Question

We are evaluating a project that costs $1,100,000, has a life of 10 years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 47,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $820,000 per year. The tax rate is 21 percent and we require a return of 16 percent on this project. a. Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) b-1. Calculate the base-case cash flow and NPV. (Do not round intermediate calculations and round your NPV answer to 2 decimal places, e.g., 32.16.) b-2. What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) 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

a) Accounting break-even point = (FC + Depreciation) / (Price - VC) = (820,000 + 1,100,000 / 10) / (50 - 25) = 37,200 units

b)

Sales	2,350,000
VC	(1,175,000)
FC	(820,000)
Depreciation	(110,000)
EBT	245,000
Tax (21%)	(51,450)
Net Income	193,550
Cash Flow	303,550
NPV	$367,126.20

b1) Base case Cash Flows = Net Income + Depreciation = $303,550

NPV can be calculated using PV function on a calculator

N = 10, I/Y = 16%, PMT = 303,550, FV = 0 => Compute PV = $1,467,126.20

NPV = PV (inflows) - Investment = 1,467,126.20 - 1,100,000 = $367,126.20

b2) Sensitivity of NPV is the change in NPV for a unit change in sales.

If unit sales = 47,001 => NPV = $367,221.66

=> Sensitivity of NPV = 367,221.66 - 367,126.20 = $95.456

c) Similarly, sensitivity of OCF to changes in variable cost can be calculated.

If VC = 26 => OCF = 266,420

=> Sensitivity of OCF = 266,420 - 303,550 = -37,130