We are evaluating a project that costs $972,000, has a four-year life, and has n

Question

We are evaluating a project that costs $972,000, has a four-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 88,800 units per year. Price per unit is $35.15, variable cost per unit is $21.40, and fixed costs are $768,000 per year. The tax rate is 35 percent, and we require a return of 13 percent on this project.

Requirement 1: Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Base-case cash flow? NPV?

Requirement 2: What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).) Sensitivity of NPV $

Requirement 3: If there is a 500-unit decrease in projected sales, how much would the NPV drop? (Do not round intermediate calculations. Input your answer as a positive value. Round your answer to 2 decimal places (e.g., 32.16).) NPV drop $

Requirement 4: What is the sensitivity of OCF to changes in the variable cost figure? (A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).) Sensitivity of OCF $

Requirement 5: If there is $1 decrease in estimated variable costs, how much would the increase in OCF be? (Round your answer to the nearest whole dollar amount (e.g., 1,234,567).) Increase in OCF

Explanation / Answer

(1) Calculation of base-case cash flow and NPV.We have,

Step1: Base case cash flow:

Base-case cash flow = [Total sales x Contribution - Fixed Cost] x(1 - tax rate) + Depreciation x Tax rate

Base-case cash flow = [ 88,800 x 13.75 - 768,000] x (1 -0.35) + 243,000 x 0.35

Base-case cash flow = [ 1,220,000 - 768,000] x 0.65 + 85,050

Base-case cash flow = 453,000 x 0.65 + 85,050 = 294,400 + 85,050 = $ 379,500

Hence, base case cash flow is $ 379,500

Step2: Net Present Value(NPV):

NPV = Present value of cash inflow - Present value of cash outflow

NPV = 379,500 X PVIFA(13%,4 years) - 972,000

NPV = 379,500 X 2.9745 - 972,000 = $ 156,822.75

Hence, the NPV of the project is $ 156,822.75

(2) Computation of the sensitivity of NPV to change in the sales figure.We have,

To calculate the sensitivity of the NPV to change in the quantity sold,we will calculate the NPV at different quantity(say 80,000 units), The NPV at this level is:

Present value of cash inflow =  [ 80,000 x 13.75 - 768,000] x (1 -0.35) + 243,000 x 0.35

Present value of cash inflow = [ 1,100,000 - 768,000 ] x 0.65 + 85,050

Present value of cash inflow =$ 300,850

NPV at 80,000 units = 300,850 x PVIFA(13 %, 4 years) - 972,000 = 300,850 x 2.9745 - 972,000

NPV at 80,000 units = - $ 77,121.67

So, the change in NPV for every unit change in sales is

= ( 156,822.75 - (- 77,121.67 ) / ( 88,800 - 80,000)

= 233,944.42 / 8,800 = $ 26.585

Hence,the sensitivity of change in NPV to change in sales figure is $ 26.585.

(3) if 500 units decrease in projected sales, NPV is drop = 500 x 26.585 = $ 13,292.50

  Hence, NPV drop = $ 13,292.50

(4) Computation of the sensitivity of OCF.We have,

For the calculation of sensitivity on OCF, We have to calculate operating cash flow at variable cost $ 20.40.We have,

Operating cash flow = 88,800(35.15 - 20.40) - 792,000] 0.65 + 85,050

Operating cash flow = [1,320,000 - 792,000] 0.65 + 85,050

Operating cash flow = $ 421,620

So, change in OCF for a $ 1 change in variable cost is

= [ 421,620 - 379,500] / ( 20.40 - 21.40) = 42,120 /- 1.00 =- $ 42,120

Hence, the sensitivity in OCF = - $ 42,120

(5) If there is $1 decrease in estimated variable costs, OCF would be increase by $ 42,120.

Project Cost $972,000 Life 4 years Depreciation per year using straight-line method (972,000 - 0) / 4 = $ 243,000 Sales units 88,000 units Sales prices $ 35.15 Variable cost per unit $ 21.40 Contribution (Sales prices - Variable cost) (35.15 - 21.40) = $ 13.75 Fixed Cost $ 768,000 Tax rate 35 % Required rate of return 13 %

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