Question

Pappy’s Potato has come up with a new product, the Potato Pet (they are freeze-dried to last longer). Pappy’s paid $175,000 for a marketing survey to determine the viability of the product. It is felt that Potato Pet will generate sales of $890,000 per year. The fixed costs associated with this will be $226,000 per year, and variable costs will amount to 22 percent of sales. The equipment necessary for production of the Potato Pet will cost $960,000 and will be depreciated in a straight-line manner for the four years of the product life (as with all fads, it is felt the sales will end quickly). This is the only initial cost for the production. Pappy's has a tax rate of 21 percent and a required return of 15 percent.

Calculate the payback period for this project.

Calculate the NPV for this project.

Calculate the IRR for this project.

Answer 1

Time line		0	1	2	3	4
Cost of new machine		-960000
=Initial Investment outlay		-960000
Sales			890000	890000	890000	890000
Profits	Sales-variable cost		694200	694200	694200	694200
Fixed cost			-226000	-226000	-226000	-226000
-Depreciation	Cost of equipment/no. of years		-240000	-240000	-240000	-240000
=Pretax cash flows			228200	228200	228200	228200
-taxes	=(Pretax cash flows)*(1-tax)		180278	180278	180278	180278
+Depreciation			240000	240000	240000	240000
=after tax operating cash flow			420278	420278	420278	420278
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-960000	420278	420278	420278	420278

Project
Year	Cash flow stream	Cumulative cash flow
0	-960000	-960000
1	420278	-539722
2	420278	-119444
3	420278	300834
4	420278	721112
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-119444))/(300834-(-119444))
2.28 Years
Project
Discount rate	0.15
Year	0	1	2	3	4
Cash flow stream	-960000	420278	420278	420278	420278
Discounting factor	1	1.15	1.3225	1.520875	1.7490063
Discounted cash flows project	-960000	365459.1	317790.5	276339.6	240295.31
NPV = Sum of discounted cash flows
NPV Project =	239884.6
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project
IRR is the rate at which NPV =0
IRR	0.268939102
Year	0	1	2	3	4
Cash flow stream	-960000	420278	420278	420278	420278
Discounting factor	1	1.268939	1.610206	2.043254	2.5927648
Discounted cash flows project	-960000	331204.2	261008.8	205690.5	162096.46
NPV = Sum of discounted cash flows
NPV Project =	1.54454E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	26.89%