We are evaluating a project that costs $974,000, has a fifteen-year life, and ha

Question

We are evaluating a project that costs $974,000, has a fifteen-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 110,000 units per year. Price per unit is $36, variable cost per unit is $23, and fixed costs are $983,740 per year. The tax rate is 35 percent, and we require a 16 percent return on this project.

A) What is the sensitivity of NPV to changes in the sales figure?

B)What is the sensitivity of OCF to changes in the variable cost figure?

C) Calculate the change in OCF if there is a $1 decrease in estimated variable costs.

Explanation / Answer

Part A)

To calculate the sensitivity of NPV to changes in the sales figure, we need to calculate the NPV at 2 different sales levels. We will take 110,000 units and 111,000 units to determine the same.

NPV will be calculated with the use of initial investment and operating cash flow for each year.

The formula for calculating NPV is:

NPV = Cash Flow Year 0 + Cash Flow Year 1(1+Discount Rate)^1 + Cash Flow Year 2(1+Discount Rate)^2 + Cash Flow Year 3(1+Discount Rate)^3 + Cash Flow Year 4(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5+....................+ Cash Flow Year 15/(1+Discount Rate)^15

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

Depreciation = Project Cost/Life

___________________

Using the values provided in the question, we get,

Depreciation = 974,000/15 = $64,933.33

___________

Operating Cash Flow (110,000) = [110,000*(36 - 23) - 983,740 - 64,933.33]*(1-35%) + 64,933.33 = $312,795.67

Operating Cash Flow (111,000) = [111,000*(36 - 23) - 983,740 - 64,933.33]*(1-35%) + 64,933.33 = $321,245.67

___________

NPV (110,000) = -974,000+312,795.67/(1+16%)^1+312,795.67/(1+16%)^2+312,795.67/(1+16%)^3+312,795.67/(1+16%)^4+312,795.67/(1+16%)^5+312,795.67/(1+16%)^6+312,795.67/(1+16%)^7+312,795.67/(1+16%)^8+312,795.67/(1+16%)^9+312,795.67/(1+16%)^10+312,795.67/(1+16%)^11+312,795.67/(1+16%)^12+312,795.67/(1+16%)^13+312,795.67/(1+16%)^14+312,795.67/(1+16%)^15 = $769,978.55

NPV (111,000) = -974000+321,245.67/(1+16%)^1+321,245.67/(1+16%)^2+321,245.67/(1+16%)^3+321,245.67/(1+16%)^4+321,245.67/(1+16%)^5+321,245.67/(1+16%)^6+321,245.67/(1+16%)^7+321,245.67/(1+16%)^8+321,245.67/(1+16%)^9+321,245.67/(1+16%)^10+321,245.67/(1+16%)^11+321,245.67/(1+16%)^12+321,245.67/(1+16%)^13+321,245.67/(1+16%)^14+321,245.67/(1+16%)^15 = $817,091.15

_________________

Sensitivity of NPV to Change in Sales Figure = (NPV at 111,000 - NPV at 110,000)/(111,000 - 110,000) = 47.11

____________________

Part B)

Sensitivity of OCF to changes in the variable cost figure requires the use of operating cash flow for 2 different variable cost figures. We will use $23 and $22 (assumed) for a quantity of $110,000.

_________________

Operating Cash Flow ($23) = [110,000*(36 - 23) - 983,740 - 64,933.33]*(1-35%) + 64,933.33 = $312,795.67

Operating Cash Flow ($22) = [110,000*(36 - 22) - 983,740 - 64,933.33]*(1-35%) + 64,933.33 = $384,295.67

Sensitivity of Operating Cash to Change in Variable Cost Figure = (Operating Cash Flow at $23 Variable Cost - Operating Cash Flow at $22)/(23 - 22) = (312,795.67 - 384,295.67)/(23 - 22) = -71,500

____________________

Part C)

Change in OCF with $1 Decrease in Variable Cost = 1*71,500 = $71,500 (Operating Cash Flow Increases by $71,500 for every $1 decrease in variable cost)

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