XYZ is an all equity firm with a beta of 0.95.  The market risk
premium is 9% and the risk-free rate is 5%.  The company is
considering a project that will bring in cash flows of $340,000 at
year end for 5 years.  The project requires an immediate investment of
1.2 million.  Should XYZ take this project if it has the same risk as
the firm as a whole?

Hi!!


According to the statement this project has the same risk as the firm
as a whole, therefore the discount rate for the project (Rp) is equal
to the expected return on the company equity (Re), applying the CAPM
we can find both:

Rp = Re = Rf + Beta*Rmp =
        = 5% + 0.95*9% =
        = 13.55%


Now calculate the NPV of the project to see if it is profitable:
NPV = PV of Cash Flows - Investment (or initial cash flow)

The hard part of the above formula is the PV of the cash flows:

        CF1                     CF5      
PV = ----------  +  ....   +  ---------- 
     (1 + Rp)^1               (1 + Rp)^5    
     


Then:

         CF1                    CF5      
NPV = ----------  +  ....   +  ---------- - I
      (1 + Rp)^1               (1 + Rp)^5    



In cases like this, when all the cash flows are equal, the PV formula
can be simplified:

      CF              1
PV = ---- * [1 - ----------] 
      Rp          (1+Rp)^5

And we will have that:

       CF             1
NPV = ---- * [1 - ----------] - I  =
       Rp          (1+Rp)^5

    = (340,000/0.1355)*[1-(1/1.1355^5)] - 1,200,000 =
    = -20,016.52

Since the project has a negative NPV it must be rejected. 

See the following page for further explanations:
"Methods/Criteria of Project Evaluation or Measures of project Worth
of Investment" by Dr. A.K. Sarma:
http://www.assamagribusiness.nic.in/agriclinics/Methods%20criteria.pdf


Search strategy:
"project evaluation"


I hope this helps you. Feel free to request for a clarification if you need it.


Regards,
livioflores-ga