We are evaluating a project that costs $1,120,000, has a ten-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 64,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $620,000 per year. The tax rate is 35 percent, and we require a return of 12 percent on this project.
a. Calculate the accounting break-even point.
b-1 Calculate the base-case cash flow and NPV.
b-2 What is the sensitivity of NPV to changes in the sales figure?
b-3 Calculate the change in NPV if sales were to drop by 500 units.
c. What is the sensitivity of OCF to changes in the variable cost figure?
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a. To calculate the accounting break-even point, we need to determine the quantity of units needed to be sold in order to cover the fixed costs.
Accounting Break-even Point = Fixed Costs / Contribution Margin
First, we need to calculate the contribution margin per unit:
Contribution Margin per Unit = Price per Unit - Variable Cost per Unit
= $50 - $25
= $25
Now, we can calculate the accounting break-even point:
Accounting Break-even Point = Fixed Costs / Contribution Margin
= $620,000 / $25
= 24,800 units
Therefore, the accounting break-even point is 24,800 units.
b-1. To calculate the base-case cash flow and NPV (Net Present Value), we need to calculate the annual operating cash flows and discount them back to the present value.
Annual Operating Cash Flow (OCF) = (Sales - Variable Costs - Fixed Costs) × (1 - Tax Rate)
Annual OCF = (64,000 units × ($50 - $25) - $620,000) × (1 - 0.35)
= (64,000 units × $25 - $620,000) × 0.65
= ($1,600,000 - $620,000) × 0.65
= $980,000 × 0.65
= $637,000
Next, we calculate the NPV using the formula:
NPV = Σ[OCF / (1 + r)^t] - Initial Investment
Where r is the required rate of return and t is the time period.
In this case, the Initial Investment is $1,120,000, r is 0.12, and t is 10 years.
NPV = $637,000 / (1 + 0.12)^1 + $637,000 / (1 + 0.12)^2 + ... + $637,000 / (1 + 0.12)^10 - $1,120,000
b-2. To calculate the sensitivity of NPV to changes in the sales figure, we can recalculate the NPV with different sales figures and observe the changes.
NPV1 = NPV with the original sales figure (64,000 units)
NPV2 = NPV with an altered sales figure
b-3. To calculate the change in NPV if sales were to drop by 500 units, we can calculate the new NPV with the altered sales figure and compare it to the original NPV.
c. To calculate the sensitivity of OCF to changes in the variable cost figure, we can recalculate the OCF using different variable cost figures and observe the changes in the OCF.