Question

The City of New York is planning to build a library in its downtown area. Due to budgetary

constraint, the City faces the decision on whether to build it all now (full development), or build

part now (delayed plan) and complete the project in 10 years later.

The City hires you to do a present cost analysis to compare the options described below for

perpetual life at 4% effective interest rate:

1. First cost                                Full development        Delayed plan

                                                         $1,800,000              $900,000 now

________________________________________ $1,100,000 in 10 years

2. Annual disbursements _______ $140,000/yr             $80,000/yr for 10 years

                                                                                           $160,000/yr thereafter

Clearly describe your engineering economic analysis and state your suggestion to the City of

New York.

Make sure to use:

To find the equivalent P	–PV(i,n,A,F,Type)
To find the equivalent A	–PMT(i,n,P,F,Type)
To find the equivalent F	–FV(i,n,A,P,Type)
To find n	NPER(i,A,P,F,Type)
To find i	RATE(n,A,P,F,Type,guess)

Where:

i = interest

n = number of periods

A = Annual Value (or Worth)

P = Present Value (or Worth)

F = Future Value (or Worth)

Answer 1

$160000 annual cost after 10 years os being incurred in both the options and hence it is irrelevant for decision making.

So the decision will be taken based upon the present value of the outflow during first 10 years.

Present value of outflow in Delayed plan -

= 900000 + [ 1100000 * PVF (4%,10 YEARS) ] + [ 80000 * PVAF (4%,10 YEARS) ]

= 900000 + [ 1100000 * 0.6756 ] + [ 80000 * 8.1109 ]

= 900000 + 743160 + 648872

= $2292032

Present value of outflow in Full Development Plan -

= 1800000 + [ 140000 * PVAF (4%,10 YEARS) ]

= 1800000 + [ 140000 * 8.1109 ]

= 1800000 + 1135526

= $2935526

Since the Present value of Cash Outflow is low in the Delayed plan, a part should be constructed now and completed 10 years later.