Answer:
5375
Explanation:
Given that:
Initial Fixed assets costing = $962000
Annual fixed costs = $403400
Variable cost per unit = $123.60
Sales price per unit = $249.00
Discount rate = 14%
Tax rate = 21%
The contribution per unit = Sales price - Variable cost
= $(249.00 - 123.60)
= $125.40
The present value break-even point(BEP) is the region of sales level where the net present value (NPV) equals zero.
Assuming that the sales level = p
i.e.
NPV = PV(of inflows - of outflows)
Inflows = (p * contribution per unit - annual fixed cost)( 1- tax rate) + depreciation * tax rate
= (p * 125.4 - 403400) ( 1 - 0.21) + depreciation * tax rate
where;
depreciation = initial fixed assest cost/ lifetime of the project
= (125.4p - 403400)*0.79 + (962000/6)*0.21
= (125.4p - 403400)*0.79 + (160333.33)*0.21
= (125.4p - 403400)*0.79 + 33670
Now, the PV of the inflows =PV factor(6 years, 14%) * inflows
Replacing the value for inflows, we have:
The PV of the outflows = Initial Fixed asset cost = $962000
∴
Equating both together using:
PV(of inflows - of outflows) = 0
((125.4p - 403400)*0.79 + 33670)* 3.8887 - 962000 = 0
((125.4p - 403400)*0.79 + 33670)* 3.8887 = 962000
(99.066p - 318686 + 33670) * 3.8887 = 962000
(99.066p - 285016) * 3.8887 = 962000
385.24p - 1108341.72 = 962000
385.24p= 962000 + 1108341.72
385.24p= 2070341.72
p = 2070341.72 / 385.24
p ≅ 5375
