Bank Management
2024-2025 Spring
Nan Li
Class Assignment 4
Due on April 28, 2025
1. Suppose your company can only invest in the following two projects, the required investment
are both $800 million, the results of the two projects in a year are as following,
Project 1
Project 2
Recession
Prob. 50%
Boom
Prob. 50%
500
0
1500
1551
Expected Expected
Value
Return
Standard Deviation
of Return
Suppose your company has no cash left after investing $800million.
1)
2)
3)
4)
5)
Computed the expected value, expected return and risk of the two projects.
Suppose your company does not have any liability, which project would you choose? Why?
Suppose your company currently has debt of $600 million, which project would you choose?
Why?
Compare your decision in 2) and 3) and what is the implication?
What is the maximum amount of the debt such that you will not choose Project 2?
2. Suppose the required reserve ratio in China is 15%, and the PBC removed the requirement of
loan-to-deposit ratio no more than 75% in Oct 2015.
1) Compute the upper limit of the money multiplier in China before and after Oct 2015.
2)
Suppose the money multiplier is 4 after October 2015, what are the possible reason that
explain the difference between the actual money multiplier and the upper limit you obtained
in part 1)?
3)
From the figure of the money multiplier and reserve ratio of large and small and medium
depository institutions in China from December 2017 to current, summarize the patterns you
identify in the figure and explain.
3. From the Treasury strip yield curve, the current required yields on one- and two-year
Treasuries are i1 = 4.65 percent and i2 = 5.50 percent, respectively. Further, the current yield
curve indicates that appropriate one-year discount corporate bonds are yielding k1 = 8.5
percent, and two-year coporate bonds are yielding k2 = 10.25 percent.
1) Calculate the one-year forward rate on the Treasuries and the corporate bond.
2) Using the current and forward one-year rates, calculate the marginal probability of repayment
on the corporate bond in years 1 and 2, respectively.
3) Calculate the cumulative probability of default on the corporate bond over the next two years.
Bank Management
2024-2025 Spring
Nan Li
4. A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to
charge a servicing fee of 50 basis points. The loan has a maturity of 8 years with a duration of
7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. The bank
has estimated the maximum change in the risk premium on the steel manufacturing sector to
be approximately 4.2 percent, based on two years of historical data. The current market
interest rate for loans in this sector is 12 percent. Using the RAROC model, determine
whether the bank should make the loan?
5. A firm has assets of $200,000 and total debts of $175,000. With an option pricing model, the
implied volatility of the value of the firm’s assets is estimated at $10,730. Under the Moody’s
Analytics method, what is the expected default frequency (assuming a normal distribution for
assets)?
6. Case Study: Loan Commitment for BSH Ship Company
BSH Company is a company in an emerging market. It mainly makes large ships of size 10,000
tons to 100,000 tons, the following is the summary of the operating income of this company
from 2011 to 2013,
2011
2012
2013
Ships ordered
8
12
21
Ships finished
4
7
11
Sales ($million)
65
87
130
Net profit ($million)
5.4
6.5
8.7
Net operating income ($million)
-0.4
-1.1
-1.4
The balance-sheet of BSH company in 2013 is as follows (in millions of dollars),
Current assets
125
Current liabilities
80
Inventory
85
Short-term debts
35
Account receivable
25
Account payable
27
Other
15
Other
18
Fixed assets
80
Long-term Liabilities
30
Other assets
5
Equity
100
Total assets
210
Liability and Equity
210
Recently, BSH Company would like to investment $5 million to build a new shipyard. Now
BSH Company asks for a loan commitment of 3 years in amount of $2 million from UOY bank.
As the credit officer in the UOY bank, will you approve this application? Why or why not?