Question

We are evaluating a project that costs $500,000 for the equipment, has a five-year life, and the market value of the equipment at the end of 5 years is 50,000. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 30,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $100,000 per year. The tax rate is 35 percent, and we require a return of 14 percent on this project.

a. Calculate the accounting break-even point.

b. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.

c. What is the sensitivity of NPV to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs.

Answer 1

a) Accounting break-even = (FC + Depreciation) / (Price - VC) = (100,000 + 100,000) / (40 - 20) = 10,000

b)

	0	1	2	3	4	5
Investment	-500,000
Salvage						50,000
Sales		1,200,000	1,200,000	1,200,000	1,200,000	1,200,000
VC		-600,000	-600,000	-600,000	-600,000	-600,000
FC		-100,000	-100,000	-100,000	-100,000	-100,000
Depreciation		-100,000	-100,000	-100,000	-100,000	-100,000
EBT		400,000	400,000	400,000	400,000	400,000
Tax (35%)		-140,000	-140,000	-140,000	-140,000	-140,000
Net Income		260,000	260,000	260,000	260,000	260,000
Cash Flows	-500,000	360,000	360,000	360,000	360,000	392,500
NPV	$752,788.63

Now, if unit sales increase by 1, then NPV = $752,833.26 => Sensitivity = $44.63

If there is 500 unit decrease, Change in NPV = -44.63 x 500 = -$22,315.03

c) If VC is increase by $1, then NPV = $685,843.55 => Sensitivity = -$66,945.08

If there is $1 decrease in VC, then NPV will increase by $66,945.08.