Question

Consider a three-year project with the following information: initial fixed asset investment = $670,000; straight-line depreciation to zero over the 4-year life; zero salvage value; price = $38.75; variable costs = $27.83; fixed costs = $308,000; quantity sold = 79,000 units; tax rate = 21 percent. How sensitive is OCF to changes in quantity sold? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer :-

Given,

Price (P) = $38.75

Variable costs (V) = $27.83

Fixed costs(FC) = $308,000

Quantity sold(Q) = 79,000 units

Tax rate (T) = 21% or 0.21

Depreciation (D) = Fixed assets investment /life of assets

D = $670,000/4 = $167,500

Sensitive is OCF (Operating cash flow) = Change in OCF / Changes in quantity sold

OCF = [(P - V)Q -FC](1 - T) + (T × D)

OCF = [($38.75 - $27.83) 79,000 - $308,000] (1 - 0.21) + (0.21 × $167,500)

OCF = ($10.92 × 79,000 - $308,000) (0.79) + $35,175

OCF = ($862,680 - $308,000) (0.79) + $35,175

OCF = $438,197.2 + $35,175

OCF = $473,372.2

If Quantity change to 79,001 then OCF is

Quantity (Q) = 79,001

OCF (New) = [(P - V)Q -FC](1 - T) + (T × D)

OCF (New) = [($38.75 - $27.83) 79,001 - $308,000] (1 - 0.21) + (0.21 × $167,500)

OCF (New) = ($10.92 × 79,001 - $308,000) (0.79) + $35,175

OCF (New) = $438,205.83 - $35,175

OCF (New) = $473,380.83

Changes in OCF = OCF (new) - OCF

Changes in OCF = $473,380.83 - $473,372.2

Changes in OCF = $8.63

Change in quantity = New quantity - Old quantity

Change in quantity = 79,000 - 79,001 = 1 unit

Sensitive is OCF = $8.63/1 unit

Sensitive is OCF = $8.63