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1
Question 3a
Your company is considering the construction of low-income houses in a town targeting first
time owners. You were instructed to estimate demand for low-income housing in the town to
guide the preparation of a feasibility study for the project. You thought about the assignment
and hypothesized that there is a relationship between demand for low-income houses and jobs
created in the town. However, you reasoned that there would be a lag time between one getting
a job and when the person buys his first home. You conducted a survey of first-time owners
in the town and found out that a significant number of home owners buy their first home about
seven (7) years after they commence working. Armed with this observation, you collected data
from the municipality on the number of houses sold in the town over the last ten years and the
corresponding number of jobs created in the town seven years before. The results are
summarized below:
Data on Number of Jobs created and demand for houses
Year
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Total
No. of jobs (x) created 7 years
before given year
(‘000)
3.0
2.5
3.5
3.4
5.0
2.8
4.5
2.8
2.4
3.1
33
Demand for low income houses (y)
by first time owners
(‘000)
1.0
0.7
1.2
1.1
1.4
0.9
1.4
1.0
0.8
1.0
10.5
x
2
y
2
xy
9.0
6.3
12.3
11.6
25.0
7.8
20.3
7.8
5.8
9.6
115.4
1.0
0.5
1.4
1.2
2.0
0.8
2.0
1.0
0.6
1.0
11.5
3.0
1.8
4.2
3.7
7.0
2.5
6.3
2.8
1.9
3.1
36.3
You plotted the above data on a scatter diagram and the data seem to suggest a linear
relationship between jobs created and demand for houses with a seven year lag. You decided
to do a simple linear regression to see if there is a relationship between jobs created and demand
for houses.
(a)
Assuming the mathematical model y = bX + a :
i.Calculate the value for “b”
ii.Calculate the value for “a”
(b)
Compute the coefficient of correlation (r) and interpret the result.
(c)
Conduct a t-test
(d)
Forecast the demand for low income houses if seven years ago the number of jobs
created was 3,600.
(Work in ‘000.)
2
Question 4a
A company is proposing to the government the construction and operation of a toll road. You
are a member of the consultancy team that is planning the project on behalf of the
company. Your role is to analyse the economic feasibility of the project from the nation’s point
of view as the company is hoping to obtain government concession on the land and a subsidy
during the first ten years of operation in the event that the traffic volume is below an agreed
level.
The planning team have done preliminary estimates which are summarized below:
• Construction cost is $400M, $400M and $400M in years 1-3 respectively.
• Average operating and maintenance cost is $50M per annum for years 4-28
• Average toll rate per vehicle trip: $70
• All costs and revenue above are in constant market prices
• Average traffic volume per day: 8,000 vehicle trips
• Average operating days per year: 360
• Economic discount rate: 8%
• Present value ordinary annuity factor at 8% for year 3 is 2.577097
• Present value ordinary annuity factor at 8% for year 28 is 11.051078
• Conversion factors to convert to shadow prices (economic prices) are as follows:
o Construction cost: 0.80
o Operating and maintenance cost: 0.70
o Revenue from toll: 0.85
• Project implementation will be over 3 years (years 1-3. Ignore year zero.)
• The appraisal life of the project is 25 operating years.
a.
Convert market prices to economic prices and calculate the economic net present value
(ENPV) of the project. Advise if the project is economically feasible from the nation’s point
of view based on the data provided and assumptions made.
3
Question 1a
The government is considering the construction of a toll road to improve transportation
between two important population centres. You are a member of a consultancy team that is
planning the project on behalf of the government. Your role is to analyse the economic
feasibility of the project from the nation’s point of view. You have been provided with the
following preliminary data by other experts on the planning team:
• Construction cost is $250M, $500M and $500M in years 1-3 respectively.
• Average operating and maintenance cost is $20M per annum for years 4-28
• Average toll rate per vehicle trip: $100
• All costs and revenue above are in constant market prices
• Average traffic volume per day: 5,000 vehicle trips
• Average operating days per year: 350
• Economic discount rate: 10%
• Present value ordinary annuity factor at 10% for year 3 is 2.486852
• Present value ordinary annuity factor at 10% for year 28 is 9.306567
• Discount factors at 10% are 0.909091, 0.826446 and 0.751315 for years 1, 2 & 3
respectively.
• Conversion factors to convert to shadow prices (economic prices) are as follows:
o Construction cost: 0.85
o Operating and maintenance cost: 0.75
o Revenue from toll: 0.8
• Project implementation will be over 3 years (years 1-3. Ignore year zero.)
• The appraisal life of the project is 25 operating years.
(a)
of
view
Convert market prices to economic prices and calculate the economic net present value
the project. Advise if the project is economically feasible from the nation’s point of
based on the data provided and assumptions made.
(b)
Assume that there is concern that the public may resist the toll rate of $100 per vehicle
trip and the government may have to reduce the toll to $75. Is the project still economically
feasible?
(c)
List two (2) possible intangible costs and two(2) possible intangible benefits.
4
Question 3b
b. Your company invited bids from suitably qualified companies to supply the specialized
equipment indicated in “a” above. Four companies tendered. Below is a summary of
relevant information extracted from the bids.
Important Variables
Company A Company B Company C Company D
Bid price ($M)
12
10
8
6
Maintenance cost/annum ($M)
1.8
1.7
2.2
2.5
Salvage value ($M)
2.5
1.8
1.5
1
Economic life (yrs)
20
15
10
5
Your company’s real discount rate is 10%. Present value ordinary annuity (PVOA) factors,
capital recovery factors (CRF) and discount factors at 10% for the respective economic lives
are as follows:
Year
PVOA
Factors at 10%
CRF
at 10%
Discount
Factors at 10%
20
8.513
0.117
0.149
15
7.606
0.131
0.239
10
6.145
0.163
0.386
5
3.791
0.264
0.621
Assuming that the company wants to minimize its long run cost, conduct an evaluation of the
bids using equivalent annual cost (EAC) as the decision criterion and advise the company with
respect to which bidder should be awarded the contract and which is the most expensive. In
addition to cost, what other criteria could be considered in deciding on the company that should
be awarded the contract?
5
Question 2b
Your company is considering the construction of low-income houses in response to a perceived demand. Before
undertaking a full feasibility study for a low-income housing project, the company instructed you to forecast the
demand for low-income houses. Based on your research, you concluded that there is a relationship between
household income in dollars and the number mortgage loans granted. You believe that the demand for low-income
houses is dependent on household income and decided to forecast demand for low-income houses using simple
linear regression. Accordingly, you decided to collect data from the housing agency which provides mortgage
loans to low-income persons. You collected data on the number of low-income mortgages granted over the past
10 years. You also collected data on the average weekly income for low-income persons for the corresponding
10 years. To compare income in real terms without the effect of inflation, you converted the weekly income to
constant prices. The results are summarized below:
Average income for low income households in dollars and number of mortgage loans granted
Year
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
TOTAL
Average weekly household income
($‘000) (x)
10.
11
9
12
13
15
12
10
8
9
109
Number of mortgages loans
granted
(‘000) (y)
x
100
121
81
144
169
225
144
100
64
81
1229
2
5.0
5.3
4.4
6.1
6.7
8.0
5.8
4.9
4.1
4.6
54.9
y
25
28.1
19.4
37.2
44.9
64
33.6
24
16.8
21.2
314.2
2
xy
50.0
58.3
39.6
73.2
87.1
120.0
69.6
49.0
32.8
41.4
621.0
Assume that you plotted the above data on a scatter diagram and the data seem to suggest a linear relationship
between average weekly household income ($’000) and the number of mortgage loans granted (‘000).
(a)
Assuming the mathematical model y = bX + a, calculate the values for “a” and “b”
(b)
Compute the coefficient of correlation (r) and interpret the result.
(c)
Conduct a t-test and determine if the correlation coefficient is significantly different from zero and interpret the
results.
(d)
The government forecasted a real increase of 12% in the weekly household income for 2015 when compared
with 2014. Forecast the demand for mortgage loans in 2015 using the model at “a” above.
6
Question 3c
(a)
You are employed to a construction company that usually rents certain equipment but with the decline
of interest rate, the company is considering buying equipment with a view to rent during slow period. The
equipment being considered are as follows:
• One grader – US$200,000
• One crane – US$250,000
• One truck – US$150,000
• One front-end loader – US$100,000
Each piece of equipment has an economic useful life of 10 years. The annual maintenance cost of the equipment
is approximately 15% of the purchase price. The company normally rents the equipment for approximately
US$210,000 per annum. (The present value ordinary annuity factor at 15% for 10 years is 5.018769 and 7.721735
at 5% for 10 years. Discount factor at 15% for year 10 is 0.247185 and 0.613913 at 5% for year 10. The CRF
factor for 10 years at 15% is 0.199252) Ignore salvage value.
i.Calculate the discount rate at which both options (purchase vs renting) would be equivalent
(crossover discount rate) and interpret the result.
ii.Calculate the equivalent annual cost (EAC) for purchasing the equipment and interpret the result.
(b)
Assuming that you are conducting the financial analysis for a manufacturing project using an integrated
spreadsheet and have worked out the detailed capital costs, revenue, etc. and are able to compute FNPV and
FIRR to the equity cash flow after debt and tax. However, for one stage of the manufacturing process, several
technologies can be used. Explain an approach you could use to determine the least cost technology.
Question 3d
A government is considering the construction of a major toll road. You are a member of the
consultancy team that is planning the project on behalf of the government. Your role is to
analyse the financial feasibility of the project and to test its viability with respect to possible
adverse changes in certain critical variables that will impact the financial and economic
feasibility of the project and advise the consulting team of the impact of these variables during
the planning phase. You have been provided with the following preliminary data by other
experts on the planning team:
• Construction cost is US$150M per year for 3 years.
• Average maintenance cost is US$15 M per annum for years 4-28
• Average toll rate per vehicle trip: US$15
• Average traffic volume per day: 12,000 vehicle trips
• Average operating days per year: 350
• Real discount rate: 10%
• Present value ordinary annuity factor at 10% for year 3 is 2.486
• Present value ordinary annuity factor at 10% for year 28 is 9.306
• Present value ordinary annuity factor at 4% for year 3 is 2.775
• Present value ordinary annuity factor at 4% for year 28 is 16.663
(a)
Calculate the financial NPV for the project and interpret the result.
(b)
Calculate the financial IRR for the project and interpret the result.
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