BEEM117
UNIVERSITY OF EXETER
BUSINESS SCHOOL
May 2022
Economics of Corporate Finance
Module Convenor: Simone Meraglia
Duration: TWO HOURS + 30 minutes upload time
No word count specified
Answer any 3 questions out of 4.
All questions are worth equal marks.
Materials to be supplied on request: None.
Approved calculators are permitted.
This is an open book exam.
1
BEEM117 TURN OVER
Question 1
Suppose you are an investor seeking to find new opportunities to invest. You have identified
two firms: L1 Corporation and BT Enterprises. L1 Corporation is debt free, while BT
Enterprises is highly leveraged. Each firm is run by an entrepreneur who can exert two levels
of effort: high or low. The project undertaken by the entrepreneur of each firm yields either a
high return RS > 0 or a low return RF ≥ 0, with RF < RS . High effort by the entrepreneur
increases the probability that the firm realizes a high return.
(a) Suppose there are perfect capital markets, no taxes, and no bankruptcy. Suppose also
that you (and other outside investors) can perfectly observe the effort exerted by the
entrepreneurs of the two firms, and you can write a contract specifying the effort you
want the entrepreneurs to exert. Does the amount of leverage of each firm affect its
market value? Explain your answer. (30% of the marks)
(b) Suppose now you and other outside investors cannot observe the effort exerted by the
entrepreneurs of the two firms. In case of a low return, the project undertaken by
the entrepreneur of each firm yields RF > 0. Does the amount of leverage of each firm
affect its market value? If yes, is there an optimal amount of debt to be issued? Explain.
(40% of the marks)
(c) Let us continue with the framework described in point (b) above. Unlike point (b),
suppose now that, in case of a low return, the project undertaken by the entrepreneur
of each firm yields RF = 0. Does the amount of leverage of each firm affect its market
value? If yes, is there an optimal amount of debt to be issued? Explain. (30% of the
marks)
BEEM117 2 TURN OVER
Question 2
An entrepreneur has to finance a project of fixed size I. The entrepreneur has “cash-on-hand”
A, where A < I. To implement the project, the entrepreneur (that is, the borrower) must
borrow I −A from lenders. If undertaken, the project either succeeds, in which case it yields
a return R > 0, or fails, in which case it delivers a zero return. The probability of success
depends on the effort exerted by the entrepreneur: if the entrepreneur exerts high effort, the
probability of success is equal to pH ; if the entrepreneur exerts low effort, the probability of
success is equal to pL, where ∆p = pH − pL > 0. If the entrepreneur exerts low effort, she
also obtains a private benefit B > 0, while there is no private benefit when the entrepreneur
exerts high effort. Define as Rb the amount of profit going to the entrepreneur, and as Rl
the amount of profit going to the lenders in case of success, where R = Rb +Rl. We assume
both players obtain zero in case the project fails. All the players are risk neutral and there is
limited liability for the entrepreneur. Lenders behave competitively, and both entrepreneur
and lenders receive zero if the project fails.
(a) Write down the “break-even constraint” for the lenders assuming that the entrepreneur
exerts high effort. (10% of the marks)
(b) Write down the entrepreneur’s “Incentive Compatibility Constraint” (ICb) and derive
the minimum level of Rb such that the entrepreneur exerts high effort. (10% of the
marks)
(c) Compute the minimum level of cash-on-hand A the entrepreneur must have to be
financed. (10% of the marks)
(d) Suppose there is a second entrepreneur who has the possibility of investing in a separate
project that also costs I. The project yields a return R > 0 in case of success, and a
return equal to zero in case of failure. The probability of success is pH (pL, respectively)
if the second entrepreneur exerts high effort (low effort, respectively). The projects of
the two entrepreneurs are independent; that is, the return of each project is independent
of the return of the other project. Like the initial entrepreneur, the second entrepreneur
has “cash-in-hand” A, and obtains a private benefit B > 0 if he exerts low effort.
Suppose A < A (for both entrepreneurs). Suppose also each entrepreneur puts weight
a ∈ [0, 1] on the other entrepreneur’s income (relative to her own income). Consider the
case of “group lending”: each entrepreneur receives a payment Rb if both entrepreneurs
succeed, and receives zero otherwise.
Write down the entrepreneur’s “Incentive Compatibility Constraint” (ICb) and derive
the minimum level of Rb such that the entrepreneur exerts high effort when he/she
believes the other entrepreneur exerts high effort too. (20% of the marks)
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(e) Determine the highest income that each entrepreneur can pledge to lenders, and write
down the “break-even constraint” for the lenders (IRl) assuming both entrepreneurs
exert high effort. Does group lending always enable financing when A < A? Explain.
(20% of the marks)
(f) Let us continue with the framework introduced in parts (d) and (e). We keep assuming
that A < A (for both entrepreneurs). Also, each entrepreneur puts weight a ∈ [0, 1] on
the other entrepreneur’s income (relative to her own income). If each entrepreneur
receives Rb when her project succeeds, independently of whether the other project
succeeds or fails, can entrepreneurs receive financing from outside investors? Explain.
(30% of the marks)
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Question 3
An entrepreneur has to finance a project of fixed size I. The entrepreneur has no cash-on-
hand (A = 0). To implement the project, the entrepreneur must borrow I from lenders. If
undertaken, the project either succeeds, in which case it yields a return R > 0, or fails, in
which case it delivers a zero return. The entrepreneur (borrower) can be one of two types. A
“good” borrower has a probability of success equal to p. A “bad” borrower has a probability
of success equal to q, where p > q. Define as Rb the borrower’s level of compensation when the
project is financed and succeeds. All the players are risk neutral and there is limited liability
for the borrower. Lenders behave competitively, and both borrower and lenders receive zero
if the project fails.
Assume pR > I > qR.
(a) Suppose first that lenders have complete knowledge of the borrower’s type. Write down
the lenders’ break-even constraint when the borrower is (i) “good” or (ii) “bad”. (10%
of the marks)
(b) What is the highest level of compensation each type of borrower can obtain? (10% of
the marks)
(c) Suppose now that lenders cannot observe the borrower’s type. Lenders believe the
borrower is “good” with probability α, and “bad” with probability 1−α. Comment on
the effect of asymmetric information on (i) the availability of credit to both types of
borrower, and (ii) if a loan is granted, on the compensation the two types of borrower
obtain from undertaking the project. (20% of the marks)
(d) Consider now the case in which A > 0, where pR > I −A > qR. Suppose the good
borrower is interested in separating herself from the bad one. How much of her wealth
A is the “good” borrower willing to invest? Show your work and explain. (40% of the
marks)
(e) In a separating equilibrium, when the project is financed, what is the lowest amount
that the outside investors obtain in case of success? Show your work. (20% of the
marks)
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Question 4
Consider a firm run by an “incumbent” manager. Suppose the incumbent manager has the
opportunity to invest in one of two different projects, Project 1 or Project 2. The incumbent
manager has a higher ability in managing Project 1 rather than Project 2. Also, if the
incumbent is fired by shareholders, she is replaced by an “alternative” manager whose ability
to manage Project 1 is lower than the incumbent’s ability.
Suppose the investment in a project is irreversible, and the shareholders’ choice of the
incumbent manager salary (as well as their decision on whether to fire her) is taken after
the investment is made. Also, assume the incumbent manager has a stake in the firm she
runs, but she does not fully control it.
(a) Suppose none of the projects gives the manager a direct utility. According to Shleifer
and Vishny (1989), which of the two projects should the incumbent manager choose?
What is the economic rationale behind this choice? Explain. (20% of the marks)
(b) Suppose the incumbent manager chooses the size of the investment in her preferred
project. Do you expect the manager to select the investment size that maximizes the
firm’s market value? If not, does the manager over-invest or under-invest with respect
to the efficient investment size? Explain your answer. (30% of the marks)
(c) Suppose now that the incumbent manager and the “alternative” manager have the same
ability in managing Project 1. We consider the case in which the manager owns a positive
fraction θ ∈ (0, 1) of the shares of the company, but she does not fully control it (that
is, θ < 1). Does the incumbent manager select the investment size that maximizes the
firm’s market value? If not, does the manager over-invest or under-invest with respect
to the efficient investment size? Show your work and explain your answer. (50% of
the marks)
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