Question

We are evaluating a project that costs $680,000, 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 64,000 units per year. Price per unit is $43, variable cost per unit is $26, and fixed costs are $685,000 per year. The tax rate is 24 percent and we require a return of 14 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.

  

Calculate the best-case and worst-case NPV figures.

Answer 1

Best case NPV

Time line		0	1	2	3	4	5
Cost of new machine		-680000
=Initial Investment outlay		-680000
Unit sales			70400	70400	70400	70400	70400
Profits	=no. of units sold * (sales price - variable cost)		1682560	1682560	1682560	1682560	1682560
Fixed cost			-616500	-616500	-616500	-616500	-616500
-Depreciation	Cost of equipment/no. of years		-136000	-136000	-136000	-136000	-136000
=Pretax cash flows			930060	930060	930060	930060	930060
-taxes	=(Pretax cash flows)*(1-tax)		706845.6	706845.6	706845.6	706845.6	706845.6
+Depreciation			136000	136000	136000	136000	136000
=after tax operating cash flow			842845.6	842845.6	842845.6	842845.6	842845.6
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-680000	842845.6	842845.6	842845.6	842845.6	842845.6
Discount factor=	(1+discount rate)^corresponding period	1	1.14	1.2996	1.481544	1.68896016	1.9254146
Discounted CF=	Cashflow/discount factor	-680000	739338.2456	648542.321	568896.773	499032.257	437747.59
NPV=	Sum of discounted CF=	2213557.189

Worst case NPV

Time line		0	1	2	3	4	5
Cost of new machine		-680000
=Initial Investment outlay		-680000
Unit sales			57600	57600	57600	57600	57600
Profits	=no. of units sold * (sales price - variable cost)		581760	581760	581760	581760	581760
Fixed cost			-753500	-753500	-753500	-753500	-753500
-Depreciation	Cost of equipment/no. of years		-136000	-136000	-136000	-136000	-136000
=Pretax cash flows			-307740	-307740	-307740	-307740	-307740
-taxes	=(Pretax cash flows)*(1-tax)		-233882.4	-233882.4	-233882.4	-233882.4	-233882.4
+Depreciation			136000	136000	136000	136000	136000
=after tax operating cash flow			-97882.4	-97882.4	-97882.4	-97882.4	-97882.4
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-680000	-97882.4	-97882.4	-97882.4	-97882.4	-97882.4
Discount factor=	(1+discount rate)^corresponding period	1	1.14	1.2996	1.481544	1.68896016	1.9254146
Discounted CF=	Cashflow/discount factor	-680000	-85861.7544	-75317.328	-66067.832	-57954.239	-50837.05
NPV=	Sum of discounted CF=	-1016038.205