Evaluate project that costs $1.5 million has a 10-year life and no salvage value

Question

Evaluate project that costs $1.5 million has a 10-year life and no salvage value. Assume depreciation is straight line over the life of the project. Sales are projected at 150K units every year over the life of the project. Price per unit is $75, variable costs are $45 per unit, and fixed costs are $1,275,000 per year. The tax rate is 30% and the required rate of return is 15% after tax.

Calculate: the accounting break-even point; the operating leverage at this break-even point; the base-case cash flow and its NPV. Also compute impact 10% decrease in expected sales or 5% increase in projected variable costs.

Explanation / Answer

a) Accounting Break Even Point:

To calculate, accounting break even point, we first need to determine the amount of depreciation.

Depreciation = Cost of The Project/Life of the Machine = $1,500,000/10 = $150,000

The formula for Accounting Break Even Point:

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

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Solution:

Accounting Break Even Point = (1,275,000 + 150,000)/($75 - $45) = 47,500 units

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b) Operating Leverage at Break Even Point:

The formula for degree of operating leverage is:

DOL = Quantity*(Selling Price - Variable Cost)/EBIT

EBIT = Quantity*(Selling Price - Variable Cost) - Fixed Cost - Depreciation

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Solution:

EBIT = 47,500*(75 - 45) - 150,000 - 1,275,000 = 0

Degree of Operating Leverage = $1,425,000/0 = Infinite

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c) Base-Case Cash Flow and NPV:

The formula for base-case cash flow and NPV is:

Base-Case Cash Flow = (Sales - Variable Costs - Fixed Costs)*(1-Tax Rate) + Depreciation*Tax Rate

NPV = Present Value of Costs - Present Value of Benefits

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Solution:

Base Case Cash Flow = (150,000*75 - 150,000*45 - 1,275,000)*(1-30%) + 150,000*30% = $2,302,500

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To calculate NPV, we first need to find the present value of operating cash flows expected througout the life of the project. For that, we can use the present value of ordinary annuity formula.

Present Value (Ordinary Annuity) = P*[((1-(1+r)^-n/r] where P is operating cash flow, r is the rate of return and n is years.

Using the values calculated above and provided in the question we get,

Present Value = 2,302,500*[((1-(1+15%)^-10)/15%] = $11,555,714.76

NPV = -1,500,000 + 11,555,714.76 = $10,055,714.76

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d) Impact of 10% decrease in Expected Sales

Step 1: Calculate Revised Operating Cash Flow

Revised Operating Cash Flow = (150,000*(1-10%)*75 - 150,000*(1-10%)*45 - 1,275,000)*(1-30%) + 150,000*30% = $1,987,500

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Step 2: Calculate Revised NPV and Determine the Change

A decrease in sales will also result in a decrease in variable cost, as total units would decrease.

Present Value of Revised Operating Cash Flow = 1,987,500*[((1-(1+15%)^-10)/15%] = $9,974,802.64

Revised NPV = -1,500,000 + 9,974,802.64 = $8,474,802.64

Change in NPV = Original NPV - Revised NPV = 10,055,714.76 - 8,474,802.64 = $1,580,912.12

NPV decreases by $1,580,912.12.

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d) Impact of 5% Increase in Variable Costs

Step 1: Calculate Revised Operating Cash Flow

Revised Operating Cash Flow = (150,000*75 - 150,000*45*(1+5%) - 1,275,000)*(1-30%) + 150,000*30% = $2,066,250

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Step 2: Calculate Revised NPV and Determine the Change

Present Value of Revised Operating Cash Flow = 2,066,250*[((1-(1+15%)^-10)/15%] = $10,370,030.67

Revised NPV = -1,500,000 + 10,370,030.67 = $8,870,030.67

Change in NPV = Original NPV - Revised NPV = 10,055,714.76 - 8,870,030.67 = $1,185,684.09

NPV decreases by $1,185,684.09.

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