Question

A company plans to start a high speed train service to accommodate the forecasted growth of state population and the subsequent need to travel. A new train terminal would be needed once the state's busiest airport reached 40 million passengers annually. Based on current growth rates, the airport should reach the 40 million mark 12 years from now. The train terminal cost is expected to be $400 million. The terminal service areas will also need attention. These include passenger security checkpoints, ticketing lines, entering/exiting weaves, terminal ramps, baggage claim, and baggage handling. Improvements in these areas will cost an additional $240 million. How much does the company need to set aside now to pay for these costs, if the department can earn 11% per year, compounded every 4 months?

Answer 1

Total cost for starting a high speed train service = $400 million + $240 million = $640 million

No of years = 12 years

Future value = Present Value (1+r)^n

Therefore Present value = FV/(1+r)^n

Interest rate = 11%

Compounding period = 12 months/4 months = 3

Therefore Interest rate per 4 months = 11%/3 = 3.666667%

No of periods = 12 years*3 = 36 periods

Present value= 640000000/(1+0.03666667)^36 = 640000000/3.656022 = $175053637.2483680 i.e. $175053637.25

Therefore the company must set aside $175053637.25 now to meet the cost