Question

Pappy’s Potato has come up with a new product, the Potato Pet (they are freeze-dried to last longer). Pappy’s paid $120,000 for a marketing survey to determine the viability of the product. It is felt that Potato Pet will generate sales of $835,000 per year. The fixed costs associated with this will be $204,000 per year, and variable costs will amount to 20 percent of sales. The equipment necessary for production of the Potato Pet will cost $865,000 and will be depreciated in a straight-line manner for the 4 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 13 percent. Calculate the payback period, NPV, and IRR. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. Enter your IRR answer as a percent.)

Answer 1

Solution:

The cost of initial investment is $865,000 as the cost of market survey is a sunk and hence it will not be included in the cost of the project.

Given Sales = $835,000,

Cost = Fixed cost + Variable cost

Cost = $204,000 + 0.20*$835,000

Cost = $371,000

Depreciation = Cost of initial investment/Useful life

Depreciation = $865,000/4

Depreciation = $216,250

Now, we calculate the operating cash flow (OCF)

OCF = (Sales - Costs) (1 - tax rate) + Depreciation tax shield

OCF = ($835,000 - $371,000) (1 - 0.23) + $216,250*0.23

OCF = $407,017.50

Payback period is when the initial investment is recovered.

Payback period = 2 + ($865,000 - $407,017.50*2)/$407,017.50

Payback period = 2 + 0.125

Payback period = 2.13 years

NPV = -Cost of investment + OCF (PVIFA @ i, n)

NPV = -865,000 + 407,017.50 (PVIFA @ 13%, 4)

NPV = -865,000 + 407,017.50

NPV = -865,000 + 407,017.50 (2.9745)

NPV = $345,661.9

At IRR, NPV equals zero

0 = -865,000 + 407,017.50 (PVIFA @ IRR, 4)

865,000 = 407,017.50 (PVIFA @ IRR, 4)

We use trial and error method and substitute IRR = 31%

NPV = -865,000 + 407,017.50 (PVIFA @ 31%, 4)

NPV = -865,000 + 407,017.50

NPV = 2132.842

Now, we substitute IRR = 32%

NPV = -865,000 + 407,017.50 (PVIFA @ 32%, 4)

NPV = -865,000 + 407,017.50

NPV = -12,025.3

Using interpolation, IRR is

= 0.31 + 0.0015

IRR = 0.3115 or 31.15%