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c. The bridge project must that is estimated to require 2 years to complete is about to go underway. The bridge is projected to cost $48 million. It will need to begin construction in 18 months. Rights-of-way acquisition, surveying, and permitting have already been completed and paid for by the program. There will be 2 additional project phases: 1) planning & design, 2) construction. Each will require payment at the end of the phase. The projected cost of the 1st phase of the project is $5.5 million. The 1st phase is expected to need the entire 18 months prior to the start of construction and must be completed before construction can begin. The 2nd phase is projected to cost the remaining $42.5 million. Its construction is also expected to be completed at the end of the 2-year period following planning & design. There will need to be a payout of 30% of the cost of construction at the end of the 1st year of construction project. The remaining 70% will be paid at the completion of the project. Assuming a discount rate of 4.25% and monthly compounding, what amount will need to be funded today to meet the complete project’s funding requirements on the payment due dates.

Question

c. The bridge project must that is estimated to require 2 years to complete is about to go underway. The bridge is projected to cost $48 million. It will need to begin construction in 18 months. Rights-of-way acquisition, surveying, and permitting have already been completed and paid for by the program. There will be 2 additional project phases: 1) planning & design, 2) construction. Each will require payment at the end of the phase. The projected cost of the 1st phase of the project is $5.5 million. The 1st phase is expected to need the entire 18 months prior to the start of construction and must be completed before construction can begin. The 2nd phase is projected to cost the remaining $42.5 million. Its construction is also expected to be completed at the end of the 2-year period following planning & design. There will need to be a payout of 30% of the cost of construction at the end of the 1st year of construction project. The remaining 70% will be paid at the completion of the project. Assuming a discount rate of 4.25% and monthly compounding, what amount will need to be funded today to meet the complete project’s funding requirements on the payment due dates.

check_circleAnswer
Step 1

As a first step let's map the requirement of cash flows in future.

  • Planning phase will require a payment of $ 5.50 mn on completion i.e. 18 months from now.
  • Construction phase will require two payments:
    • First payment of 30% of $ 42.5 mn = $ 12.75 mn, at the end of first year of the construction project. Effectively this payment occurs at 18 + 12 = 30 months from now.
    • Second payment of balance amount of 70% of $ 42.5 mn = $ 29.75 mn at the end of 2 years after construction commences. Effectively this payment occurs at 18 + 24 = 42 months from now.

 

Step 2

Interesr rate = 4.25% per annum

Compounding frequency ; Monthly

Hence discount rate = r =  interest rate per period = 4.25%/12 = 0.3542%

Step 3

The present value (PV) of any future cash flow (FV) is given by the formula as shown on whiteboard, where r is the disc...

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