5. We are evaluating a project that costs $864,000, has an eight-year life, and

Question

5. We are evaluating a project that costs $864,000, 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 71,000 units per year. Price per unit is $49, variable cost per unit is $33, and fixed costs are $765,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project.

a. Calculate the accounting break-even point. What is the degree of operating leverage at the accounting break-even point?

b. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.

c. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs.

Explanation / Answer

Part a :

Accounting Break even point is the level of sales that is necessary to cover both variable costs and fixed total costs, such that thenet operating income is Zero.

To calculate break even point first we have tocalculate depreciation

Depreciation (D) = $864,000 / 8 = $ 108,000 every year

Break even point = Total fixed costs / (Sale price per unit - variable cost per unit)

= Total fixed costs / Contribution margin per unit

= (765,000+ 108,000) / 16

= 54,563 units

DEGREE OF OPERATING LEVERAGE (DOL)

To calculate the accounting breakeven, we must realize at this point, on;y at this point OCF is equal to depreciation. So, the DOL at the accounting breakeven is :

DOL = 1+ (Fixed cost/ OCF)

= 1+ (765,000 / 108,000)

= 8.08

Part b :

We will use tax shield to calculate OCF

OCFbase = [ (P-V)Q - FC] (1-T) +TD

= [ (49-33) 71,000 - 765,000] (1-0.35) + 0.35* 108,000   

= $278,950

Now we can calculate NPV using our base case projections. There is no salvage value, so NPV is:

NPV base = - $864,000 + $278,950 (PVIFA10%, 8y)

= $ 624,177.66

To calculate sensitivity of the NPV to changes in the quantity sold, we will calculate NPV at a different quantity say 81000

OCF new = [ (49-33) 81,000 - 765,000] (1-0.35) + 0.35* 108,000   

= $382,950

NPV new =  - $864,000 + $382,950 (PVIFA10%, 8y)

= $ 1,179,010

So change in NPV for every unit change in sales

= (624,177.66-1,179,010)/ (71,000-81,000)

= $ 55.483

If sales were to drop by 500 units, then NPV would drop by ;

NPV drop = $ 55.483 (500) = $ 27,741.62

You can choose any quantity in place of 81000, answer would remain same.

Part c:

To find out how sensitive OCF is to change in variable cost, We will compute OCF at variable cost of $ 34. Again the number we choose is irrelevant. So using tax shield approach, OCF at a VC of $34 is

= [ (P-V)Q - FC] (1-T) +TD

= [ (49-34) 71,000 - 765,000] (1-0.35) + 0.35* 108,000   

= $232,800

So, the change in OCF for a $1change in variable costs is

= ($278,950 - $232,800) / ($33-$34)

= - $46,150

So, if variable costs decrease by $1 , OCF would increase by $46,150

Projected Sales (Q) 71000 units Price per unit (P) $49 Variable cost per unit (V) $33 Contribution Per unit $16 (49-33) Fixed costs (FC) $765,000 Accounting breakeven point 54,563 units

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