Suppose
Stanislaus is thinking about enhancing park facilities with **an initial cost
of $200,000** to install and **$1,000 a year to maintain** (which must be
paid at the end of each year). About **5,000
people** currently visit these parks about **2 times each year **and their
**enjoyment** would be increased by about **$1.00** on each visit. Another **thousand** that were reluctant
to visit without these facilities will now also visit the parks about **10
times a year **and receive about **$1.00 worth of pleasure** each time. **The
interest rate is 5 percent**.

a) What is the approximate **present
value of the project’s costs**?

$200,000
now + 1,000 a year forever Note formula for a perpetuity PV=A/r

$200,000
now + 1,000/.05

$200,000 + 20,000

What
is the approximate **net present value** of the project based on the data
you have?

NPV
= PV (benefits) – PV(costs)

Each
year benefits = 5,000
people x 2 visits x $1 **+** 1,000
people x 10 visits x $1

Each
year benefits = $20,000

PV
(benefits) = $20,000/.05

\ NPV = $400,000 – 220,000

Is the project admissible?

Yes
since NPV is positive.

b) Suppose the maintenance cost
estimates and benefit estimates were in **current dollars** and the interest
rate of **5% was in nominal terms**.
Someone points out they **expect 3% inflation**. How would your estimates of the approximate
present value of the project’s costs, benefits, and net present value change?

Real
interest rate = Nominal interest rate – inflation rate

Real
interest rate = 5% - 3% = 2%

PV
(costs) = $200,000
now + 1,000/.02 = $250,000

PV
(benefits) = $20,000/.02
= $1,000,000

\ NPV = $1,000,000 – 250,000
= $750,000

c) Suppose the facilities cost
$200,000 to install, but even with the maintenance **after three years they
would have to be scrapped**. The salvage
value at that point is just equal to the costs of removal. What would be the approximate present value
of the project’s costs? What would be the approximate present value of the
project’s benefits? Is the project admissible?

Note
formula for a costs in a single period in the future PV=A/(1+r)^{t}

PV
(benefits) = 20,000/(1+.02)
+ 20,000/(1+.02)^{2} + 20,000/(1+.02)^{3} = $57,677

\ NPV = $57,677– $202,883= **-**$145,206

**d) **There’s another project that
would benefit a different group of **1,000 people $100 each immediately** at
a total **cost of $50,000**. They
argue since their project is less expensive and has a positive net present
value that you should under take it.
Unfortunately, due to insufficient budget you can only do one of the
projects. What **"distributional weight" would make you indifferent
between the proj****ects?**

All
happens now so no discounting

1,000
people x $100 benefit = $100,000 benefit

net
benefit = $100,000 – 50,000 = $50,000

Compared
to a) need weight X such that $50,000 X = $180,000

\ X = $180,000/ 50,000 = 3.6

Compared
to b) need weight X such that $50,000 X = $750,000

\ X = $750,000/ 50,000 = 15

Compared
to c) no weight is needed since the first project is inadmissible you would
already prefer this project.