Consider a 2 yr project with initial fixed asset investment=$495,000, straight line depreciation to zero over the 2 yr life, zero salvage value, selling price =$39, variable costs=$20. fixed costs=$210,000, quantity sold=150,000 units, tax rate=31%. How sensitive is (OCF) to changes in quantity sold?
To calculate the sensitivity of Operating Cash Flow (OCF) to changes in quantity sold, we need to calculate the OCF for the initial quantity sold and then calculate the OCF for a different quantity sold. The formula for OCF is as follows:
OCF = (Quantity Sold x (Selling Price - Variable Cost)) - Fixed Costs - Tax
1. Calculate OCF for the initial quantity sold:
Quantity Sold = 150,000 units
Selling Price = $39
Variable Cost = $20
Fixed Costs = $210,000
Tax Rate = 31%
OCF = (150,000 x ($39 - $20)) - $210,000 - (31% x ((150,000 x ($39 - $20)) - $210,000))
OCF = (150,000 x $19) - $210,000 - (0.31 x (150,000 x $19 - $210,000))
OCF = $2,850,000 - $210,000 - (0.31 x ($2,850,000 - $210,000))
OCF = $2,850,000 - $210,000 - (0.31 x $2,640,000)
OCF = $2,850,000 - $210,000 - $817,440
OCF = $1,822,560
2. Calculate OCF for a different quantity sold (let's say 180,000 units):
Quantity Sold = 180,000 units
OCF = (180,000 x ($39 - $20)) - $210,000 - (31% x ((180,000 x ($39 - $20)) - $210,000))
OCF = (180,000 x $19) - $210,000 - (0.31 x (180,000 x $19 - $210,000))
OCF = $3,420,000 - $210,000 - (0.31 x ($3,420,000 - $210,000))
OCF = $3,420,000 - $210,000 - (0.31 x $3,210,000)
OCF = $3,420,000 - $210,000 - $993,900
OCF = $2,216,100
3. Calculate the sensitivity of OCF to changes in quantity sold:
ΔOCF = OCF for different quantity sold - OCF for initial quantity sold
ΔOCF = $2,216,100 - $1,822,560
ΔOCF = $393,540
Therefore, the Operating Cash Flow (OCF) is sensitive to changes in quantity sold, with a sensitivity of $393,540.
To determine how sensitive the Operating Cash Flow (OCF) is to changes in quantity sold, we need to calculate the OCF for the given scenario and then calculate the change in OCF for different quantities sold. Here's the step-by-step process to calculate the OCF and its sensitivity:
1. Calculate the annual depreciation expense:
Since the asset has a 2-year life and zero salvage value, the annual depreciation expense is equal to the initial fixed asset investment divided by the project's life:
Depreciation Expense = Initial Fixed Asset Investment / Project Life
Depreciation Expense = $495,000 / 2 = $247,500 per year
2. Calculate the annual fixed costs:
Since the fixed costs are given as $210,000, the annual fixed costs remain the same throughout the project's life.
3. Calculate the total variable costs:
The variable costs per unit are given as $20, and the quantity sold is given as 150,000 units. Therefore, the total variable costs can be calculated as:
Total Variable Costs = Variable Cost per Unit * Quantity Sold
Total Variable Costs = $20 * 150,000 = $3,000,000
4. Calculate the annual revenues:
The selling price per unit is given as $39, and the quantity sold is given as 150,000 units. Therefore, the annual revenues can be calculated as:
Annual Revenues = Selling Price per Unit * Quantity Sold
Annual Revenues = $39 * 150,000 = $5,850,000
5. Calculate the annual pre-tax net income:
The pre-tax net income can be calculated by subtracting the annual depreciation expense, total variable costs, and annual fixed costs from the annual revenues:
Pre-tax Net Income = Annual Revenues - Annual Depreciation Expense - Total Variable Costs - Annual Fixed Costs
Pre-tax Net Income = $5,850,000 - $247,500 - $3,000,000 - $210,000 = $2,392,500
6. Calculate the annual taxes:
The tax rate is given as 31%. Therefore, the annual taxes can be calculated by multiplying the pre-tax net income by the tax rate:
Annual Taxes = Pre-tax Net Income * Tax Rate
Annual Taxes = $2,392,500 * 0.31 = $741,575
7. Calculate the annual net income:
The annual net income can be determined by subtracting the annual taxes from the pre-tax net income:
Annual Net Income = Pre-tax Net Income - Annual Taxes
Annual Net Income = $2,392,500 - $741,575 = $1,650,925
8. Calculate the annual depreciation tax shield:
The annual depreciation tax shield can be calculated by multiplying the annual depreciation expense by the tax rate:
Annual Depreciation Tax Shield = Annual Depreciation Expense * Tax Rate
Annual Depreciation Tax Shield = $247,500 * 0.31 = $76,575
9. Calculate the Operating Cash Flow (OCF):
The OCF can be determined by adding the annual net income and the annual depreciation tax shield:
OCF = Annual Net Income + Annual Depreciation Tax Shield
OCF = $1,650,925 + $76,575 = $1,727,500
10. Calculate the sensitivity of OCF to changes in quantity sold:
To measure the sensitivity of OCF to changes in quantity sold, you need to calculate the change in OCF when the quantity sold changes. Specifically, you need to determine how much OCF changes for every unit change in quantity sold.
For this, you can use the concept of contribution margin, which is the difference between the selling price per unit and the variable cost per unit:
Contribution Margin = Selling Price per Unit - Variable Cost per Unit
Contribution Margin = $39 - $20 = $19
The change in OCF for every unit change in quantity sold can, therefore, be calculated as:
Change in OCF per unit = Contribution Margin - Depreciation Expense
Change in OCF per unit = $19 - $247,500 = -$247,481
This means that the OCF decreases by approximately $247,481 for each additional unit not sold and increases by the same amount for each additional unit sold.
Therefore, the OCF is highly sensitive to changes in quantity sold, as it decreases significantly for each unit not sold and increases significantly for each additional unit sold.