Pappy ?s Potato has come up with a new product, the Pet Potato (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 Pet Potato will generate sales of $380,000 per year. The fixed
costs associated with this will be $145,000 per year, and variable
costs will amount to 20 percent of sales. The equipment necessary for
production of the Potato Pets will cost $240,000 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 only initial cost for the production. Pappy?s is in
a 40 percent tax bracket and has a required return of 13 percent.
Calculate the payback period, NPV and IRR.

Hi suj115!!


First of all we need to calculate the initial investment:

In this case the total initial investment (I) is the sum of the
marketing survey plus invests in plant and equipment:

I = $120,000 + $240,000 = $360,000


The next step is to calculate the cash flow for each year:

For each of the four years Yi (i = 1 to 4) we have that:

Depreciation = D = (Invest in plant and equipment) / 4 = 
                 = $240,000 / 4 =
                 = $60,000 

If we call Ri = revenues of Yi and Ei = expenses of Yi, then for each
year: 

Ri = $380,000  (i = 1 to 4)

Ei = Fixed costs + Variable Costs =
   = $145,000 + 0.20*$380,000 = 
   = $221,000                     (i = 1 to 4)


Taxes will be:

Ti = T * (Ri - Ei - D) =                with T = 0.4
   = 0.4*($380,000 - $221,000 - $60,000) =
   = 0.4*($99,000) =
   = $39,600                    (i = 1 to 4)


Now we can write the cash flow formula for each year:

CFi = Ri - Ei - T*(Ri - Ei - D)

Note that (Ri - Ei) is the Net Operating Profit for the year i; then
we can say that in general:
CF = Net Operating Profit - Taxes 

Then:

CFi = 380,000 - 221,000 - 39,600 = $119,400  (i = 1 to 4).

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PayBack Period:
Payback Period (PB) calculation give us an idea on how long it will
take for a project to recover the initial investment.
If Y is the year before the full recovery of the investment I, U is
the unrecovered cost at the start of last year and CFi is the CF of
the year Y+1 then:
PB = Y + U/CFi 

Note that at the end of the third year the initial investment is not
recovered, so the payback period is greater than 3:
Y = 3
U = 360,000 - 3*119,400 = 360,000 - 358,200 = $1,800 
CF4 = $119,400 

Then:

PB = 3 + 1,800/119,400 = 3 + 0.015 = 3.015

Note: Each month is the 1/12 (= 0.083) part of the year, and 0.015 is
greater than zero and less than 1/12, so we can "round" the 3.015 to 3
years and 1 month.

---------------------------------------------------------

NPV:

Some definitions:

Present Value (PV):

         CF1           CF2            CF3            CF4  
PV  = ---------  +  ----------  +  ----------  +  ----------
      (1 + r)^1     (1 + r)^2	  (1 + r)^3      (1 + r)^4  

Where r is the required return.


If all the cash flows are equal (like in this problem):
      CF             1
PV = ---- * [1 - ---------] 
       r          (1-r)^4

Net Present Value (NPV):

NPV = PV - I         where I = Total Initial Investment



PV = 119,400/0.13 * [1 - 1/(1.13)^4] =
   = $355,151.88 

NPV = PV - I =
    = $355,151.88 - $360,000 =
    = -$4,848.12


----------------------------------------------------------

IRR:

IRR is the discount rate r at which the NPV equals zero:

NPV = PV - I = 0


Then IRR is the discount rate r at which:

PV = I


So you must find the r that solves the following equation:

        CF1         CF2          CF3          CF4  
PV = --------- + ---------- + ---------- + --------- = I
     (1 + r)^1   (1 + r)^2    (1 + r)^3    (1 + r)^4  


You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)

Here is a brief guide to do this using an MS Excel spreadsheet for this problem:
1) Select a column for the project's Cash flows (for example column "A").
2) Input the project's Cash Flows starting from the initial investment
(this is a negative input) and followed by the CF1 to CF4 cash flows,
each one in one cell of the column.
3) Click on the cell where you want your IRR calculated (say B1). 
4) Enter "=IRR(" (without the quotes) and then highlight the column A
then close the parenthesis and hit enter.

For the project A the column A will have:
A1: -360,000 ; A2: to A5: 119,400 ;
B1: =IRR(A1:A5)

You will find that IRR = 12.35% .

This is why the NPV is negative, because the IRR is less than the
required rate of return.
So for the estipulated rate of return of 13%, this 4 years project is
not an aceptable one, you will lose money with it.
The following page will give you additional reference about this:
"Project Evaluation and Selection Analysis Techniques":
http://cbdd.wsu.edu/kewlcontent/cdoutput/TR505r/page15.htm


-----------------------------------------------------------

I hope that this helps you. If you find something unclear or need
further assistance, please post a request for an answer clarification
before rate this answer. I will gladly respond to your requests.


Best regards.
livioflores-ga

Thank you very much livioflores

Thank you for the rating and the generous tip!!

Regards.
livioflores-ga

What would be different if there were an additional investment of
$100,000 in Year 3?

I can phrase this in the form of a repeat question if need be.

Thanks.