Tutorial 2 Course “Financial Intermediation” - Lehrstuhl für ...

UNIVERSITÄT HOHENHEIM
INSTITUT FÜR BETRIEBSWIRTSCHAFTSLEHRE
LEHRSTUHL FÜR BANKWIRTSCHAFT UND
FINANZDIENSTLEISTUNGEN
PROF. DR. HANS-PETER BURGHOF
Tutorial 2
Course “Financial Intermediation”
Exercise 1: (Chapter 1.4, p. 38: “Banks as Delegated Contractors”)
An entrepreneur has the following investment opportunity that generates two possible
returns in the future.
Investment I = 20
Return in condition 1 y1 = 40
Return in condition 2 y2 = 15
Return for liquidation by lender
of capital L = 10
Interest rate i = 0%
Probability of condition 1 p = 0.5

To finance the investment, the entrepreneur can choose between capital market
financing (issue a bond without the possibility to renegotiate) and bank financing (take
out a bank loan with renegotiation possibility). In the case of renegotiation, the bank gets
the revenue w = 0.5 (y-L), where y is the particular project revenue. Moreover, the
lender of capital has the opportunity to liquidate the project preliminary, if the credit
payment is in default. The lender of capital accepts the credit agreement only if the loan
amount is covered by the expected repayment. The entrepreneur can simulate
bankruptcy.
a) Consider the case of bond financing:
Compute the contractually guaranteed repayment amount DA for which the lender
of capital consents to finance the investment.
Compute the agency costs ACA in this contract. For this purpose, compare the
project’s net present values for equity financing and for bond financing.
b) Consider the case of bank financing:
Compute the contractually guaranteed repayment amount DB, for which the
lender of capital consents to finance the investment.
Compute the agency costs ACA in this contract. For this purpose, compare the
project’s net present values for equity financing and for bank financing.

Exercise 2: (Chapter 3.3, p. 36: “Risk Enhancement and Banking Operations”)
There is a bank with the following characteristics:
K = 1.2 R = 2 r = 0.1
K is a risk-free position with secure repayment K in every period.
R is a risky position with the repayment
o R with probability p
o 0 with probability (1-p)
r is the market rate of interest.
a) If the bank maximizes the value of its total capital, from which value of p does the
bank prefer the risky project?
b) Depositors obtain the amount of D in every period. From which value of p does the
bank select the risky project if the bank maximizes the value of its equity (E)? The
bank has no bail-out guarantee in case of bankruptcy.
i) For D = 1.15
ii) For D = 0.9
c) Now, from which value of p does the bank select the risky project if the bank
maximizes the value of its equity (E) and if the bank has a bail-out guarantee?
d) Given a project R with a probability of success p = 0.5. Compute the capital
structure (that is, D) for which the bank just selects the project R, assuming case B
(bail-out guarantee).
e) Assume there is no bail-out guarantee. Compute the capital structure (D) for which
the value of the total capital is maximized (“optimal” capital structure).

f) Please show that a fixed risk premium c does not influence the bank’s incentive
structure, assuming case B (with bail-out guarantee). The risk premium is fixed if it
has to be paid regardless of the investment decision R of K.
g) Please show that a proportional risk premium can influence the bank’s incentive
structure, assuming case B (with bail-out guarantee). The risk premium is
proportional if it rises with the project’s probability of failure in which the bank
invests, i.e. (1-p)*c.
Additional exercise:
h) Please show: stricter equity norms of the type dept capital/total capital ≤ X, that is
D/TC ≤ X, can lead to a greater risk aversion of the bank management. Assume
case L (bankruptcy without bail-out guarantee).
Hint: Express p as a function of D and substitute D by a function in X. Analyze the
effect of a reduction of X.