Question

The City of Boston is considering adding new buses for its current mass-transit system that links from the Hartsfield International Airport to major city destinations on a nonstop basis. The total investment package is worth $6 million and expected to last 9 years with a $840,000 salvage value. The annual operating and maintenance costs for buses would be $1 million during the first year, and will grow by 7% each year over the previous year thereafter. If the system is used for 560,000 trips per year, what would be the fair price to charge per trip to have a profitability index of 1? Assume that the City of Boston uses a 6% interest rate for city-sponsored projects. Hint: refer to the present worth formula for a geometric gradient to calculate the present worth of annual costs.

Answer 1

calculation of price per trip to hava Profitability Index of 1

Profitability Index=Present value of cashinflows/Present value of cash outflows

Profitability Index=1, when Present value of inflows=present value of outflows

PV of trip Charges+PV of salvage Value =PV of total investments+PV of annual operation and maintenance cost

PV of trip Charges = PV of investments+PV of annual operation and maintenance cost-PV of salvage Value

$6,000,000+PVIFAG(6%,9,7%)-PVIF($840,000)

PVIFAG means PV @6% dicounted rate for 9 years for costswith a growth rate of 7%

This can be calculated usinf the formula PV=P/Ke-g)*{1-{(1+g)/(1+ke)}ⁿ

Where P=Initial Cost =$100,000

Ke=cost of capital =6%

g =growth rate of costs=7%

n=Number of years =9

When giving Values,we will get PV of operating and maintenance costs =$8,818,100

PVIF(6%,9)=0.591898,Thus PV of salvage value=$840,000*0.591898=$497,194.71

When sustituting these values in the above underlined equation,we get

PV of trip charges =$6,000,000+$8,818,100-$497,194.71=$14,320,905

FAIR VALUE OF TRIP*560,000*PVIFA(6%,9) =$14,320,905

FAIR Value of a trip *560,000*6.801692 =$14,320,905 (PVIFA means sum of DF for 9 years @6%Discounting from annuity tables)

Fair value of a trip *3,808,947.67372 =$14,320,905

FAIR VALUE PER TRIP =$14,320,905/3,808,947.67372 =$3.76

^Where