a1)
Breakeven = Fixed expenses / Contribution per unit
Depreciation per year = 874800/ 9 = $ 97200 per year
Total Fixed Cost = $ 765,000 + $ 97200 per year = $ 8,62,200 per year
Contribution per unit = $ 55- $ 39 = $ 16
So, breakeven = 862200/ 16 = 53887.5 units
a2)
Degree of Operating leverage = Sales - Variable cost / (Sales - variable cost - fixed cost)
So, at accounting break-even unit, operating leverage = 53887.5 ($ 55- $ 39)/ [53887.5 ($ 55- $ 39) - 862200]
= 0
Degree of Operating leverage at accounting break-even units is 0.
b3)
We will use the tax shield approach to calculate the OCF.
The OCF is:
OCF base= [(P – v)Q – FC](1 – tc) + tc D
OCFbase= [($55 – 39)(85,000) – $765,000](0.76) + 0.24($97,200)
OCF base= $475,528
Now we can calculate the NPV using our base-case projections.
There is no salvage value or NWC, so the NPV is:
NPV base= –$874,800 + $475,528 (PVIFA 11%,9)
NPV base= -$874,800 + $ 475,528 x 5.5370 = $1,758,198.536
b2)
To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 86,000 units.
OCF at this sales level is = [($55 – 39)(86,000) – $765,000](0.76) + 0.24($97,200)
OCF = $487,688
And the NPV at this sales level is
NPV = –$874,800 + $487,688 (PVIFA 11%,9) = -$874,800 + $ 487,688 x 5.5370 = $1,825,528.46
So, NPV for every unit change in sales is = (1825528.46 - 1758198.54)/ (86000-85000) = $67.33
c)
To find out how sensitive OCF is to a change in variable costs,we will compute the OCF at a variable cost of $40.
So, using the tax shield approach, the OCF at a variable cost of $40 is:
OCF new= [($55 – 40)(85,000) – $765,000](0.76) + 0.24($97,200) = $410928
So, the change in OCF for a $1 change in variable costs is:
(410,928 – 475,528)/(40 - 39) = $ 64,600
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