We are evaluating a project that costs $500,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 50,000 units per year. Price per unit is $40, variable cost per unit is $25, and fixed costs are $600,000 per year. The tax rate is 35 percent, and we require a return of 12 percent on this project. Calculate the the accounting break-even point. Calculate the base-case cash flow and NPV. Calculate the sensitivity of NPV to changes in the sales figure. Calculate the sensitivity of OCF to changes in the variable cost figure.
To calculate the accounting breakeven, we first need to find the depreciation for each year.
Thedepreciation is:
Depreciation
= $500,000/8
Depreciation = $ 62500
per yearAnd the accounting breakeven is:
QA= ($600,000 + 62,500)/($40 – 25)
QA
= 441670 units
To calculate the accounting breakeven, we must realize at this point (and only this point), theOCF is equal to depreciation.
So, the DOL at the accounting breakeven is:DOL = 1 + FC/OCF = 1 + FC/DDOL
= 1 + [$600,000/$62,500]DOL
= 11
b.
We will use the tax shield approach to calculate the OCF. The OCF is:
OCFbase
= [(P – v)Q – FC](1 –
T) +TD
OCFbase
= [($40 – 25)(50,000) – $600,000](0.65) + 0.35($62,500)
OCFbase= $119,375
Now we can calculate the NPV using our base-case projections. There is no salvage value orNWC, so the NPV is:
NPVbase
= –$500,000 + $119375(PVIFA12%,8)
NPVbase= $93007
To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate theNPV at a different quantity.
We will use sales of 40,000 units.
The NPV at this sales level is:
OCFnew= [($40 – 25)(60,000) – $600,000](0.65) + 0.35(62,500)
OCFnew
= $216875
And the NPV is:
NPVnew
= -500,000 + $216875(PVIFA12%,8)
NPVnew= $1027348
So, the change in NPV for every unit change in sales is
:
Change in NPV/change in quantity
= ($1027348– $ 93007)/(60,000 – 50,000)
´
= +$93
