Question

# Consider a 9-year project with the following information: initial fixed asset investment = \$430,000; straight-line depreciation...

Consider a 9-year project with the following information: initial fixed asset investment = \$430,000; straight-line depreciation to zero over the 9-year life; zero salvage value; price = \$32; variable costs = \$17; fixed costs = \$167,700; quantity sold = 98,943 units; tax rate = 33 percent. How sensitive is OCF to changes in quantity sold?

 Initial Investment \$430,000.00 Selling Price \$32.00 Variable Cost \$17.00 Fixed Cost \$167,700.00 Quantity Sold 98943 units Tax Rate 33.00% Depreciation = \$430,000/9 \$47,777.78 OCF = ((SP-VC) x Q -FC) x (1-T) + (T x D) OCF = ((32-17) x 98943 -167,700) x (1-33%) + (33% x \$47,777.78) \$897,784.82 NPV=-Initial Outlay + OCF (PVIFA10%, 9) + Salvage value NPV=- 430000 + 897784.82 (PVIFA10%, 9) + 0 \$4,740,364.14 Quantity Sold OCF NPV Base Case 98,943 \$897,784.82 \$4,740,364.14 Optimistic + 10% 108,837 987,563 \$5,257,400.56 Pessimistic - 10% 89,049 808,006 \$4,223,327.73 Sensitivity = ?OCF/?Q = (\$897,784 - \$987,563)/(98943-108,837) 9.07 Sensitivity = ?NPV/?Q = (\$4740364 - \$5257400)/(98943-108,837) \$52.26 For every additional unit sold, OCF goes up by \$9.07 and NPV by \$52.26

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