Question

You’ve been asked to evaluate a project. Your estimates say that the first cashflow of $120k will occur one year from today. You believe the cashflows will increase by 4% per year for 4 additional years. After that point, the cashflows will remain the same for 5 years. The upfront cost to take the project is $950k, and the appropriate discount rate is 6%. What is the project’s NPV? PLEASE POST THE ANSWER IN THE EQUATION FORMAT - NO NEED TO SOLVE FOR ACTUAL NUMBER.

Answer 1

{Strating year cash flow=   $120,000
Increase rate for 4 years =   4%
So equation for actual cash flow = Previous cash flow*(1+growth rate)  
for year 2 =120000*(1+4%)  
and so on  
  
NPV equation = PV of cash inflow - PV of cash outflow  
PV of cash flows = Cash flows * PVF  
PVF = 1/(1+discout rate)^n  
for year 1= 1/(1+6%)^1  
for year 2= 1/(1+6%)^2 and so on.  
  

Calculation of P.V. of cash flows          
Discount rate (i)= 6.5% or   0.06      
Period (n)   Amount    P.V.F.= 1/(1+i)^n   Amount *PVf
          
       1/(1+0.06)^n  
          
Year 1   120000.00   0.9434   113207.55
Year 2   124800.00   0.8900   111071.56
Year 3   129792.00   0.8396   108975.87
Year 4   134983.68   0.7921   106919.72
year 5   140383.03   0.7473   104902.36
year 6   140383.03   0.7050   98964.49
year 7   140383.03   0.6651   93362.73
year 8   140383.03   0.6274   88078.05
year 9   140383.03   0.5919   83092.50
year 10   140383.03   0.5584   78389.15
          
So PV of Cash inflows is            986963.97
          
NPV=   986963.97   -950000 = 36963.97

NPV is positive
So it is worth taking.          

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