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Economics 102

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					                             The Catholic University of America - ECON 102 – Section 2
                             Principles of Microeconomics - Instructor: Marco Stampini
Homework #3. Assigned: Friday 10 November. Due: Friday 17 November in class (or earlier if by email). Please
remember to write your name on each page of the solution. You can work together, but are expected to write
down individually.


1) 20 per cent of grade
You need to purchase a new heating system. A conventional system lasts 20 years, costs $10,000 to install (at t =
0) and approximately $3,000 per year to operate (t = 1,2,… 20). The Energy Star model also lasts 20 years, costs
$20,000 (at t = 0) but only costs $ 2,000 per year to operate (t = 1,2,… 20). Assume a 10 percent interest rate as
a benchmark in making financial decisions.
    A)   Using the tools of analysis presented in class, which heating system is more convenient?
    B)   The production of electricity typically results in pollution. How would your answer change if Harry had to
         pay an environmental charge that increases the annual operating cost of both heating systems by 50
         percent?
A) I consider Energy Star as the project, and the standard model as baseline. CF of Energy Star minus
Standard model: - 10,000 at t=0 (it costs 10,000 more), +1,000 for t=1 to 20 (it saves 1,000 dollars a
year). Therefore: PNV(Energy Star) = -10000+1000*8.5136= -1486 . Energy Star is not convenient.
B) Because of the environmental charge, the operating cost of the standard model rises to 4,500, the
one of Energy Star to 3,000. The saving becomes 1,500 a year. Therefore,
PNV(Energy Star) = -10000+1500*8.5136= -2770. Energy Star becomes more convenient.

(The solution is correct also if Energy Star and Standard model are treated separately, and
the decision is made on the basis of the comparison between the present value of the costs of
each – This is valid for all problems. However, students should note that this alternative
procedure is slower and less elegant than the one presented in this solution).


2) 20 per cent of grade
A friend has given you an IOU whereby she will pay you $100 per year for the next 30 years (t from 1 to 30). In
the 30th year, he will also pay you 1,000 dollars.
A) Assuming a market interest rate of 5%, what is the value of the IOU?
B) What is the value of the IOU if the interest rate increases to 10%?
C) What is the value of the IOU if the interest rate falls to 0%?
D) Based on (a), (b), and (c), what is the relationship between the rate of interest and the value of bonds?
A) The value of the bond is equal to the maximum amount we would be willing to pay in order to get
the bond. It is the cost at t=0 which makes the PNV=0. Therefore,
Value=100*15.3725+1000*0.2314=1769 dollars. In fact, this means that PNV= -1769
+100*15.3725+1000*0.2314=0
B) Value=100*9.4269+1000*0.0573=1000 dollars

C) Value =100*30+1000*1=4000 dollars
D) The higher the interest rate, the lower is the current value of the bond.


3) 20 per cent of grade
A recent graduate needs to choose between two MBA programs, to attend at t=0. The one of MIT costs 50,000
dollars; the one of UM costs 5,000. If she follows the former (MIT), she will earn an income of 110,000 dollars per
year from t=1 to t=6, then the income will grow to 125,000 dollars per year from t=7 to t=10. If she follows the
latter, she will earn an income of 107,000 dollars per year from t=1 to t=8, then the income will grow to 115,000
dollars per year from t=9 to t=10.
Which master will she choose if the interest rate is equal to 10 percent? Explain fully and show all calculations.


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I consider MIT as the project, UM as baseline. MIT costs 45,000 dollars more at t=0. It guarantees
higher income for 3,000 dollars from t=1 to t=6, 18,000 dollars at t=7 and 8, 10,000 dollars at t=9 and
10. Therefore:
PNV(MIT)= -45000+3000*4.3553+18000*(0.5132+0.4665)+10000*(0.4241+0.3855)= -6203

It is more convenient to apply for UM.


4) 20 per cent of grade
You can buy a house for 900,000 dollars (in t=0). The market interest rate is 10 percent. If you buy, you will pay
15,000 dollars per year in taxes and maintenance costs. After ten years (at t=10), you will sell the house. You
expect to make 1,400,000 dollars.
If you do not buy, you can rent a similar place for 40,000 dollars per year.
(Show the calculations that motivate your answer)
    a)   Will you buy or rent?
    b)   If the interest rate was 5%, would you rent or buy?
    c)   Based on the answers to (a) and (b), higher interest rates make buying more or less convenient?
A) PNV(buying)= -900000 + 25000*6.1446 + 1400000*0.3855 = -206685. Renting is more
convenient.
B) PNV(buying)= -900000 + 25000*7.7217 + 1400000*0.6139 = +152503. Buying is more
convenient. (In fact, if the interest rate is lower, an alternative investment guarantees lower
return. Having the house, which appreciates by half million dollars – nominally – is better
than putting money in a bank account).
C) Higher interest rates make buying less convenient (given the current price and the future
sale price). It is better to put the money in a bank account, and rent.


5) 20 per cent of grade
You currently pay 1,800 dollars per year for electricity, to your local company. You can reduce the expense to
1,050 dollars per year (from t=1 to t=20) by installing solar panels on the roof of your house. Assume a time
horizon of 20 years. The cost of installing the panels is $7,000 (at t=0). At t=20, you will have to pay 1,000
dollars for the recycling of the solar panels.
True or False. You will save money by installing the solar panels on your house. Assume an interest rate of 5%.
(Show the calculations that motivate your answer)
PNV(solar panels) = -7000 + 750*12.4622 – 1000*0.3769 = 1969. Installing solar panels is
convenient.




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