Question

You are considering a new product launch. The project will cost $2,325,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 320 units per year; price per unit will be $19,300, variable cost per unit will be $13,850, and fixed costs will be $710,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 25 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? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.)

	Scenario Unit Sales Variable Cost Fixed Costs NPV Base 320 $13,850 $710,000 Best Worst

b.	Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the cash break-even level of output for this project (ignoring taxes)? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-1.	What is the accounting break-even level of output for this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-2.	What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

b.ΔNPV/ΔFC

c.Cash break-even

d-1.Accounting break-evend

-2.Degree of operating leverage

Answer 1

Part 1)

Step 1: Calculate Annual Cash Flow Under Each Scenario

The value of annual cash flow under each scenario is determined as below:

	Base Case	Best Case	Worst Case
Sales	6,176,000.00 (320*19,300)	6,793,600.00 [320*(1+10%)*19,300]	5,558,400.00 [320*(1-10%)*19,300]
Less Variable Costs	4,432,000.00 (320*13,850)	4,387,680.00 [320*(1+10%)*13,850*(1-10%)]	4,387,680.00 [320*(1-10%)*13,850*(1+10%)]
Fixed Costs	710,000.00	639,000.00 [710,000*(1-10%)]	781,000.00 [710,000*(1+10%)]
Annual Depreciation (2,325,000/4)	581,250.00	581250.00	581250.00
EBT	452,750.00	1,185,670.00	-191,530.00
Less Taxes	113,187.50	296,417.50	-47,882.50
EAT	339,562.50	889,252.50	-143,647.50
Add Annual Depreciation	581,250.00	581,250.00	581,250.00
Annual Cash Flow	$920,812.50	$1,470,502.50	$437,602.50

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Step 2: Calculate NPV Under Each Scenario

The formula for calculating NPV is given as below:

NPV = -Initial Investment + Annual Cash Flow Year 1/(1+Required Rate of Return)^1 + Annual Cash Flow Year 2/(1+Required Rate of Return)^2 + Annual Cash Flow Year 3/(1+Required Rate of Return)^3 + Annual Cash Flow Year 4/(1+Required Rate of Return)^4

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NPV (Base Case) = -2,325,000 + 920,812.50/(1+9%)^1 + 920,812.50/(1+9%)^2 + 920,812.50/(1+9%)^3 + 920,812.50/(1+9%)^4 = $658,174.56

NPV (Best Case) = -2,325,000 + 1,470,502.50/(1+9%)^1 + 1,470,502.50/(1+9%)^2 + 1,470,502.50/(1+9%)^3 + 1,470,502.50/(1+9%)^4 = $2,439,016.18

NPV (Worst Case) = -2,325,000 + 437,602.50/(1+9%)^1 + 437,602.50/(1+9%)^2 + 437,602.50/(1+9%)^3 + 437,602.50/(1+9%)^4 = -$907,290.48

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Tabular Representation:

Scenario	Unit Sales	Variable Cost	Fixed Costs	NPV
Base	320	$13,850	$710,000	$658,174.56
Best	352	$12,465	$639,000	$2,439,016.18
Worst	288	15,235	$781,000	-$907,290.48

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Part b)

Let us assume that the fixed costs are $720,000. Now, we will have to calculate revised annual cash flow and NPV.

Sales	6,176,000.00
Less Variable Costs	4,432,000.00
Revised Fixed Costs	720,000.00
Annual Depreciation	581,250.00
EBT	442,750.00
Less Taxes	110,687.50
EAT	332,062.50
Depreciation	581,250.00
Revised Annual Cash Flow	$913,312.50

Revised NPV = -2,325,000 + 913,312.50/(1+9%)^1 + 913,312.50/(1+9%)^2 + 913,312.50/(1+9%)^3 + 913,312.50/(1+9%)^4 = $633,876.66

Now, we can calculate the sensitivity of base-case NPV to changes in fixed costs with the use of formula given below:

Sensitivity = Change in NPV/Change in Fixed Costs = (658,174.56 - 633,876.66)/(710,000 - 720,000) = -$2.43

Based on the above calculations, it can be concluded that for every dollar increase in fixed cost, NPV falls by $2.43.

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Part c)

The cash break-even level of output for the project is determined as follows:

Cash Break-Even Level = Fixed Cost/(Selling Price - Variable Cost)

Substituting values in the above formula, we get,

Cash Break-Even Level = (710,000)/(19,300 - 13,850) = 130.28 units

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Part d-1)

The accounting break-even level of output for the project is arrived as below:

Accounting Break-Even Level = (Fixed Cost +Depreciation)/(Selling Price - Variable Cost)

Substituting values in the above formula, we get,

Accounting Break-Even Level = (710,000 + 581,250) /(19,300 - 13,850) = 236.93 units

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Part d-2)

The degree of operating leverage at the accounting break-even point is calculated as follows:

Degree of Operating Leverage = 1 + Fixed Cost/Depreciation

Substituting values in the above formula, we get,

Degree of Operating Leverage = 1 + 710,000/581,250 = 2.222