P1117 Sensitivity Analysis LO1 Consider a 9year project with

P11-17 Sensitivity Analysis [LO1 Consider a 9-year project with the following information: Initial flxed asset investment $390,000; straight- line depreciation to zero over the 9-year life; zero salvage value; price = $25; variable costs = $14; fixed costs = $187,200; quantity sold-116,064 units, tax rate-30 percent. How sensitive is OCF to changes in quantity sold? (Do not round your intermediate calculations.) O $9.93 O $0.13 O $8.78 O $5.47 O $770

Solution

Operating cash flow = [(P – v) Q – FC] (1 – T) + Depreciation

P = Price = $ 25

v = Variable cost = $ 14

Q = Quantity

FC = Fixed cost = $ 187,200

T = Tax rate = 30 % = 0.30

Depreciation = $ 390,000/9 = $ 43,333.33

Operating cash flow for 116,064 units = [($ 25 - $ 14) x 116,064](1 – 0.3) + $ 43,333.33

                                                                = [($ 11 x 116,064) - $ 187,200] x 0.7 + $ 43,333.33

                                                               = ($1,276,704 - $ 187,200) x 0.7 + $ 43,333.33

                                                               = $ 1,089,504 x 0.7 + $ 43,333.33

                                                               = $ 762,652.80 + $ 43,333.33

                                                               = $ 805,986.13

Let’s compute Operating cash flow for any other level of production, suppose 117,064 units.

Operating cash flow for 116,064 units = [($ 25 - $ 14) x 117,064](1 – 0.3) + $ 43,333.33

                                                                = [($ 11 x 117,064) - $ 187,200] x 0.7 + $ 43,333.33

                                                               = ($1,287,704 - $ 187,200) x 0.7 + $ 43,333.33

                                                               = $ 1,100,504 x 0.7 + $ 43,333.33

                                                               = $ 770,352.80 + $ 43,333.33

                                                               = $ 813,686.13

The sensitivity of the OCF to changes in the quantity sold is:

Sensitivity = OCF/Q = ($ 813,686.13 - $ 805,986.13)/ (117,064 - 116,064)

                                        = $ 7,700/1,000 = $ 7.70

Hence option “$ 7.70” is correct answer.