Question

1. The Port Authorities of New York and New Jersey estimate that the annual net revenues for the George Washington Bridge (GWB) will total $13M by the end of this year (t=1). At the end of three years (t=4) you expect a toll increase of 10%. Revenues will then remain constant for the next 6 years (year 4 through 10). Because the GWB is such an important artery for the New York City area, the Port Authorities would like to reinvest this revenue in a comprehensive maintenance and repair program. However, it will take two years (t=3) before plans and specifications can be developed and contracts awarded. What is the annual amount the Port Authorities should expect to spend for a five-year contract (uniform cash flows starting at the end of years 3 through 8)? The Port Authorities use a MARR of 7% for all public works projects.

Answer 1

First,we, will find the Present value of annual net revenues for the GWB

ie.PV of revenues= PV at Yr.0 of annuity of $ 13 mln. For the first 3 yrs. PLUS PV at Yr.0 of ( PV of annuity of $ 13*1.1=14.3 mln. For the yrs. 4 to 10,ie. 7 yrs.)----both discounted at the MARR of 7%

ie.(13*(1-1.07^-3)/0.07)+(14.3*(1-1.07^-7)/0.07/1.07^3)=

97.02561

Mlns.

This is the PV of the annual amount the Port Authorities should expect to spend for a five-year contract (uniform cash flows starting at the end of years 3 through 8

ie. It is a 5 yr. contract for yr. 4 Starting & yr.8 ending

the first pmt. Made at end yr. 3

last pmt. Made at end yr.8

total of 6 pmts.

so, we need to find the PV at Yr. 0 of the PV at end yr. 2 of an annuity amt.??--ie. 6 pmts. At 7% p.a.

as we have the PV of revenues to spend as $ 97.02561 mln. From 1. above

so, equating both revenues & expenses,

97.02561= (Pmt.*(1-1.07^-6)/0.07)/1.07^2

Solving for pmt., we get the annual spending on the comprehensive maintenance and repair program

23.3051

mlns.

For the 2nd part,

We can either calculate as PV of ordinary annuity as at end of Yr. 2   & divide by 1.07^2

OR

as PV of annuity due (beginning of yr.pmt.) as at the beginning of Yr. 3 --for 6 pmts. ----& divide by 1.07^3

Both the answers will be the same.