Question

A project requires an initial fixed asset investment of $148,000, has annual fixed costs of $39,800, a contribution margin of $14.62, a tax rate of 21 percent, a discount rate of 15 percent, and straight-line depreciation over the project's 3-year life. The assets will be worthless at the end of the project. What is the financial break-even point in units per year? (Hint: First solve for EAC and then use the formula)

Answer 1

Answer:

The firm needs to sale for 5,708 units to break even finnancially.

Explanation:

We convert the fixed asset investment into an annuity:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 148,000

time 3

rate 0.15

$148000 \div \frac{1-(1+0.15)^{-3} }{0.15} = C$

C  $ 64,820.590

Now, the amount above the annual fixed cost of 39,800 will be considered a gain for tax purposes, we need to increase it by 21% o give the sales before taxes.

before taxes target contribution:

64,820.59 / 1.20 = 54,017.16

We also have a depreciation component which generates a tax shield:

(148,000 / 3) x 21% = (10,360)

Now, we solve for the break even point of the sum of this components:

39,800 + 54,017.16 - 10,360= 83,457.16‬ dollars

Each units generates 14.62 dollars we divide and obtain the sales per year in untis:

83,457.16 / 14.62 = 5.708,42