We are evaluating a project that costs $670,000, has a five-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 59,000 units per year. Price per unit is $44, variable cost per unit is $24, and fixed costs are $760,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.
Calculate the best-case and worst-case NPV figures
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To calculate the best-case and worst-case NPV figures, we need to first calculate the annual cash flows for both cases.
Best-case scenario:
1. Calculate the total revenue: 59,000 units * $44 per unit = $2,596,000
2. Calculate the total variable costs: 59,000 units * $24 per unit = $1,416,000
3. Calculate the total fixed costs: $760,000
4. Calculate the operating profit: Total revenue - Total variable costs - Total fixed costs = $2,596,000 - $1,416,000 - $760,000 = $420,000
(Note: This represents the annual profit before taxes and depreciation)
5. Calculate the annual depreciation expense: $670,000 / 5 years = $134,000
6. Calculate the taxable income: Operating profit - Depreciation expense = $420,000 - $134,000 = $286,000
7. Calculate the taxes: Taxable income * Tax rate = $286,000 * 0.35 = $100,100
8. Calculate the annual cash flow: Operating profit - Taxes + Depreciation expense = $420,000 - $100,100 + $134,000 = $453,900
Worst-case scenario:
Repeat steps 1-5 to calculate the operating profit and depreciation expense.
6. Calculate the taxable income.
7. Calculate the taxes.
8. Calculate the annual cash flow.
Once you have the annual cash flows for both the best-case and worst-case scenarios, you can calculate the NPV using the following formula:
NPV = (Cash flow Year 1 / (1 + required return)^1)
+ (Cash flow Year 2 / (1 + required return)^2)
+ (Cash flow Year 3 / (1 + required return)^3)
+ (Cash flow Year 4 / (1 + required return)^4)
+ (Cash flow Year 5 / (1 + required return)^5)
- Initial investment
To calculate the NPV for both scenarios, substitute the respective cash flows and the initial investment of $670,000 into the formula.
Best-case NPV = [(Cash flow Year 1 / (1 + 0.18)^1) + (Cash flow Year 2 / (1 + 0.18)^2) + (Cash flow Year 3 / (1 + 0.18)^3) + (Cash flow Year 4 / (1 + 0.18)^4) + (Cash flow Year 5 / (1 + 0.18)^5)] - $670,000
Worst-case NPV = [(Cash flow Year 1 / (1 + 0.18)^1) + (Cash flow Year 2 / (1 + 0.18)^2) + (Cash flow Year 3 / (1 + 0.18)^3) + (Cash flow Year 4 / (1 + 0.18)^4) + (Cash flow Year 5 / (1 + 0.18)^5)] - $670,000
By substituting the known values, you can calculate both the best-case and worst-case NPV figures.