Question

The New York downtown is planning to develop a piece of land and three mutually exclusive projects were proposed. A playground with 4 years of project life, a swimming pool with 5 years of project life and a volleyball court with 6 years of project life. All three projects each have initial capital costs of $200 and annual net benefits of $140, $120, $110 respectively. Assuming a 10% cost of capital, how would you rank them?

Excel format would be the best

Answer 1

To rank mutual exclusive projects, NPV criteria is used. project having higher NPV would be ranked first and so on.  
NPV = PV of annual benefits - initial outlay  
cost of capital =   10%
  
Playground project life=   4
Annual benefits =   140
PV of annual benefits =   $443.78
initial cost   200
NPV=   $243.78
  
swimming pool project life   5
Annual benefits =   120
PV of annual benefits =   $454.89
initial cost   200
NPV=   $254.89
  
volleyball court project life=   6
Annual benefits =   110
PV of annual benefits =   $479.08
initial cost   200
NPV=   $279.08
  
So Volleyboll will be ranked    1
swimming pool will be ranked    2
playground will be ranked   3
  
Note : Excel formula used for PV of annual benefits =  
=-pv(rate,life,annual benefits) use cell reference for figures  
=-pv(10%,4,140)  

=$443.78
  
NpV formula= PV-initial cost