Question

You are running a grocery store thinking about installing the Sushi 1000 vending machine. The machine costs $100k today (year 0) and will last five years (years 1-5). Assume annual sales in years 1 through 5 will be $75k, costs will be $50k, and depreciation will be $20k (straight-line). Assume a discount rate of 10%. Calculate the cash flows and NPV of this project first assuming a corporate tax rate of 0% and then assuming a corporate tax rate of 40%.

Answer 1

1) tax rate = 0%

Time line		0	1	2	3	4	5
Cost of new machine		-100000
=Initial Investment outlay		-100000
Sales			75000	75000	75000	75000	75000
Profits	Sales-variable cost		75000	75000	75000	75000	75000
Fixed cost			-50000	-50000	-50000	-50000	-50000
-Depreciation	Cost of equipment/no. of years		-20000	-20000	-20000	-20000	-20000
=Pretax cash flows			5000	5000	5000	5000	5000
-taxes	=(Pretax cash flows)*(1-tax)		5000	5000	5000	5000	5000
+Depreciation			20000	20000	20000	20000	20000
=after tax operating cash flow			25000	25000	25000	25000	25000
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-100000	25000	25000	25000	25000	25000
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051
Discounted CF=	Cashflow/discount factor	-100000	22727.273	20661.157	18782.87	17075.336	15523.03
NPV=	Sum of discounted CF=	-5230.3308

1) tax rate =40%

Time line		0	1	2	3	4	5
Cost of new machine		-100000
=Initial Investment outlay		-100000
Sales			75000	75000	75000	75000	75000
Profits	Sales-variable cost		75000	75000	75000	75000	75000
Fixed cost			-50000	-50000	-50000	-50000	-50000
-Depreciation	Cost of equipment/no. of years		-20000	-20000	-20000	-20000	-20000
=Pretax cash flows			5000	5000	5000	5000	5000
-taxes	=(Pretax cash flows)*(1-tax)		3000	3000	3000	3000	3000
+Depreciation			20000	20000	20000	20000	20000
=after tax operating cash flow			23000	23000	23000	23000	23000
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-100000	23000	23000	23000	23000	23000
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051
Discounted CF=	Cashflow/discount factor	-100000	20909.091	19008.2645	17280.24	15709.309	14281.19
NPV=	Sum of discounted CF=	-12811.904