Finance 30210
Practice Midterm #1
1) Suppose that you have the opportunity to invest $50,000 in a new restaurant in
South Bend. (FYI: Dr. HG Parsa of Ohio State University has done a study that
shows that 59% of restaurants fail within the first three years!).
a) Given the following data, what is your opportunity cost here? Explain.
Asset
5 year Government Bond
DJIA (Stocks)
“Junk” Bonds (CCC or below)
Annual Return
1.25%
7%
13%
Note: CCC bonds have an average default rate of 27%
b) Now, suppose that as a part owner, you are allowed to eat for free as
often as you like. How does this change your calculation from (a)?
2) Suppose that Amtrak builds a new train line from Chicago to Los Angeles.
Unfortunately, the train line passes through thousands of acres of cornfields in
Iowa. When the train passes through the cornfields, it throws off sparks that
destroy the corn. The corn farmers take Amtrak to court in an attempt to get the
train line shut down.
a) What would be the “right” outcome in this case? Explain.
b) The Coase theorem states that as long as negotiation between the two
parties involved is relative costless, the “right” outcome will result
regardless of how the judge might rule. Explain.
3) Consider the following productivities:
Services
Manufacturing
United States
6 Units/hr.
2 Units/hr.
England
3 Units/hr.
6 Units/hr.
a) Calculate the opportunity cost of services in the US and England
b) Calculate the opportunity cost of manufacturing in the US and England. Who
has the comparative advantage in services?
c) Suppose that the average price of Services is $20 per unit and the average
price of manufact6uring is $20. What trade pattern will emerge? What will
wages be in England and the US?
d) Suppose that the inflation rate in England is 3% while the inflation rate in the
US is 5%. How is your answer in (c) affected
4) Suppose that you have the following demand and supply curve for sneakers:
Qd  400  3P
Qs  200  2 P
a)
b)
c)
d)
Solve for the equilibrium price and quantity.
Calculate consumer expenditures on sneakers
Calculate the elasticity of demand at the equilibrium found in (a)
Would a 5% increase in price cause consumer expenditures to rise or fall?
Explain.
5) Suppose that you have the following demand curve:
Q  120  4P  .001I
You know that the current market price is $10 and average income is $40,000.
a) Calculate the market’s consumer surplus.
b) Calculate the market’s total willingness to play.
6) Suppose that you have the following demand curve.
Q  400  6P  .005I
Q Represents quantity demanded, P represents price and I represents average
income.
You know that the current market price is $20 and average income is $20,000
a) Calculate current demand.
b) Calculate the price elasticity of demand.
c) Calculate the income elasticity of demand
7) Suppose that you are concerned about drug use in the US. You are interested in
what the impact would be if authorities could be more effective at getting drugs
off the streets. The DEA has estimated the following data:




Elasticity of Demand for Cocaine: -.55
Elasticity of Supply: 1.0
Current Market Price Cocaine: $80 per gram
Current Cocaine Sales (annual): 950M grams
a) We are using a simply supply/demand framework:
Qd  a  bP
Qs  c  dP
Use the data above to find the parameters a,b,c, and d.
b) As a check of the estimated model, solve for the equilibrium price and
quantity.
c) Suppose that the DEA is able to seize 100M grams of cocaine and take
it off the market. What will happen to the equilibrium price and
quantity?
d) How will cocaine revenues for drug dealers be affected?
e) What happens to consumer surplus?
8) Suppose that you observed the following set of data:
Average Business School tuition: $30,000
Average Salary for non-MBA’s: $50,000 per year
Average MBA salary: $90,000 per year.
The length of an MBA program is 2 years and is assumed that and MBA will have
a working career of 20 years after graduation. Further, suppose that, instead of
going to get an MBA, you could keep your current non-MBA job and invest what
you could have used to pay for tuition, risk free, at 4% per year.
a) Is this set of data consistent with market equilibrium? Explain.
b) If your answer to (a) is no, how will markets adjust?
9) Suppose that a busy restaurant charges $9 for its octopus appetizer. At this price,
an average of 48 people order the dish each night. When it raises the price to $12,
the number ordered per night falls to 42.
a) Assuming that demand is linear, find the demand curve the restaurant
faces.
b) What price should the restaurant charge to maximize revenues?
10) Suppose that you are a cattle rancher. You are deciding when to take your cattle to
market to sell. You currently have a herd of 100 cattle. Each cow currently
weighs 650 pounds and is gaining 50 pounds per month. Your feed costs are $40
per month per cow. Cattle prices are currently $8 per pound, but have been falling
at the rate of $0.10 per month. If you are maximizing profits, how many month
from now should you sell your cows?
11) Suppose that you are a pizza shop. Your profits depend on your sales of pizza
and beer. Specifically, your profits as a function of Pizza sales (P) and beer sales
(B) is given by:
Profits  80  120P  140B  8P2  12B2  4PB
Solve for the profit maximizing choices for gasoline and heating oil.
12) Suppose that your sales are a function of both price (P) and advertising expenses
(E) given by
Q  3,000  8 p  25 A  2 pA  .5 p 2  3 A2
Solve for the combination of price and advertising that maximizes sales.
13) We need to enclose a field with a fence. We have 500 feet of fencing and a
building is on one side and so won’t need any fencing. Determine the
dimensions of the field that will enclose the largest area.
Building
Field
14) Suppose that Apple is selling IPads in both the US and Europe. Sales in each
country are a function of the level of advertising and given by
2
SUS  12  6 AUS  1.2 AUS
S E  8  2 AE  .2 AE2
Solve Apples’ maximization problem; maximize total sales across the two
districts subject to a total advertising budget of $4M. How would a $1M increase
in Apples’ advertising budget influence sales?
15) In the game blackjack, face cards are worth 10 points, aces are worth 1 or 11, and
all other cards are worth their face value. You are dealt two cards with the
objective of getting more points than the dealer. A “Blackjack” is 21. Assuming
a fresh deck (i.e. no cards have been dealt), what are the odds of getting
blackjack?
16) Assuming two decks of cards (again, assume a fresh deck), if the dealer is
showing an ace, what are the odds that the dealer has blackjack?
17) Suppose that you are playing craps. If you roll the dice 10 times, what are the
odds that 4 of your rolls come up with a total of seven?
18) Consider the following regression analysis of player performance measures and
average winnings per tournament in the PGA (Professional Golf).
a) First, let’s consider driving distance (Note: The average driving distance
is 287 yards with a variance of 68):
W   D 
Where W is average winnings and D is driving distance in yards.
SUMMARY
OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.20
0.04
0.03
54041.64
196.00
ANOVA
df
Regression
Residual
Total
Intercept
Average Drive
SS
1.00 23093588860.13
194.00 566576795050.79
195.00 589670383910.92
Coefficients
-331133.39
1315.17
Standard Error
134365.65
467.70
MS
23093588860.13
2920498943.56
t Stat
a) What would be the impact on a player’s average winnings of a 20 yard
increase in his average driving distance? What would be a 95%
confidence interval for the impact of a 20 yard increase in a player’s
average drive?
b) Calculate a forecast with a 95% confidence interval for a player with a
300 yard drive.
c) How far must a player be able to drive the ball on average to expect to
have positive earnings?
Now, suppose that I altered the regression by taking the natural log of
winnings.
lnW     D  
.
-2.46
2.81
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.108
0.012
0.007
0.984
196.000
ANOVA
Regression
Residual
Total
Intercept
Average Drive
df
1.000
194.000
195.000
SS
2.237
188.027
190.264
Coefficients
6.567
0.013
Standard
Error
2.448
0.009
MS
2.237
0.969
t Stat
2.683
1.519
a) Now, what impact would a 20 yard increase in driving distance have
on average winnings?
b) Calculate forecast for average winnings for a player with an average
drive of 300 yards.
19) Consider the following time series regression:
P    t  
Where P is total non-farm payrolls in the US and t is time in months. The data
used is monthly data from Jan 1939 until August 2016 (t = 0 is Jan 1939). We
have 931 observations (so, the average for time is 466 and the variance is 72,463)
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.990
0.981
0.981
4867.781
932.000
ANOVA
df
1
930
931
SS
1120288062756.780
22036623597.343
1142324686354.120
Coefficients
26509.512
128.864
Standard Error
318.642
0.593
Regression
Residual
Total
Intercept
Time
MS
1120288062756.780
23695294.191
t Stat
83.195
217.437
a) On average, how many jobs do we create per year in the US?
b) Calculate a forecast for Non-farm payrolls for December 2016 ( t = 935) with
a 95% confidence interval.
Now, suppose that I added seasonal dummies for the first three quarters
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.990
0.981
0.981
4832.911
932
ANOVA
df
Regression
Residual
Total
Intercept
Time
D1
D2
D3
4
927
931
SS
1120672723961.980
21651962392.140
1142324686354.120
Coefficients
27245.376
128.853
-1757.508
-488.961
-667.040
Standard Error
419.879
0.588
448.255
448.251
448.729
MS
280168180990.495
23357025.234
t Stat
64.889
218.984
-3.921
-1.091
-1.487
a) Is there evidence for seasonality in employment in the US?
b) Calculate a new forecast for Dec. 2016 (don’t worry about the Standard Dev.)
20) Suppose that I repeated the above analysis, but I converted payrolls to logs….
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.9874
0.9749
0.9748
0.0700
932
ANOVA
df
Regression
Residual
Total
Intercept
Time
D1
D2
D3
SS
MS
4
927
931
176.3536
4.5464
180.9001
44.0884
0.0049
Coefficients
10.5350
0.0016
-0.0247
-0.0100
-0.0090
Standard Error
0.0061
0.0000
0.0065
0.0065
0.0065
t Stat
1731.5119
189.5660
-3.7960
-1.5329
-1.3868
How does this change the analysis above?