Midterm Review Problems STAT 2112
1. Part I . Place-Plus, a real estate development firm is considering several alternative
development projects. These include building and leasing an office park, purchasing a
parcel of land and building and office building to rent, buying and leasing a warehouse,
building a strip shopping centre, and building and selling condominiums. The financial
success of these projects depends on interest rate movement in the next five years. The
various development projects and their five-year financial return ($ millions) given that
interest rates will decline, remain stable, or increase are shown in the following payoff
table.
Interest Rates
Project A.
Decline Stable Increase b.
' -38
Office park 3. 2- 0.5 = 2.7 2.4 -
1.7 = 0.7 4.5 -
4.5 =
°
1.63
11.75
Office building 1.5 = 1.7 1.9 = 0.5 2.4 = 2.1 1.26
' 5'
Warehouse 1.7 1.4 I 1.0 3.5 1.5
'
= 1.5 = =
' -67
Shopping center 0.7 = 2.5 2.4 = 0
3.6 = 0.9 1.61
Condominiums 2.26 3.2 = 0 1.5 = 0.5 0.6 = 3.9 0.75
probability 0.5 0.4 0.1
Determine the best investment using the following decision criteria.
a. Maximax office park 4.5 :
b. Maximin condominium : 0.6
c. Equally likely (Laplace) criterion office park 2
Shopping center
d. Criterion of realism (Hurwicz criterion). Use an value of 0.3. office building
e. Opportunity Loss Criterion.
office building
Part II. The Place-Plus has hired an economist to assign a probability to each direction
interest rates may take over the next five years. The economist has determined that there is a
0.50 probability that interest rates will decline, a 0.40 probability that rates remain stable, and
a 0.10 probability that rates will increase.
a. Using expected value, determine the best project. condominium
b. Using expected opportunity loss, determine the best project. condominium
0.4×2.4+0.1×4.5
Determine the expected value of the prefect information. 0.5×3.2
+
c.
= 3.01 = EVWPI
EVPI = EVWPI -
EVWOPI
= EVWPI -
max EMV
= 3.01 -
2.26 =
0.75
= 0.75 millions
, Midterm Review Problems STAT 2112 by Prof. A. Gokhman 2
2. An investor must decide between two alternative investments – stocks and bonds. The
return for each investment given two future economic conditions is shown in the following
payoff table.
Economic Conditions
Investment Good Poor
.4 .6
Stocks $10 000 $ − 4 000 EVWP 2=0.4×1000
+
0.6×2000
Bonds 7 000 2 000
a. Construct a decision tree for this problem. What is the recommended decision using
expected value criterion?
invest in bonds
b. What the maximum amount of money would the investor pay for additional
information on future economic conditions?
b EVPZ
10,00×0.4
" boo
good
.
Stocks a. ooo x 0.6 5,200 -
4,000
poor
-
a.on 7. ooo x 0.4 = 1,200
41000
bonds good 0.6
poor 2. ooo x
3. For the problem in question 2. , suppose that the investor has decided to hire a professional
economic analyst who will provide additional information about future economic
conditions. Based on the analyst’s past record in forecasting future economic conditions,
the investor has estimated .70 probability that the analyst would present a favorable report
given the future economic conditions are good, and .90 probability that the analyst would
present an unfavorable report given the future economic conditions are poor.
a. Use this information to revise the decision tree.
b. Determine the decision strategy the investor should follow.
c. Determine the maximum fee the investor should pay the analyst.
4. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18
ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2
ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of
platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit
and a bracelet, $400. The store wants to determine the number of necklaces and bracelets to
make in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.
1. Part I . Place-Plus, a real estate development firm is considering several alternative
development projects. These include building and leasing an office park, purchasing a
parcel of land and building and office building to rent, buying and leasing a warehouse,
building a strip shopping centre, and building and selling condominiums. The financial
success of these projects depends on interest rate movement in the next five years. The
various development projects and their five-year financial return ($ millions) given that
interest rates will decline, remain stable, or increase are shown in the following payoff
table.
Interest Rates
Project A.
Decline Stable Increase b.
' -38
Office park 3. 2- 0.5 = 2.7 2.4 -
1.7 = 0.7 4.5 -
4.5 =
°
1.63
11.75
Office building 1.5 = 1.7 1.9 = 0.5 2.4 = 2.1 1.26
' 5'
Warehouse 1.7 1.4 I 1.0 3.5 1.5
'
= 1.5 = =
' -67
Shopping center 0.7 = 2.5 2.4 = 0
3.6 = 0.9 1.61
Condominiums 2.26 3.2 = 0 1.5 = 0.5 0.6 = 3.9 0.75
probability 0.5 0.4 0.1
Determine the best investment using the following decision criteria.
a. Maximax office park 4.5 :
b. Maximin condominium : 0.6
c. Equally likely (Laplace) criterion office park 2
Shopping center
d. Criterion of realism (Hurwicz criterion). Use an value of 0.3. office building
e. Opportunity Loss Criterion.
office building
Part II. The Place-Plus has hired an economist to assign a probability to each direction
interest rates may take over the next five years. The economist has determined that there is a
0.50 probability that interest rates will decline, a 0.40 probability that rates remain stable, and
a 0.10 probability that rates will increase.
a. Using expected value, determine the best project. condominium
b. Using expected opportunity loss, determine the best project. condominium
0.4×2.4+0.1×4.5
Determine the expected value of the prefect information. 0.5×3.2
+
c.
= 3.01 = EVWPI
EVPI = EVWPI -
EVWOPI
= EVWPI -
max EMV
= 3.01 -
2.26 =
0.75
= 0.75 millions
, Midterm Review Problems STAT 2112 by Prof. A. Gokhman 2
2. An investor must decide between two alternative investments – stocks and bonds. The
return for each investment given two future economic conditions is shown in the following
payoff table.
Economic Conditions
Investment Good Poor
.4 .6
Stocks $10 000 $ − 4 000 EVWP 2=0.4×1000
+
0.6×2000
Bonds 7 000 2 000
a. Construct a decision tree for this problem. What is the recommended decision using
expected value criterion?
invest in bonds
b. What the maximum amount of money would the investor pay for additional
information on future economic conditions?
b EVPZ
10,00×0.4
" boo
good
.
Stocks a. ooo x 0.6 5,200 -
4,000
poor
-
a.on 7. ooo x 0.4 = 1,200
41000
bonds good 0.6
poor 2. ooo x
3. For the problem in question 2. , suppose that the investor has decided to hire a professional
economic analyst who will provide additional information about future economic
conditions. Based on the analyst’s past record in forecasting future economic conditions,
the investor has estimated .70 probability that the analyst would present a favorable report
given the future economic conditions are good, and .90 probability that the analyst would
present an unfavorable report given the future economic conditions are poor.
a. Use this information to revise the decision tree.
b. Determine the decision strategy the investor should follow.
c. Determine the maximum fee the investor should pay the analyst.
4. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18
ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2
ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of
platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit
and a bracelet, $400. The store wants to determine the number of necklaces and bracelets to
make in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.
