Economics 4440/5440 Homework #3 Dr. Michael Nieswiadomy Economics of Natural Resources and the Environment Due: Oct. 20, 2015, 11:59 p.m. All answers should be typed. Assemble everything into one combined pdf or MS Word document. 1) (20 points) Assume that Alessi Balsamic Vinegar sells for $3.50 for a 4 year old bottle and that a 20 year old bottle sells for $10.50. Calculate the annual rate of return that the company is expecting to earn. Show your work. Do not use a calculator with a built-in function for calculating rate of return. You can use a calculator for natural logarithms and Euler’s constant. Hint: use natural logarithms. Solution:- Here, Price of 4 year old Vinegar bottle (P 4 ) = $3.50 Price of 20 year old vinegar bottle (P 20 ) =$10.50 We know, F = P (1+r) n Where, F = future value P = present value r = rate of annual return n = number of years So, $3.50 = P (1+r) 4 ...............................................eq n (1) $10.50 = P (1+r) 20 ……………………………. eq n (2) Dividing eq n (2) by eq n (1) we get 4 20 ) 1 ( ) 1 ( 5 . 3 5 . 10 r P r P Or, 3 = (1+r) 16 Taking log on both sides
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Economics 4440/5440 Homework #3 Dr. Michael Nieswiadomy
Economics of Natural Resources and the Environment Due: Oct. 20, 2015, 11:59 p.m.
All answers should be typed. Assemble everything into one combined pdf or MS Word
document.
1) (20 points) Assume that Alessi Balsamic Vinegar sells for $3.50 for a 4 year old
bottle and that a 20 year old bottle sells for $10.50. Calculate the annual rate of
return that the company is expecting to earn. Show your work. Do not use a
calculator with a built-in function for calculating rate of return. You can use a
calculator for natural logarithms and Euler’s constant. Hint: use natural
logarithms.
Solution:-
Here,
Price of 4 year old Vinegar bottle (P4) = $3.50
Price of 20 year old vinegar bottle (P20) =$10.50
We know,
F = P (1+r) n
Where, F = future value
P = present value
r = rate of annual return
n = number of years
So,
$3.50 = P (1+r) 4 ...............................................eqn(1)
$10.50 = P (1+r) 20……………………………. eqn(2)
Dividing eqn(2) by eqn(1) we get
4
20
)1(
)1(
5.3
5.10
rP
rP
Or, 3 = (1+r) 16
Taking log on both sides
Log3 = 16 log (1+r)
Or, 0.4771 = 16 log (1+r)
Or, )1log(16
4771.0r
Or, 0.02982 = log (1+r)
Now,
)1log(02982.0 ree
Or, 1.0294 = 1+r
Or, r = 0.0294
Therefore, required annual return is 2.94%
2) (20 points) Calculate the levelized payment for a $1 annuity lasting 50 years
growing at 3% and discounted at 5%. Show your work, using the technique that I
showed you in class.
Solution:-
Here, A = $1
n = 50
Rate of Discount ( r ) = 5% =0.05
Annual growth Rate ( g) = 3% = 0.03
Net discounted rate (r*) = 1
1
1
g
r
= 103.1
05.1
= 0.0194
Formula to calculate present value of annuity =
nrr
A
**1
11
We can calculate the levelized Payment for 50 years
PVannuity =
500194.01
11
0194.0
1
=
500194.1
11546.51
=
6135.2
11546.51
=
6135.2
6135.1546.51
= 6135.2
1722.83 =$31.82
Therefore, Levelized payment for a $1 annuity lasting for 50 years at 3% growth rate and
5% discount rate is $31.82.
3) (20 points) Go to www.cityofdenton.com. You should find a pdf document that
has this header
Consumer Information Denton Municipal Utilities
The effective date at the bottom of the page is Oct. 1, 2015. Find the residential
monthly water rates for the Summer (May through October) for the 4 blocks: 1st
block: up to 15,000 gallons; 2nd block: 15,001 to 30,000 gallons; 3rd block: 30,001
to 50,000 gallons; and 4th block: 50,000 + gallons.
a) Print out these results and attach them to your homework. Highlight them
with a “yellow highlighter” in MS Word of Adobe Acrobat.
Residential Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
Residential Renewable Energy
Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Renewable Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
General Service Small Facility Charge $15.80/bill (single phase) $21.10/bill (three phase) Energy Charge First 2,500 KWH 7.67¢/KWH All additional KWH 4.02¢/KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
Commercial Renewable Energy
1,000 KWH Blocks RCA* Rate/KWH 100% of Actual Energy Consumption RCA* Rate/KWH *The Energy Cost Adjustment (ECA) and Renewable Cost Adjustment (RCA) rates are adjusted periodically as the energy market fluctuates. Call for current rates. **The Transmission Cost Recovery Factor (TCRF) rate is adjusted periodically as ERCOT transmission tariffs fluctuate. Call for current rates.
SOLID WASTE RATES
Residential Refuse and Recycling
Trash Cart Size One Cart Two Carts Large Trash Cart $32.00/bill $58.50/bill Standard Trash Cart $26.75/bill N/A (Each rate includes one standard-size recycling cart. A second recycling cart is available at no extra cost.)
Commercial Front and Side Load
WATER RATES Residential
Facility Charge 3/4” Meter $13.85/bill 1” Meter $18.40/bill
(Billing based on 90 percent of monthly water consumption.)
DRAINAGE RATES
Residential Square Feet in Block Monthly Charge per Bill
Container Size Billing per Cubic Yard Commercial Side Load $32.50 Front Load (<4 cubic yards) $25.00 Front Load (>4 cubic yards) $22.50 (All solid waste commercial rates are based upon one collection per week.)
Commercial Open Top (Roll-Off) Monthly Rental $160.00 Collection Charge* $270.00 *Plus landfill fees based on weight.
c) Draw the price schedule similar to one of those in Figure 9.4 in your text.
Make sure to show the each block point e.g., 15,000 gallons, 30,000 gallons &
50,000 gallons. You can draw this in Word using its drawing feature (Insert,
Shapes, Drawing Canvas).
Solution:-
Per
Unit
Cost
$
Usage
Gallons
3.8
5.5
30000
7.4
9.7
5
15000
Inverted block rate structure
50000 50000+
4) (20 points) Go to www.cityofdenton.com. Use the same information sheet
described above. Find the residential solid waste (i.e., garbage) rates in dollars.
a. (6 pts.) What is the charge for a large cart, medium cart, and a small cart
per month? Mark them with a “yellow highlighter” in MS Word or Adobe
Acrobat.
Solution:-
Consumer Information
Denton Municipal Utilities
ELECTRIC RATES
Residential Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
Residential Renewable Energy
Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Renewable Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
General Service Small Facility Charge $15.80/bill (single phase) $21.10/bill (three phase) Energy Charge First 2,500 KWH 7.67¢/KWH All additional KWH 4.02¢/KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically
Commercial Renewable Energy
1,000 KWH Blocks RCA* Rate/KWH 100% of Actual Energy Consumption RCA* Rate/KWH *The Energy Cost Adjustment (ECA) and Renewable Cost Adjustment (RCA) rates are adjusted periodically as the energy market fluctuates. Call for current rates. **The Transmission Cost Recovery Factor (TCRF) rate is
WATER RATES Residential
Facility Charge 3/4” Meter $13.85/bill 1” Meter $18.40/bill
adjusted periodically as ERCOT transmission tariffs fluctuate. Call for current rates.
SOLID WASTE RATES
Residential Refuse and Recycling
Trash Cart Size One Cart Two Carts Large Trash Cart $32.00/bill $58.50/bill Standard Trash Cart $26.75/bill N/A (Each rate includes one standard-size recycling cart. A second recycling cart is available at no extra cost.)
Commercial Front and Side Load
Container Size Billing per Cubic Yard Commercial Side Load $32.50 Front Load (<4 cubic yards) $25.00 Front Load (>4 cubic yards) $22.50 (All solid waste commercial rates are based upon one collection per week.)
Commercial Open Top (Roll-Off) Monthly Rental $160.00 Collection Charge* $270.00 *Plus landfill fees based on weight.
(Billing based on 90 percent of monthly water consumption.)