exercise:Af1adcbd1c

A municipal government is evaluating two potential public works projects, a Community Park Revitalization (CPR) and a Downtown Infrastructure Upgrade (DIU), over a 4-year planning horizon. They need to compare the present value of the net benefits (benefits minus costs) of these projects to allocate funds efficiently. The annual effective discount rate for public projects is [math]5\%[/math].

Project CPR (Community Park Revitalization):

• Initial cost (outflow at time [math]t=0[/math]): $[math]200,000[/math]
• Projected net annual benefits (inflows at year-end):
  • End of Year 1: $[math]60,000[/math]
  • End of Year 2: $[math]75,000[/math]
  • End of Year 3: $[math]80,000[/math]
  • End of Year 4: $[math]65,000[/math]

Project DIU (Downtown Infrastructure Upgrade):

• Initial cost (outflow at time [math]t=0[/math]): $[math]180,000[/math]
• Projected net annual benefits (inflows at year-end):
  • End of Year 1: $[math]50,000[/math]
  • End of Year 2: $[math]60,000[/math]
  • End of Year 3: $[math]X[/math] (unknown benefit)
  • End of Year 4: $[math]70,000[/math]

The municipal council has decided that Project DIU will only be approved if its Net Present Value (NPV) is equal to or greater than the NPV of Project CPR.

Calculate the minimum value of [math]X[/math] (the net benefit at the end of Year 3 for Project DIU) required for Project DIU to be approved.

• $68,122.78
• $75,095.39
• $78,852.10
• $80,000.00
• $82,798.12