UNIVERSITY OF SOUTHAMPTON ECON3015W1
SEMESTER 1 EXAMINATION 2014/15
PRINCIPLES OF FINANCE
Duration: 120 mins (2 Hours)
ANSWER ALL QUESTIONS
Only University approved calculators may be used.
A foreign language translation dictionary (paper version) is permitted
provided it contains no notes, additions or annotations.
Copyright 2015 ©University of Southampton Number of Pages
4
2 ECON3015W1
1. 2-Period Investment-Consumption Model (25 points)
An investor with an initial endowment of £25,000 is confronted with the following
productivity curve:
C1 = 240 (25,000 – C0)
1/2
where C0 denotes consumption at present, and C1 consumption in the future. Assume the
interest rate for borrowing and lending is 20%. The investor’s utility function is defined as:
U(C0,C1) = C0C1
Answer the following questions using the 2-period Consumption-Investment model.
Points will be allocated if the graphs are fully-labeled and neat.
(a) How much will the investor invest in production?
(b) What is the NPV of the investment chosen by the investor?
(c) What is the optimal allocation of consumption for the two periods?
(d) What is the PV of his total consumption?
(e) Does the investor borrow or lend in the capital market? Give a numerical answer.
(f) Why is it important that the capital markets are perfect? How would the answer change if
the borrowing rate was bigger than the lending rate.
2. The Value of Information (25 points)
You can choose between two different portfolios, A and B that produce the following
uncertain returns in the two possible states of the world:
Good Bad
Portfolio A 100 0
Portfolio B 60 80
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3 ECON3015W1
Before making your choice you receive one of two costless messages, m1 or m2, that convey
some information about the future realization of the state of the world. Consider the
following specifications of the information structure (each row gives you the conditional
probabilities of the two states of the world, given the message you receive):
Perfect Information No Information Noisy Information
Good Bad Good Bad Good Bad
m1 1 0 m1 0.5 0.5 m1 0.8 0.2
m2 0 1 m2 0.5 0.5 m2 0.2 0.8
(a) Draw the decision tree corresponding to each of the above specification of the
information structure. Use arrows to denote the optimal path.
(b) Let a = {A,B}, e = {Good, Bad}, m = {m1,m2} and denote the conditional probability of e
given m by p(e|m) and the return to portfolio A in state of the world e by U(A,e). The value
of the information is defined as:
S p(m) max S p(e|m)U(A,e) m e
Suppose you are equally likely to receive any of the two messages. What is the value of the
information in each of the above scenarios?
(c) Would you be led to conclude that the Efficient Market Hypothesis holds in this setting?
(d) Now consider a market that is efficient, but not perfect (information is costly), where a
large number of traders can choose whether to acquire Lots of Information at a high cost or
Little Information at a low cost. After having decided what package of information to buy,
traders are randomly matched in pairs and the payoffs from the interaction are summarized
in the following payoff matrix:
Trade Column
Lots of Info Little Info
Trader Row Lots of Info -4,-4 8,-2
Little Info -2,8 4,4
Denote by p the fraction of traders in the market that have bought Lots of Information. Show
that for p = 2/3 the market is in an equilibrium.
PLEASE TURN OVER
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4 ECON3015W1
3. Coordination Games (25 points)
(a) Provide the payoff matrix of the Coordination game assuming the base wage is 300, the
bonus factor is set at 6 and the effort cost is 5 per hour. Similar to the examples in class,
assume there are five effort levels (i.e. 0 hours, 10 hours, 20 hours, 30 hours, and 40 hours)
and four employees within the firm.
(b) Find the Nash equilibria of the payoff matrix in (a).
(c) Provide the payoff matrix of the Coordination game assuming the base wage is 300, the
bonus factor is set at 4 and the effort cost is 5 per hour. Similar to the examples in class,
assume there are five effort levels (i.e. 0 hours, 10 hours, 20 hours, 30 hours, and 40 hours)
and four employees within the firm.
(d) Find the Nash equilibria of the payoff matrix in (c).
4. Decisions from Experience (25 points)
(a) What is the “experience-description” gap?
(b) What is the Clicking Paradigm?
(c) What is the Law of Effect?
(d) What is the Very Recent Effect?
(e) Name the three response models in the instance-based model I-SAW.
END OF PAPER
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Social Sciences Examination Feedback
2014/2015
Module Code & Title: ECON3015 Principles of Finance
Module Coordinator: Christos A. Ioannou
Mean Exam Score: 61
Percentage distribution across class marks:
UG Modules
1 st (70% +) 46 (30%)
2.1 (60-69%) 32 (21%)
2.2 (50-59%) 42 (27%)
3rd (40-49%) 28 (18%)
Fail (25-39%) 5 (3%)
Uncompensatable Fail
(<25%)
1 (0.6%)
PGT Modules
70% +
60-69%
50-59%
<50%
Overall strengths of candidates’ answers:
Students were very capable of performing computations. Many knew, for example, how to find work
out points of tangency (question 1), how to compute the value of information (question 2), and how
to calculate the payoffs for the co-ordination game (question 3).
Overall weaknesses of candidates’ answers:
Students were weak in expressing the reasons behind their working. Some either made no
statements, and produced answers that consisted only of working; others made ambiguous
statements. The most common occurrence of the latter was in question 1, in which many students
wrote MRT = -(1+r) without describing this as the condition for tangency; in other words, it was
difficult to distinguish the equilibrium condition from being a definition of the MRT.
Pattern of question choice:
Too many students either did not attempt, or wrote very poor solutions for, questions 3 and 4.
Questions 1 and 2 were relatively well done. This is not surprising, since the topics and similar
questions were examined in the coursework. Questions 3 and 4, however, were not examined in the
coursework, and the related materials were taught at the beginning and end of the course,
respectively. Questions 3 and 4 were a case of either students knew the topic or they did not; those
that knew the topics earned high marks in the questions, and overall in the exam; those that did not
know the topics performed poorly overall.
Issues that arose with particular questions:
Question 1 – indifference curves were often drawn without strict convexity; many of the diagrams
were too small and/or untidy and confusing.
Question 2 – almost every student did not identify the stages of the decision tree, i.e. Message,
Action, State, etc.
Question 3 – many students did not appropriately label the row and column of the payoff matrix;
their answers did not suggest they knew the columns represent the minimum effort among the
other workers.
Question 4 – Students could not make the distinction between the different concepts, and often
wrote, for all the concepts, that the concepts were about an agent making decision from experience.
Further comments not covered above:
Handwriting was very poor (ether too small or illegible) for too many students.
Discipline vetting completed By (Name): Zacharias Maniadis Date: 05/02/2015
UNIVERSITY OF SOUTHAMPTON ECON3015W1
SEMESTER 1 EXAMINATION 2012/13
PRINCIPLES OF FINANCE
Duration: 120 mins
ANSWER ALL QUESTIONS
Only University approved calculators may be used.
A foreign language translation dictionary (paper version) is permitted
provided it contains no notes, additions or annotations.
Copyright 2013 ©University of Southampton Page 1 of 5
2 ECON3015W1
1. (25 points) 2-Period Investment-Consumption Model
An investor with an initial endowment of £25,000 is confronted with the following productivity curve:
C1 = 240 (25,000 – C0)
1/2
where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate for
borrowing and lending is 20%. The investor’s utility function is defined as:
U(C0,C1) = C0C1
Answer the following questions using the 2-period Consumption-Investment model.
Points will be allocated if the graphs are fully-labeled and neat.
(a) How much will the investor invest in production?
(b) What is the NPV of the investment chosen by the investor?
(c) What is the optimal allocation of consumption for the two periods?
(d) What is the PV of his total consumption?
(e) Does the investor borrow or lend in the capital market? Give a numerical answer.
(f) Why is it important that the capital markets are perfect? How would the answer change if the
borrowing rate was bigger than the lending rate.
2. (15 points) Net Present Value, Bonds, and Common Stock
(a) Briefly explain the term “yield to maturity.”
(b) What are debentures?
(c) What is a callable bond?
(d) Suppose you take out a £250,000 house mortgage from your local savings bank. The bank requires
you to repay the mortgage in equal annual installments over the next 30 years. What is your annual
payment if the annuity factor is 8?
(e) What are exchange-traded funds (ETFs)?
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3 ECON3015W1
3. Valuing Common Stock (15 points)
(a) Current forecasts are for ABC Company to pay dividends of £5, £5.25, and £5.50 over the next three
years, respectively. At the end of three years you anticipate selling your stock at a market price of £95.
What is the price of the stock given a 10% expected return?
(b) Noble’s stock was selling for £40 per share at the start of 2011. Dividend payments for the next year
are expected to be £1.75 a share. What is the dividend yield, assuming a growth rate of 6%?
(c) Our company forecasts to pay a £8 dividend next year, which represents 100% of its earnings. This
will provide investors with a 12.5% expected return. Instead, we decide to plowback 40% of the
earnings at the firm’s current return on equity of 25%.
(i) What is the value of the stock before the plowback decision?
(ii) What is the value of the stock after the plowback decision?
(iii) What is the Present Value of Growth Opportunities (PVGO)?
4. (12 points) Information
You can choose between two different portfolios, A and B, that produce the following uncertain returns
in the two possible states of the world:
Good Bad
Portfolio A 100 0
Portfolio B 60 80
Before making your choice you receive one of two costless messages, m1 or m2, that convey some
information about the future realization of the state of the world. Consider the following specifications
of the information structure (each row gives you the conditional probabilities of the two states of the
world, given the message you receive):
Perfect Information No Information Noisy Information
Good Bad Good Bad Good Bad
m1 1 0 m1 0.5 0.5 m1 0.8 0.2
m2 0 1 m2 0.5 0.5 m2 0.2 0.8
(i) Draw the decision tree corresponding to each of the above specification of the information structure.
Suppose you receive message m1. What would your optimal choice be in any of the above scenarios?
Question Continues on Page 4
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4 ECON3015W1
(ii) Let a = {A,B}, e = {Good, Bad}, m = {m1,m2} and denote the conditional probability of e given m by
p(e|m) and the return to portfolio A in state of the world e by U(a,e). The value of the information is
defined as:
S p(m) max S p(e|m)U(a,e) m a e
Suppose you are equally likely to receive any of the two messages. What is the value of the information
in each of the above scenarios? Would you be led to conclude that the Efficient Market Hypothesis
holds in this setting?
5. (25 points) Capital Asset Pricing Model (CAPM)
Consider the Capital Asset Pricing Model (CAPM) of equilibrium asset pricing.
(a) What are the main assumptions of the model? What is the Capital Market Line (CML)? What is the
Security Market Line (SML)?
(b) Explain how the CAPM provides a simple rationale for the following portfolio strategy:
• Diversify your holdings of risky assets according to the proportions of the market portfolio;
• Mix this portfolio with the risk free asset to achieve a desired risk-return combination.
(c) Consider the following applications of the CAPM.
(i) The ABC Company is contemplating issuing stocks to finance investment in producing a new type of
dummy, the Golden-Dummy. The annual return to the market portfolio is expected to be 20% and the
current risk-free interest rate is 10%. The analysts further believe that the expected return to the GoldenDummy
project will be 25% annually. What is the maximum value of beta (from the SML) that would
induce the ABC Company to issue stocks?
(ii) The current price of a share of stock in the XYY company in Italy is 2 Euro (Euro denotes the
European currency) and its expected yield over the year is 15%. The market risk premium in Italy is
10% and the risk-free interest rate is 5%. What would happen to the stocks’ current price if its expected
future payout remains constant while the covariance of its rate of return with the market portfolio falls
by 50%?
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5 ECON3015W1
6. (8 points) Financial Statements
The numbers below (in millions) come from the income and balance sheet of Devon Energy in 2011.
Revenues $ 12,000
Depreciation Expense 2,000
Interest Expense 1,000
Net Income 5,000
Total Assets 40,000
Total Liabilities 20,000
Stockholder’s Equity 20,000
(a) Calculate the Asset Turnover.
(b) Calculate the Operating Profit Margin.
(c) Calculate the Return on Equity (ROE).
END OF PAPER
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