Question

We are evaluating a project that costs $611,800, has a seven-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 85,000 units per year. Price per unit is $42, variable cost per unit is $29, and fixed costs are $700,000 per year. The tax rate is 21 percent, and we require a return of 10 percent on this project. a-1.Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) a- What is the degree of operating leverage at the accounting break-even point? (Do 2. not round intermediate calculations and round your answer to 3 decimal places, e.g, 32.161.) b-1.Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your cash flow answer to the nearest whole number, e.g., 32. Round your NPV answer to 2 decimal places, e.g., 32.16.) b- What is the sensitivity of NPV to changes in the quantity sold? (Do not round 2. intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Answer 1

b-1.Base-case cash flows = [ { ( Selling Price - Variable Cost) x Quantity - Fixed Costs} x ( 1 - T ) ] + Depreciation x T = [ $ { 42.00 - 29.00 ) x 85,000 - 700,000 } x ( 1 - 0.21 ) ] + $ 87,400 x 0.21 = $ 319,950 + $ 18,354 = $ 338,304.

NPV = Base-case cash flows x [ { 1 - ( 1 / 1.10 ) ⁷ } / 0.10 ] - Initial Investment = $ 338,304 x 4.8684 - $ 611,800 = $ 1,035,199.19

b-2. If we increase quantity sold to 86,000 units,

Cash flows = [ { $ 13 x 86,000 - 700,000 } x 0.79 } + $ 18,354 = $ 348,574.

NPV = $ 348,574 x 4.8684 - $ 611,800 = $ 1,085,197.66

Sensitivity of NPV to change in quantity sold = $ ( 1,085,197.66 - 1,035,199.19) / 1,000 = 49.99 times.

c. If variable cost decreases by $ 1,

Operating cash flows = [ { ( 42 - 28) x 85,000 - 700,000 } x 0.79} x 0.79 ] + $ 18,354 = $ 405,454

Change in Operating cash flows = $ 405,454 - $ 338,304 / - $ 85,000 = $ 67,150 / - $ 85,000 = - 0.79 times