Question

We are evaluating a project that costs $896,000, has 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 100,000 units per year. Price per unit is $38, variable cost per unit is $25, and fixed costs are $900,000 per year. The tax rate is 35%, and we require a 15% return on this project.

1. Calculate the accounting break-even point. What is the degree of operating leverage at the accounting break-even point? (77,847 units; 9.04)
2. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.(Base case: $299,200; $446,606.60; After 500 unit decline: $294.975; $427,647.66)
3. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs. ($364,200; $65,000)
4. In the previous problem, suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within + or – 10%.Calculate the best-case and worst-case NPV.

Answer 1

Answer a:

Contribution per unit = Price per unit - Variable cost per unit = $38 - $25 = $13

Depreciation per year = (Project cost - Salvage value) / Useful life = $896,000 / 8 = $112,000

Accounting break-even = (Fixed cost + Depreciation) /contribution per unit = ($900,000 + 112,000) / 13 = 77,847 units

Accounting break-even = 77,847 units

Fixed cost = $900,000

At accounting break-even, net income = $0

Operating cash flow = Net Income + Depreciation

At accounting break even, Operating cash flow = $0 + $112,000 =$112,000

Degree of operating leverage = 1 + (Fixed cost /Operating cash flow) = 1 + $900,000 / $112,000 = 9.04

Degree of operating leverage = 9.04

Answer b:

As calculated in above table:

Base-case operating cash flow = $299,200

Base-case NPV = $446,606.60

Cash flow and NPV on 500-unit decrease in projected sales are calculated as below:

Cash flow on 500-unit decrease in projected sales = $294,975

NPV on 500-unit decrease in projected sales = $427,647.66

Answer c:

$1 decrease in variable cost = $1 increase in contribution

Change in OCF on $1 decrease in variable cost = Change in contribution per unit * 100,000 * (1 - Tax rate)

= $100,000 * (1 - 35%)

= $65,000

OCF = $299,200 + $65,000 = $364,200

OCF on $1 decrease in estimated variable costs = $364,200

Sensitivity of OCF $1 decrease in estimated variable costs = $65,000

Answer d:

Best case will be when: Price increases by 10%, quantity increases by 10%, variable costs decreases by 10%, and fixed costs decreases by 10%,

Best case NPV = $3,109,607.54

Calculations:

Worst case will be when: Price decreases by 10%, quantity decreases by 10%, variable costs increases by 10%, and fixed costs increases by 10%,

Worst case NPV = - $1,848,882.72

Calculations: