14. We can use the equation for DOL to calculate fixed costs. The fixed costs must be:
DOL = 3.42 = 1 + FC / OCF
If the output rises to 18,500 units, the percentage change in quantity sold is:
CHAPTER 27 – 2
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 breakeven, the IRR is zero percent since the project recovers the initial
NPV = I [(1/N)(PVIFAR%,N) – 1]
CHAPTER 27 – 3
c. The definition of the financial breakeven 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 84,000 units will be:
OCF = [(P – v)Q – FC](1 – TC) + TCD
We will calculate the OCF at 85,000 units. The choice of the second level of quantity sold is
arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same
sensitivity. So, the OCF at this level of sales is:
The sensitivity of the OCF to changes in the quantity sold is:
18. At 84,000 units, the DOL is:
DOL = 1 + FC / OCF
The accounting breakeven is:
QA = (FC + D) / (P – v)
And, at the accounting breakeven level, the DOL is:
CHAPTER 27 – 4
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
Using the tax shield approach, the OCF and NPV for the base case estimate is:
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
fixed costs. We will use fixed costs of $516,000. The OCF using this level of fixed costs and
the other base case values with the tax shield approach, we get:
And the NPV is:
The sensitivity of NPV to changes in fixed costs is:
CHAPTER 27 – 5
c. The cash breakeven is:
QC = FC / (P – v)
d. The accounting breakeven is:
QA = (FC + D) / (P – v)
At the accounting breakeven, the DOL is:
DOL = 1 + FC / OCF
For each 1% increase (decrease) in unit sales, OCF will increase (decrease) by 2.18%.
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
New clubs $715 75,000 = $53,625,000
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:
Var. Costs
New clubs –$383 75,000 = –$28,875,000
The pro forma income statement will be:
Sales $47,225,000
Variable costs 25,015,000
CHAPTER 27 – 6
Using the bottom up OCF calculation, we get:
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) 75,000 82,500 67,500
Price (new) $715 $787 $644
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 $787 82,500 = $64,886,250
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:
Var. Costs
New clubs –$347 82,500 = –$28,586,250
CHAPTER 27 – 7
The pro forma income statement will be:
Sales $60,146,250
Variable costs 25,580,250
Using the bottom up OCF calculation, we get:
OCF = Net income + Depreciation = $13,083,600 + 4,300,000
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 $644 67,500 = $43,436,250
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:
Var. Costs
The pro forma income statement will be:
Sales $35,376,250
Variable costs 23,872,250
Costs 10,340,000
Using the bottom up OCF calculation, we get:
CHAPTER 27 – 8
OCF = NI + Depreciation = –$1,881,600 + 4,300,000
And the worst-case NPV is: