# ENGINEERIN 3302 Develop the matrix of investment alternatives

June 14, 2018

Problem 1

Project 1, 2, 3 with a lives of 5 years are being considered
with cash flow estimated to be as follows

Project 1(k\$)

Project 2(k\$)

Project 3 (k\$)

Investment

65,000

58,000

93,000

Annual Revenue

23,000

19,500

29,000

Annual Cost

5,000

4,500

6,000

Salvage Value

0

10,000

15,000

Suppose that proposal 1 and 3 are mutually exclusive,
project 2 is contingent on project 1. The budget limit is \$130,000.
(a)
Develop the matrix of investment alternatives,
indicate which one is not feasible, and give reason for the infeasibility (5
points)
(b)
Develop the composite cash flows for the
feasible alternatives (5 points)
(c)
Suppose the MARR is 10%, determine the best
alternative using Present Worth analysis. (5 points)

Problem 2

You have to solve the following problem for the CEO of Super
Superconductors, Inc. (SSC). She needs the answer in writing by 10:00 PM
tonight. SSC makes a superconducting wire that operates at the temperature of
liquid nitrogen; it sells about 10,000 kilometers of this product per year.
There are rumors, however, that a competing company (Superconductors R US
(SRU)) is producing a wire that superconducts at the temperature of liquid
oxygen, which is higher – (90 °K vice 77 °K), thus it is easier to use. SSC has a project proposed
for R&D for a superconductor that works at liquid oxygen temperatures, but
it hasn’t produced a material that is profitable to produce. The CEO thinks
that there is a 40% chance that SRU has produced the better superconductor. If
SRU has managed to develop the better superconductor, and SSC fails to produce
an equivalent product, sales of the existing product will decrease by 50%.
Otherwise, sales stay the same.

SSC’s CEO can authorize \$50 million to do the R&D
project. The R&D project can produce an oxygen temperature superconductor,
but it isn’t clear if the result will be an inexpensive product or an expensive
one – there is a 50 – 50 chance of either outcome. If the R&D produces an
inexpensive superconducting wire, SSC will switch from making the current wire
to the new, cheap oxygen temperature wire. If SSC makes the cheap wire and SRU has an oxygen-level
superconducting wire also, then SSC’s sales of the new product will be 8,000
km/yr. If SSC makes the cheap wire and SRU doesn’t
have an oxygen-level superconducting wire also, then SSC’s sales of the new
product will be 15,000 km/yr.

If the R&D can only produce an expensive version, SSC’s
CEO will have to decide to make the old product or the new one. If they
continue to make the old one, sales will drop 50% if SRU does produce a new
oxygen temperature superconductor and stay the same if it doesn’t. However, if
SSC makes the new superconductor instead of the old one, sales will be 3,000
km/yr. if SRU does produce a new oxygen temperature superconductor and 7,500
km/yr. if it doesn’t.

Assume that SSC makes \$10 /meter (1 km = 1,000 meters) if it
sells the old superconducting wire,
\$18/meter for the inexpensive oxygen temperature superconducting wire,
and \$7/meter for the expensive oxygen temperature superconducting wire (these
are net profits). Assume that the decision will be made based on the first
year’s sales (with either the old or new superconducting wire, depending upon
the decision).

Should SSC’s CEO spend the \$50 million on R&D? If she
does, should she sell the newer oxygen-level superconducting wire that comes
out of R&D?
(1)
Draw an influence diagram showing this problem.
(10)
(2)
Draw a decision tree showing this problem. (10)
(3)
Solve either one by hand for the answer. (10)

Problem 3

The manager of Fort Motors is considering developing one of
two proposed new car models, A and B. For Model A, it is estimated that a
one-time investment of \$1000,000 will be required by product design at the
beginning of the first year. For model
B, a one-time investment of \$500,000 to product design is needed at the
beginning of the first year. The introduction of either model to the market
depends on the result of market survey that will be conducted after the concept
car is designed. The period required
from design to beginning production of either car model is expected to be 2
years. If the model is not introduced, the investment to the product design can
not be recovered. Based on the initial analysis, the probability for model A
not introduced to marker is estimated to be 0.4. The probability for model B
not introduced to marker is estimated to be 0.3.

If the car model A is introduced to market, it will need a
one-time investment of \$3000,000 to modify the existing production line at the
end of year 2. The market demand for this car model can either be High, Medium,
or Low. The probability is estimated to
be P (high)=0.3, P (medium)=0.4 P (Low)=0.3. Depending on the market demand the
net annual revenue is estimated to be \$2500,000 for high demand, \$2,000,000 for medium demand, and \$1,500,000
for low demand. The production of Model A will be continued for 5 years.

If the car model B is introduced to market, it will need a
one-time investment of \$500,000 to modify the existing production line at the
end of year 2. The market demand for this car model can also be either High,
Medium, or Low, with P (high)=0.5, P(medium)=0.3, P(Low)=0.2. Depending on the
market demand, the net annual revenue is estimated to be \$1,000,000 for high
demand, \$600,000 for medium demand, and
\$400,000 for low demand. The production of Model B will be continued for 5
years.

(a)
Suppose Fort Motor’s design team can only afford
to design one car model, structure this problem with a decision tree, draw the
cash flow diagram for each decision path, find the present worth for each
decision path. (10 points)
(b)
Suppose the MARR of Fort Motor is 10%, solve the
decision problem for Fort Motor’s manager using EMV based on present worth. (10 points)
(c)
Draw the risk file and the cumulative risk
profile for the selected strategy. What conclusion can you draw from looking at
the profiles? (10points)

Problem4

As a manager of a small business, you are considering to
introduce a new product. The production requires a new machine. You figure out
that you could buy it for \$190,000, but the price could be in between \$180,000
and \$200,000. Because of the budget limitation you can only pay 60% of the
machine price with your own saving. You
will borrow the other 40% with an interest rate around 9% per year (but subject
to change in between 8.5% and 10%).

The demand of this product is predicted to be 15,000 per
year and but could be in between 14800 and 15500. The unit price could be in
between \$2 and \$3, and now you believe that \$2.5 is a reasonable price right
now. The raw material cost is estimated to be \$0.9 but could be in between \$0.5
and \$1.2. The operation cost of the equipment is around \$0.2 for one product
but could be in between \$0.1 and \$0.25.
The maintenance cost for this equipment is estimated to be \$2000 per
year but could be in between \$1500 and \$2300.

Suppose you could always invest your cash in the money
market that give a return at 8% per year for sure.

a)
Construct the Influence Diagram for this
decision problem and identify the inputs and mathematic models that relate
these inputs (decision variables) to the decision problem. (5)
b)