Question

We are evaluating a project that costs $670,000, has a life of 5 years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 59,000 units per year. Price per unit is $44, variable cost per unit is $24, and fixed costs are $760,000 per year. The tax rate is 23 percent and we require a return of 16 percent on this project.

What is the sensitivity of NPV to changes in the sales figure? (Change)NPV/(change)Quantity What is the sensitivity of OCF to changes in the variable cost figure? (change)OCF/(Change)VC

Answer 1

Year	Sales(unit)	Revenue (Sales*Price/unit)	Variable Cost (Unit*VC)	Fixed Cost	Depreciation (Initial Cost/5)	PBT (Revenue-VC-Fixed Cost)	Tax( (PBT-Depreciation)*tax rate)	PAT (PBT-TAX)	Discounted Present Value (PAT/1.16^year)
0	0	-670000	0	0	0	-670000	0	-670000	-670000
1	59000	2596000	1416000	760000	134000	420000	65780	354220	322018.2
2	59000	2596000	1416000	760000	134000	420000	65780	354220	292743.8
3	59000	2596000	1416000	760000	134000	420000	65780	354220	266130.7
4	59000	2596000	1416000	760000	134000	420000	65780	354220	241937
5	59000	2596000	1416000	760000	134000	420000	65780	354220	219942.8
								NPV (Sum of all Present Value)	672772.5

For sales of 59000 unit NPV is 672772.5 and using the same model if sale is 50000 then NPV becomes 147369.4. So, sensitivity= change of NPV/change of quantity=(672772.5-147369.4)/(59000-50000)=$58.37

Similarly, in the above scenario OCF(PAT+Depreciation) =488220 when VC=24 and OCF=442790 when VC=25

So, sensitivity= (442790-488220)/(25-24)=$-45430