You are evaluating a project that costs $840,000, has seven-year life, and has n

Question

You are evaluating a project that costs $840,000, has seven-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 90,000 units per year. Price per unit is $40, variable cost per unit is $24, and fixed costs are $900,000 units per year. Tax rate is 40%, and you require a 12% return 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 300-unit decrease in project sales

Please show all the details. Thanks!!!

Explanation / Answer

1.

Break-even Sales Units = FC+d/ p ? v

Where FC is fixed cost, d= depreciation per year p = price per unit and v is variable cost per unit

= 900,000+120,000/(40-24)

=900,000/16 = 63,750 units is the accounting break even point

2.

Base cash flow is 324,000 per year

NPV = 324,000*((1-(1+r)^-n)/r)-intial investment

where r = .12 or 12% and n=7 that is 7 years.

NPV = 1,478,657 - 840,000 = 638,657

Senistivity of NPV to changes in the sales figure

lets change the unit sold from 90,000 to 91,000, the Cash inflow per year will be 333,600

NPV = 333,600*((1-(1+r)^-n)/r)-intial investment

where r = .12 or 12% and n=7 that is 7 years.

NPV = 1,522,469 - 840,000 = 682,469

Thus, the change in NPV per unit change in Q is (682,469 - 638,657) / (91,000 - 90,000) = 43.81

In other words, for every additional unit sold, NPV increases by $43.81. A 300 unit decrease in Q decreases NPV by 300*43.81 = $13143.6

Sales    3,600,000 Variable cost    2,160,000 Fixed cost       900,000 Profit before tax       540,000 Profit after tax       324,000

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