Answer:
The firm needs to sale for 5,708 units to break even finnancially.
Explanation:
We convert the fixed asset investment into an annuity:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV 148,000
time 3
rate 0.15
[tex]148000 \div \frac{1-(1+0.15)^{-3} }{0.15} = C\\[/tex]
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
