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Q: Calculation of NPV ( Answered 5 out of 5 stars,   0 Comments )
Question  
Subject: Calculation of NPV
Category: Business and Money > Finance
Asked by: goodgirl1-ga
List Price: $2.00
Posted: 20 Dec 2004 12:42 PST
Expires: 19 Jan 2005 12:42 PST
Question ID: 445211
XYZ company has come up with a new product.  XYZ paid $120,000 for a
marketing survey to determine the viability of the product.  Sales are
forecasted at $380,000 per year.  Fixed costs are $145,000 per year
and variable costs will amount to 20% of sales.  The equipment
necessary for production will cost $240,000 and will be depreciated in
a straightline manner for the four years of the product life.  This is
only initial cost for the production.  XYZ is in a 40% tax bracket and
has a required return of 13 percent.  Calculate the payback period,
NPV and IRR
Answer  
Subject: Re: Calculation of NPV
Answered By: livioflores-ga on 20 Dec 2004 14:57 PST
Rated:5 out of 5 stars
 
Hi goodgirl1!!


The first thing that we need to calculate is the initial investment:

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

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


Now we need to calculate the cash flow for each year:

Name each of the four years as Yi (i = 1 to 4).


We have that the Depreciation (D) for each year is:

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


Now we name Ri = revenues (sales) of Yi and Ei = expenses of Yi, then for each
year, then we have that: 

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

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


Tax calculation for each year:

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)


The cash flow formula is:

CF = Net Operating Profit - Taxes 

Note that (Ri - Ei) is the Net Operating Profit for the year i; then:

CFi = Ri - Ei - Ti


Then:

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

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

PayBack Period (PB):
Payback Period 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:

First we need to define the Present Value (PV):

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

where R is the required return.


When all CFi are the same as in this problem we have that (for 4 years):

      CF             1
PV = ---- * [1 - ---------] 
       R          (1+R)^4


Net Present Value (NPV):

NPV = PV - I         (I = Total Initial Investment calculated above)


Since R = 13% = 0.13 we have:

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

Then:
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 <==> PV = I


Then you must find R that solves the equation:

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


You can use many different techniques to calculate the IRR:
-Trial & Error
-Financial 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% .


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

Note that the NPV is negative and the IRR is less than the required
rate of return of 13%. This means that this 4 years project is not
acceptable.

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


I hope that this helps you. Please request for an answer clarification
if need it before rate this answer. I will gladly respond to your
requests.


Best regards.
livioflores-ga
goodgirl1-ga rated this answer:5 out of 5 stars

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