Question

A 7-year project is expected to generate annual sales of 8,600 units at a price of $73 per unit and a variable cost of $44 per unit. The equipment necessary for the project will cost $293,000 and will be depreciated on a straight-line basis over the life of the project. Fixed costs are $175,000 per year and the tax rate is 34 percent. How sensitive is the operating cash flow to a $1 change in the per unit sales price?

• $3,333

• $3,777

• $5,676

• $4,221

• $5,108

Answer 1

Base Case Operating Cash Flow

Annual Sales = $627,800 [8,600 x $73]

Variable Cost = 378,400 [8,600 x $44]

Fixed Expenses = 175,000

Depreciation Expense = $41,857 per year [$293,000 / 7 Years]

Annual Operating Cash Flow = [(Annual Sales - Costs) x (1 – Tax Rate)] + [Depreciation x Tax Rate]

= [($627,800 - $378,400 - $175,000) x (1 – 0.34)] + [$41,857 x 0.34]

= $49,104 + $14,231

= $63,335

Operating cash flow to a $1 change in the per unit sales price

Annual Sales = $619,200 [8,600 x $72]

Variable Cost = 378,400 [8,600 x $44]

Fixed Expenses = 175,000

Depreciation Expense = $41,857 per year [$293,000 / 7 Years]

Annual Operating Cash Flow = [(Annual Sales - Costs) x (1 – Tax Rate)] + [Depreciation x Tax Rate]

= [($619,200 - $378,400 - $175,000) x (1 – 0.34)] + [$41,857 x 0.34]

= $43,428 + $14,231

= $57,659

Sensitivity to the operating cash flow to a $1 change in the per unit sales price

Change in the Operating Cash Flow = Base Case Operating cash flow – Operating cash flow if the sale price changes

= $63,335 - $57,659

= $5,676

“Therefore, the Sensitive change in the operating cash flow to a $1 change in the per unit sales price will be $5,676”