Question

An investment has an initial cash outflow of $210,000 for fixed assets that will be depreciated straight-line to zero over the 4-year life of the project. The sales price is $19.95 a unit, annual fixed costs are $237,000, the variable costs per unit are $8.87, and the tax rate is 23 percent. At what annual sales quantity will the investment break even on an accounting basis?

Select one:

a. 29,889 units

b. 24,092 units

c. 32,088 units

d. 30,135 units

e. 26,129 units

Answer 1

Break even sales is when we get profit = 0, for that we need to find PV ratio and contribution.

P/V ratio = Contribution / Sale price

Contribution is nothing but the difference between sale price and variable cost.

or 55.54%

When we divide Total Fixed Costs by PV ratio we get Revenue or total sales in dollars.

Total Fixed costs include annual fixed costs and depreciation.

Depreciation = 210,000 / 4 = 52,500 per year.

Total fixed cost = 237,000 + 52,500 = 289,500

Therefore,

.................(note: in calculating revenue I have not rounded off pv ratio)

Now divide revenue by sale price per unit, then you will get units sold.

Number of units sold = 521,256.77 / 19.95

= 26,128.16

or 26,129 units

Let us verify it: