Question

A. Sensitivity Analysis and Break-Even Point We are evaluating a project that costs $780,000, has an eight-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 92,000 units per year. Price per unit is $37, variable cost per unit is $23, and fixed costs are $875,000 per year. The tax rate is 35 percent, and we require a return of 15 percent on this project.

B. Scenario Analysis In the previous problem, 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.

Answer 1

Best case NPV is $2,104,660.81, while worst case NPV is -$1,502,186.06

• Cost of project = $780,000
• Life of project = 8 years
• Depreciation per year = $780,000 / 8 = $97,500

Calculating the best case NPV:

For the best case, the firm will take quantity and price to be 10% above the base case and variable and fixed costs to be 10% below the base case.

• Quantity sold = 1.1 * 92,000 = 101,200 units
• Selling price = 1.1 * $37 = $40.70
• Total Sales = 101,200 * $40.70 = $4,118,840
  
• Variable cost per unit = 0.9 * $23 = $20.70
• Total variable cost = $20.70 * 101,200 = $2,094,840
• Fixed costs = 0.9 * $875,000 = $787,500
  
• Gross profit = Sales - Costs = $4,118,840 - ($2,094,840 + $787,500) = $1,236,500

Depreciation = $97,500

• EBIT = Gross Profit - Depreciation = ($1, 236,500 - $97,500) = $1,139,000
• Interest expense = $0
• EBT = EBIT - Interest expense = $1,139,000- 0 = $1,139,000
• Taxes (35%) = $398,650
• Net income = $740,350

Now, Depreciation is a noncash expense, so

Operating cash flow = Net income + Depreciation = $740,350+ $97,500 = $642,850

• Cost of capital = 15% = 0.15

Net Present Value =−$780,000+642,850(1+0.15)1+642,850(1+0.15)2+......+642,850(1+0.15)8=$2,104,660.81

Calculating the worst case NPV:

For the best case, the firm will take quantity and price to be 10% below the base case while variable and fixed costs to be 10% above the base case.

• Quantity sold = 0.9 * 92,000 = 82,800 units
• Selling price = 0.9 * $37 = $33.30
• Total Sales = 82,800 * $33.30 = $2,757,240
  
• Variable cost per unit = 1.1 * $23 = $25.30
• Total variable cost = $25.30 * 82,800 = $2,094,840
• Fixed costs = 1.1 * $875,000 = $962,500
  
• Gross profit = Sales - Costs = $2,757,240- ($2,094,840+ $962,500) = -$300,100

Depreciation = $97,500

• EBIT = Gross Profit - Depreciation = -$397,600
• Interest expense = $0
• EBT = EBIT - Interest expense = -$397,600
• Taxes (35%) = -$139,160
• Net income = -$258,440

Depreciation is a noncash expense. So,

Operating cash flow = Net income + Depreciation = -$160,940

• Cost of capital = 15% = 0.15

Net Present Value =−$780,000+−160,940(1+0.15)1+−160,940(1+0.15)2+......+−160,940(1+0.15)8=−$1,502,186.06