You are considering a new product launch. The project will cost $2,200,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 150 units per year; price per unit will be $29,000, variable cost per unit will be $17,500, and fixed costs will be $590,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 34 percent.

You are considering a new product launch. The project will cost $2,200,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 150 units per year; price per unit will be $29,000, variable cost per unit will be $17,500, and fixed costs will be $590,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 34 percent.

  

a.

Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (Negative amount should be indicated by a minus sign. Round your NPV answers to 2 decimal places. (e.g., 32.16))

Scenario	Unit Sales	Variable Cost	Fixed Costs	NPV
Base		$	$	$
Best
Worst

b.	Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places. (e.g., 32.161))

ΔNPV/ΔFC

$

  

c.	What is the cash break-even level of output for this project (ignoring taxes)? (Round your answer to 2 decimal places. (e.g., 32.16))

  

Cash break-even

  

d-1	What is the accounting break-even level of output for this project? (Round your answer to 2 decimal places. (e.g., 32.16))

  

Accounting break-even

d-2	What is the degree of operating leverage at the accounting break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))

  

Degree of operating leverage

Explanation:

a.

The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase.

Using the tax shield approach, the OCF and NPV for the base case estimate is:

  

OCFbase = [($29,000 – 17,500)(150) – $590,000](0.66) + 0.34($2,200,000/4)

OCFbase = $936,100

NPVbase = –$2,200,000 + $936,100(PVIFA12%,4)

NPVbase = $643,262.72

The OCF and NPV for the worst case estimate are:

OCFworst = [($29,000 – 19,250)(135) – $649,000](0.66) + 0.34($2,200,000/4)

OCFworst = $627,385

  

NPVworst = –$2,200,000 + $627,385(PVIFA12%,4)

NPVworst = –$294,412.58

  

And the OCF and NPV for the best case estimate are:

OCFbest = [($29,000 – 15,750)(165) – $531,000](0.66) + 0.34($2,200,000/4)

OCFbest = $1,279,465

  

NPVbest = –$2,200,000 + $1,279,465(PVIFA12%,4)

NPVbest = $1,686,182.18

b.

To calculate the sensitivity of the NPV to changes in fixed costs we choose another level of fixed costs. We will use fixed costs of $600,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get:

OCF = [($29,000 – 17,500)(150) – $600,000](0.66) + 0.34($2,200,000/4)

OCF = $929,500

And the NPV is:

NPV = –$2,200,000 + $929,500(PVIFA12%,4)

NPV = $623,216.22

  

The sensitivity of NPV to changes in fixed costs is:

ΔNPV/ΔFC = ($643,262.72 – 623,216.22)/($590,000 – 600,000)

ΔNPV/ΔFC = –$2.005

For every dollar FC increases, NPV falls by $2.005.

c.

The cash breakeven is:

QC = FC/(P – v)

QC = $590,000/($29,000 – 17,500)

QC = 51.30

d.

The accounting breakeven is:

QA= (FC + D)/(P – v)

QA = [$590,000 + ($2,200,000/4)]/($29,000 – 17,500)

QA = 99.13

At the accounting breakeven, the DOL is:

DOL = 1 + FC/OCF

DOL = 1 + ($590,000/$550,000) = 2.073

For each 1% increase in unit sales, OCF will increase by 2.073%.