Project Evaluation.  Revenues generated by a new fad product are
forecast as follows:

Year 			Revenues
1 			$40,000
2 			  30,000
3 			  20,000
4 			  10,000
Thereafter 		        0

Expenses are expected to be 40 percent of revenues, and working
capital required in each
year is expected to be 20 percent of revenues in the following year. 
The product requires an
immediate investment of $50,000 in plant and equipment.

a.  What is the initial investment in the product?  Remember working capital.

b.  If the plant and equipment are depreciated over 4 years to a
salvage value of zero using
straight-line depreciation,  and the firm ?s tax rate is 40 percent, 
what are the project cash
flows in each year?

c.  If the opportunity cost of capital is 10 percent,  what is project NPV?
d. What is project IRR?

Hi again tangothecat!!

a.  What is the initial investment in the product?  Remember working capital.


The total initial investment (I) is the sum of the invest in plant and
equipment (in this case $50,000) plus the initial Working Capital
required (in this case is the 20% of the Revenues of Year 1 =
0.20*$40,000 = $8,000):

I = $50,000 + $8,000 = $58,000

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b.  If the plant and equipment are depreciated over 4 years to a
salvage value of zero using straight-line depreciation, and the firm
?s tax rate is 40 percent, what are the project cash flows in each
year?


For each year Yi (i = 1 to 4):

Depreciation = D = (Invest in plant and equipment) / 4 = 
                 = $12,500

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

Ti = T * (Ri - Ei - D)  with T = 0.4


Working Capital Change for year Yi:
 
ChWCi = Current WC - Previous Year WC


Now we can write the cash flow formula:

CFi = Ri - Ei - T - ChWCi

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 - Net Change in Working Capital
 

Then:

CF1 = 40,000 - 16,000 - 0.4*(11,500) - (-2,000) = $21,400

CF2 = 30,000 - 12,000 - 0.4*(5,500) - (-2,000) = $17,800

CF3 = 20,000 - 8,000 - 0.4*(-500) - (-2,000) = $14,200

CF4 = 10,000 - 4,000 - 0.4*(-6,500) - (-2,000) = $10,600


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c. If the opportunity cost of capital is 10 percent, what is project NPV?


Remember that:

Present Value:

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


and Net Present Value:

NPV = PV - I         where I = Initial Investment


PV = $52,073.90 

NPV = $52,073.90 - $58,000.00 = 
    = -$5,926.10

(this is a negative NPV)

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d. What is project IRR?

IRR is the discount rate r that satisfies the following equation:

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

In other words IRR is the discount rate that makes the NPV equals to zero.


Use an Excel spreadsheet to calculate the IRR using the following inputs:
Column A values:         Column B
A1: -58,000              B1: =IRR(A1:A5)
A2: 21,400
A3: 17,800
A4: 14,200
A5: 10,600

IRR =  4.59%

(the IRR is less than the required discount rate).

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I hope that this helps you. Again if you find something unclear, imcomplete
or wrong please let me know, I will gladly respond to your requests.


Best regards.
livioflores-ga