Question

The City of Calgary is considering the construction of a new high school in order to accommodate a growing population. Before they proceed, they would like to conduct a Benefit/Cost analysis using different time horizons and interest rates. An economist for the City has tabulated the following benefits and costs in the table below.

Building costs (design, planning and construction)	$9,000,000
Land costs	1,000,000
Initial cost for roads and parking facilities	5,000,000
Initial cost for parking facilities	500,000
Initial cost to furnish and equip building	500,000
Annual operating and maintenance costs	650,000
Annual savings from busing students	300,000
Annual benefits to community*	1,600,000
Estimated annual cost of congestion	100,000
Estimated annual cost due to loss of property values	300,000

*This value was estimated by a City survey. The survey asked people their willingness to pay for a high school in their neighbourhood.

1. a) Calculate the NPV with interest rates of 3 percent, 5 percent and 8 percent and with time horizons at 30 and 60 years. Comment on how different interest rates and time horizons affect the economic value of this public project.
   (Note: Show your calculation for one NPV. You do not need to show them for each one)

2. b) For someone working on the Calgary School Board, (a Spender) what interest and time horizon would they be promoting?

Answer 1

a.

We can see the benefit are same for all years, to calculate the present value of same amount we use present value of annuity formula which gives us the present value of a series or same amount.

The formula is

PV= P*[1-(1+r)^-n/r]

Where

P = Periodic payment

r = rate per period

n = number of periods

Net present value is sum of initial investment and present value of future payments

So NPV for 3% and 30 years will be $ 660,375.15

So NPV for 3% and 60 years will be $ 7,524,229.15

All other NPV are shown in working

We can see that NPV of various interest rate and term varies according to rate of interest and term. with higher term and higher rate of interest the NPV becomes negative.

b. For someone working on the Calgary School Board 3% and 60 years will be promoting as this gives the highest NPV among all.