Question

Consider a four-year project with the following information: Initial fixed asset investment =$655,000; straight-line depreciation to zero over the four-year life; zero salvage value; price =$28; variable costs =$16; fixed costs =$245,000; quantity sold =61,000 units; tax rate =21 percent. How sensitive is OCF to changes in quantity sold? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) △OCF/ΔQ

Answer 1

To determine the sensitivity of operating cash flow (OCF) to changes in quantity sold, we can use the formula ΔOCF/ΔQ = (ΔRevenue - ΔVariable Costs - ΔFixed Costs) × (1 - Tax Rate). By substituting different values for ΔQ, we can calculate the resulting change in OCF. For example, assuming ΔQ = 1,000, the change in OCF is $12,000.

Step-by-step explanation:

To determine the sensitivity of operating cash flow (OCF) to changes in quantity sold, we need to calculate the change in OCF for a given change in quantity sold.

Using the formula:

ΔOCF/ΔQ = (ΔRevenue - ΔVariable Costs - ΔFixed Costs) × (1 - Tax Rate)

We can find the change in OCF by subtracting the OCF at the original quantity sold from the OCF at the new quantity sold.

Let's calculate:

Original OCF:

1. Revenue = Quantity Sold × Price = 61,000 × $28 = $1,708,000
2. Variable Costs = Quantity Sold × Variable Costs per unit = 61,000 × $16 = $976,000
3. Fixed Costs = $245,000
4. OCF = Revenue - Variable Costs - Fixed Costs = $1,708,000 - $976,000 - $245,000 = $487,000

New OCF:

1. New Quantity Sold = 61,000 + ΔQ
2. Revenue = (61,000 + ΔQ) × $28
3. Variable Costs = (61,000 + ΔQ) × $16
4. Fixed Costs = $245,000
5. OCF = Revenue - Variable Costs - Fixed Costs = [(61,000 + ΔQ) × $28] - [(61,000 + ΔQ) × $16] - $245,000

Now that we have the formulas, we can calculate the sensitivities by substituting different values for ΔQ and calculating the resulting change in OCF.

For example, if we assume ΔQ = 1,000:

1. New Quantity Sold = 61,000 + 1,000 = 62,000
2. New Revenue = 62,000 × $28 = $1,736,000
3. New Variable Costs = 62,000 × $16 = $992,000
4. New OCF = $1,736,000 - $992,000 - $245,000 = $499,000
   By comparing the new OCF with the original OCF, we can determine the change in OCF for the given change in quantity sold. Therefore, the sensitivity of OCF to a change in quantity sold is: ΔOCF/ΔQ = ($499,000 - $487,000) = $12,000