x Q - FC - D] x (1 - T) + D	1,154,900	356,700
Discount rate	R	18%	18%
NPV	= - C0 + C / R x [1 - (1 + R)-N]	3,295,381	503,595