Question

Pappy’s Potato has come up with a new product, the Potato Pet (they are freeze-dried to last longer). Pappy’s paid $145,000 for a marketing survey to determine the viability of the product. It is felt that Potato Pet will generate sales of $860,000 per year. The fixed costs associated with this will be $214,000 per year, and variable costs will amount to 18 percent of sales. The equipment necessary for production of the Potato Pet will cost $900,000 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 25 percent and a required return of 13 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., 32.16.)
c.	Calculate the IRR for this project.

Answer 1

The cash flows of the project are as given below :

Revenue forecast	0	1	2	3	4
Revenues (A)		860,000	860,000	860,000	860,000
Variable costs (B = 18% x A)		(154,800)	(154,800)	(154,800)	(154,800)
Fixed Costs (C)		(214,000)	(214,000)	(214,000)	(214,000)
Depreciation (D= H /4)		(225,000)	(225,000)	(225,000)	(225,000)
EBIT (E = A+B+C+D)		266,200	266,200	266,200	266,200
Taxes @ 25% (F = E x 25%)		(66,550)	(66,550)	(66,550)	(66,550)
Net Income (G = E + F)		199,650	199,650	199,650	199,650
Depreciation (D)		225,000	225,000	225,000	225,000
Capital Expenditure (H)	(900,000)
Free Cash Flow (O =G+D+H)	(900,000)	424,650	424,650	424,650	424,650
Cost of Capital (Discount Rate) R	13.00%
PV Of Free Cash Flow	(900,000)	375,796	332,563	294,304	260,446
NPV (Sum of PV of all CF)	363,109
IRR (IRR function in excel)	31%
PI (PV of future CF/ Investment)	1.40

Capital Expenditure = 900,000 (does not include marketing survey cost for the product) and it has to be depreciated by way of straight line method for 4 years

Depreciation = 900000/4 = 225000
1. Pay back period is the period by when the investment is recovered

Year	Free Cash Flows	Cumulative Cash Flow
0	(900,000)	(900,000)
1	424,650	(475,350)
2	424,650	(50,700)
3	424,650	373,950
4	424,650	798,600

Here the payback lies between 2nd & 3rd year, when cumulative cash flow becomes positive

Payback period = 2 + 50700/ 424650 = 2.12 years

Free Cash Flow = Net Income + Depreciation + equipment cost

PV of cash Flow = CFt / (1+k) ^ t

where, CFt is the cash flow in year t

k = discount rate or cost of capital or required return

t is the year of cash flow

NPV = PV of all cash flows - Investment in equipment

NPV = 424650/ (1+13%) ^1 + 424650/ (1+13%)^2 + 424650 / (1+13%)^3 + 424650/ (1+13%) 6 4 - 900,000

= 375796 + 332563+ 294304 + 260446 - 900000

= 1263109 - 900000

= $363,109

3. IRR of the project is calculated using IRR function in excel.

IRR = IRR(13%,-900000,424560,424560,424560,424560) = 31.32%