14. We can use the equation for DOL to calculate fixed costs. The fixed costs must be:
DOL = 3.26 = 1 + FC/OCF
If the output rises to 18,500 units, the percentage change in quantity sold is:
The percentage change in OCF is:
So, the operating cash flow at this level of sales will be:
If the output falls to 16,500 units, the percentage change in quantity sold is:
The percentage change in OCF is:
So, the operating cash flow at this level of sales will be:
15. Using the equation for DOL, we get:
At 18,500 units:
At 16,500 units:
Intermediate
16. a. At the accounting break-even, the IRR is zero percent since the project recovers the initial
c. The definition of the financial break-even is where the NPV of the project is zero. If this is true,
then the IRR of the project is equal to the required return. Assuming that the required return is
17. Using the tax shield approach, the OCF at 76,000 units will be:
OCF = [(P – v)Q – FC](1 – TC) + TCD
We will calculate the OCF at 77,000 units. The choice of the second level of quantity sold is
The sensitivity of the OCF to changes in the quantity sold is:
OCF will increase by $7.90 for every additional unit sold.
18. At 76,000 units, the DOL is:
And, at the accounting break-even level, the DOL is:
19. a. The base-case, best-case, and worst-case values are shown below. Remember that in the best-
case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease,
and costs increase.
Scenario Unit Sales Variable Cost Fixed Costs
Base 210 $10,600 $560,000
Using the tax shield approach, the OCF and NPV for the base-case estimate are:
The OCF and NPV for the worst-case estimate are:
And the OCF and NPV for the best-case estimate are:
b. To calculate the sensitivity of the NPV to changes in fixed costs we choose another level of
And the NPV is:
The sensitivity of NPV to changes in fixed costs is:
For every dollar fixed costs increase (decrease), NPV decreases (increases) by $2.40.
c. The cash break-even is:
d. The accounting break-even level is:
QA = (FC + D)/(P – v)
At the accounting break-even, the DOL is:
DOL = 1 + FC/OCF
For each 1 percent increase (decrease) in unit sales, OCF will increase (decrease) by 2.15
percent.
20. The marketing study and the research and development are both sunk costs and should be ignored.
We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs
and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new
project will be:
Sales
For the variable costs, we must include the units gained or lost from the existing clubs. Note that the
variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will
save these variable costs, which is an inflow. So:
Variable Costs
New clubs –$405 60,000 = –$24,300,000
The pro forma income statement will be:
Sales $44,170,000
Variable costs 20,500,000
Using the bottom-up OCF calculation, we get:
OCF = NI + Depreciation
So, the payback period is:
The NPV is:
And the IRR is:
21. The best-case and worst-cases for the variables are:
Base-Case Best-Case Worst-Case
Unit sales (new) 60,000 66,000 54,000
Price (new) $845 $930 $761
Best-case
We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs
and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new
project will be:
Sales
New clubs $930 66,000 = $61,347,000
For the variable costs, we must include the units gained or lost from the existing clubs. Note that the
variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will
save these variable costs, which is an inflow. So:
Variable Costs
New clubs –$365 66,000 = –$24,057,000
The pro forma income statement will be:
Sales $56,514,000
Variable costs 21,117,000
Using the bottom-up OCF calculation, we get:
OCF = Net income + Depreciation
And the best-case NPV is:
Worst-Case
We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs
and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new
project will be:
Sales
New clubs $761 54,000 = $41,067,000
For the variable costs, we must include the units gained or lost from the existing clubs. Note that the
variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will
save these variable costs, which is an inflow. So:
Variable Costs
New clubs –$446 54,000 = –$24,057,000
The pro forma income statement will be:
Sales $32,840,000
Variable costs 19,397,000
Using the bottom-up OCF calculation, we get:
OCF = NI + Depreciation
And the worst-case NPV is: