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
![= inflows * \dfrac{( 1-(1.14)^{-6})}{0.14}](https://tex.z-dn.net/?f=%3D%20inflows%20%2A%20%5Cdfrac%7B%28%201-%281.14%29%5E%7B-6%7D%29%7D%7B0.14%7D)
![= inflows * 3.8887](https://tex.z-dn.net/?f=%3D%20inflows%20%2A%203.8887)
Replacing the value for inflows, we have:
![=((125.4p - 403400)*0.79 + 33670)* 3.8887](https://tex.z-dn.net/?f=%3D%28%28125.4p%20-%20403400%29%2A0.79%20%2B%2033670%29%2A%203.8887)
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