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.

no excel, please :)

a- Calculate the accounting break-even point. What is the degree of operating leverage at the accounting break-even point? (77,847 units; 9.04)

b- 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)

c- 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)

Answer 1

Initial Investment = $896,000
Useful Life = 8 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $896,000 / 8
Annual Depreciation = $112,000

Answer a.

Sales Volume = 100,000
Selling Price per unit = $38
Variable Cost per unit = $25
Fixed Costs = $900,000

Contribution Margin per unit = Selling Price per unit - Variable Cost per unit
Contribution Margin per unit = $38 - $25
Contribution Margin per unit = $13

Accounting Breakeven Point = (Fixed Costs + Depreciation) / Contribution Margin per unit
Accounting Breakeven Point = ($900,000 + $112,000) / $13
Accounting Breakeven Point = 77,847 units

Contribution Margin = Contribution Margin per unit * Sales Volume
Contribution Margin = $13 * 77,847
Contribution Margin = $1,012,011

Operating Income = Contribution Margin - Fixed Costs
Operating Income = $1,012,011 - $900,000
Operating Income = $112,011

Degree of Operating Leverage = Contribution Margin / Operating Income
Degree of Operating Leverage = $1,012,011 / $112,011
Degree of Operating Leverage = 9.04

Answer b.

If sales volume is 100,000 units:

Operating Cash Flow = [Contribution Margin per unit * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Operating Cash Flow = [$13 * 100,000 - $900,000] * (1 - 0.35) + 0.35 * $112,000
Operating Cash Flow = $400,000 * 0.65 + 0.35 * $112,000
Operating Cash Flow = $299,200

NPV = -$896,000 + $299,200 * PVIFA (15%, 8)
NPV = -$896,000 + $299,200 * (1 - (1/1.15)^8) / 0.15
NPV = $446,606.60

If sales volume is 99,500 units:

Operating Cash Flow = [Contribution Margin per unit * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Operating Cash Flow = [$13 * 99,500 - $900,000] * (1 - 0.35) + 0.35 * $112,000
Operating Cash Flow = $393,500 * 0.65 + 0.35 * $112,000
Operating Cash Flow = $294,975

NPV = -$896,000 + $294,975 * PVIFA (15%, 8)
NPV = -$896,000 + $294,975 * (1 - (1/1.15)^8) / 0.15
NPV = $427,647.66

Answer c.

If variable cost per unit is $25:

Contribution Margin per unit = Selling Price per unit - Variable Cost per unit
Contribution Margin per unit = $38 - $25
Contribution Margin per unit = $13

Operating Cash Flow = [Contribution Margin per unit * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Operating Cash Flow = [$13 * 100,000 - $900,000] * (1 - 0.35) + 0.35 * $112,000
Operating Cash Flow = $400,000 * 0.65 + 0.35 * $112,000
Operating Cash Flow = $299,200

If variable cost per unit is $24:

Contribution Margin per unit = Selling Price per unit - Variable Cost per unit
Contribution Margin per unit = $38 - $24
Contribution Margin per unit = $14

Operating Cash Flow = [Contribution Margin per unit * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Operating Cash Flow = [$14 * 100,000 - $900,000] * (1 - 0.35) + 0.35 * $112,000
Operating Cash Flow = $500,000 * 0.65 + 0.35 * $112,000
Operating Cash Flow = $364,200

Sensitivity of OCF = Change in OCF / Change in Variable Cost per unit
Sensitivity of OCF = ($364,200 - $299,200) / ($24 - $25)
Sensitivity of OCF = -$65,000

OCF will increase by $65,000 with decrease in variable cost per unit by $1