Question

Pappy's Potato has come up with a new product, the Potato Pet (they are freeze-dried to last longer). Pappy's paid $160.000 for a marketing survey to determine the viability of the product. It is felt that Potato Pet will generate sales of $875.000 per year. The fixed costs associated with this will be $220.000 per year, and variable costs will amount to 24 percent of sales. The equipment necessary for production of the Potato Pet will cost $930,000 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 23 percent and a required return of 16 percent. a. Calculate the payback period for this project. (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. Calculate the NPV for this project. (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g., 32.18.) c. Calculate the IRR for this project. (Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. Payback period b. NPV C. IRR

Answer 1

Time line		0	1	2	3	4
Cost of new machine		-930000
=Initial Investment outlay		-930000
							100.00%
Sales			875000	875000	875000	875000
Profits	Sales-variable cost		665000	665000	665000	665000
Fixed cost			-220000	-220000	-220000	-220000
-Depreciation	Cost of equipment/no. of years		-232500	-232500	-232500	-232500	0	=Salvage Value
=Pretax cash flows			212500	212500	212500	212500
-taxes	=(Pretax cash flows)*(1-tax)		163625	163625	163625	163625
+Depreciation			232500	232500	232500	232500
=after tax operating cash flow			396125.00	396125.00	396125	396125
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-930000	396125.00	396125.00	396125.000	396125

a
Project
Year	Cash flow stream	Cumulative cash flow
0	-930000	-930000
1	396125	-533875
2	396125	-137750
3	396125	258375
4	396125	654500
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-(-137750))/(258375-(-137750))
2.35 Years
b
Project
Discount rate	0.16
Year	0	1	2	3	4
Cash flow stream	-930000	396125	396125	396125	396125
Discounting factor	1	1.16	1.3456	1.560896	1.8106394
Discounted cash flows project	-930000	341487.1	294385.4	253780.5	218776.31
NPV = Sum of discounted cash flows
NPV Project =	178429.31
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
c
Project
IRR is the rate at which NPV =0
IRR	0.253312789
Year	0	1	2	3	4
Cash flow stream	-930000	396125	396125	396125	396125
Discounting factor	1	1.253313	1.570793	1.968695	2.4673905
Discounted cash flows project	-930000	316062.4	252181.6	201212	160544.11
NPV = Sum of discounted cash flows
NPV Project =	3.50497E-07
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	25.33%