ECON4140 (2013) Mid-Term 1 - Answers
1. Short definitions (see text)
2. Imagine that you live in a city that currently does not require bicycle riders to wear
helmets. Furthermore, imagine that you enjoy riding your bicycle without wearing a
helmet.
a. From your perspective, what are the major costs and benefits of a proposed city
ordinance that would require all bicycle riders to wear helmets
b. What are the categories of costs and benefits from society’s perspective?
c. Repeat this analysis with an adjustment that requires only children under 12 to wear
helmets. (Do not forget enforcement costs) (25 marks)
a. For individual riders the important costs are: the purchase price of a helmet, the
reduced pleasure of riding your bicycle while wearing a helmet, diminished
appearance when you take the helmet off (bad hair), the inconvenience of keeping
the helmet available and maybe for some increased sense of safety (leading to
increased risk taking due to moral hazard). The most significant categories of
benefits are probably: reduced risk of serious head injury (morbidity) and reduced
risk of death (mortality).
b. These are:
 program enforcement (a cost)
 reduced health care costs (a benefit), although this may not be as high as one
might expect if bicyclists ride more aggressively because they feel safer (this is
called off-setting behaviour or moral hazard)
 increased pollution, due to cyclists switching to cars (a cost) – a likely minor
issue
c. The analysis is essentially no different, just that enforcement costs may fall if this
limit is widely accepted and it becomes a norm.
Note: Changes in the sales of helmets or bikes occurs in the secondary market and are
not counted in the primary market.
3. A town’s recreation department is trying to decide how to use a piece of land. One
option is to put up basketball courts with an expected life of eight years. Another is to
install a swimming pool with an expected life of 24 years. The basketball courts would
cost $180,000 to construct and yield net benefits of $40,000 at the end of each of the
eight years. The swimming pool would cost $2.25 million to construct and yield net
benefits of $170,000 at the end of each of the 24 years. Each project is assumed to have
zero salvage value at the end of its life. Using a real discount rate of 4 percent, which
project offers larger net benefits?
As only one of these projects can be built on the site, they are mutually exclusive.
The comparison is complicated because the swimming pool has an expected life three
times longer than the basketball courts. Imagine we rebuild the basketball courts at
the end of year 8 and year 16.
Solution Approach 1
Consider first the NPV of each project separately:
NPV(one basketball court project)
8
  $180,000  
i 1
40,000
 $89,310
(1  0.04) i
NPV(one swimming pool project)
24
  $2,250,000  
i 1
170,000
 $341,984
(1  0.04) i
If we choose on the basis of this comparison, then the swimming pool has a larger
present value of net benefits. A proper comparison, however, would be between one
swimming pool and three successive basketball court projects so that the site is used
in each case for the same length of time.
NPV(three successive basketball court projects)
= $89,310 + $89,310/(1+.04)8 + $89,310/(1+.04)16 (see how the NPV at year 8 is
then “rediscounted at year 8 (actually year 16) and year 16 (actually year 24)
= $89,310 + $65,258 + $47,683
= $202,251
Thus, three successive basketball court projects offer a lower present value of net
benefits than the swimming pool project. One should build the pool.
Solution Approach 2
An alternative approach for comparing these projects of different lengths is to divide
each project’s NPV by its appropriate annuity factor to find its equivalent annual net
benefits, an approach called "amortization." The appropriate annuity factor in each
case can be obtained by using the formula for the present value of an annuity
The 8-year annuity factor = [1-(1+.04)-8]/(.04) = 6.7327
Annualized NB for the basketball court = ($89,310)/6.7327 = $13,265
The 24-year annuity factor = [1-(1+.04)-24]/(.04) = 15.247
Annualized NB for the swimming pool = ($341,984)/(15.247) = $22,430
The basket ball court project offers net benefits equivalent to an annuity paying
$13,265 each year over its life. The swimming pool offers net benefits equivalent to
an annuity paying $22,430 each year over its life. Choose the pool.
4. The environmental protection agency of a county would like to preserve a piece of land
as a wilderness area. The current owner has offered to lease the land to the county for
20 years in return for a lump-sum payment of $1.1 million, which would be paid at the
beginning of the 20-year period. The agency has estimated that the land would generate
$110,000 per year in benefits to hunters, bird watchers, and hikers. Assume that the
lease price represents the social opportunity cost of the land and that the appropriate
real discount rate is 5 percent.
a. Assuming that the yearly benefits, which are measured in real dollars, accrue at
the end of each of the 20 years, calculate the net benefits of leasing the land.
b. Some analysts in the agency argue that the annual real benefits are likely to grow
at a rate of 2 percent per year due to increasing population and county income.
Recalculate the net benefits assuming that they are correct.
a. The present value of the real yearly benefits is most easily calculated using the
formula for the present value of an annuity (you can also do this the long way)
PV(benefits) = ($110,000)[1-(1+.05)-20]/(.05)
= $1,370,843
NPV = $1,370,843 - $1,100,000
= $270,843
b. In this case we can use the present value of an annuity with a growth rate in benefits
of 2 percent: (or do it the long way, manually calculating annual increases in net
benefit)
First, calculate (.05-.02)/(1+.02) = .0294
PV(benefits) = [($110,000)/(1+.02)][1-(1+dg)-20]/dg] = $1,613,370
NPV = $1,613,370-$1,100,000 = $513,370