Suppose a bank has 100 million dollars of assets to invest. It can either invest
ID: 2779018 • Letter: S
Question
Suppose a bank has 100 million dollars of assets to invest. It can either invest in risky or safe loans. Safe loans will be worth $105 M in one year with certainty. Risky loans will be worth either $70 M or $130 M in one year, each with equal probability.
a. Suppose the bank has $80 million in one-year time deposits. For simplicity, assume that they pay no interest, so that the bank's liability will still be $80 M in one year. Assume that the deposits are insured by the government, and for simplicity assume that the bank does not have to pay a premium for this insurance. If the bank's assets are worth less than $80 M in one year, the government will shut the bank down and pay the difference between $80 million and the value of assets. [HINT: SET UP THE BANK’S BALANCE SHEET]
b. Compute the probability that the bank will fail, the expected value of the bank's net worth and the expected size of the government's bailout in one year if the bank invests its assets in safe loans.
d. Do the same assuming the bank invests in risky loans.
e. Which investment strategy would the government prefer the bank to undertake? Which strategy will the bank choose, assuming that the bank's primary objective is to ensure its survival, and its secondary objective is to maximize its expected net worth.
Explanation / Answer
Answer (a)
Time Deposits held by the Bank = $ 80 Million
If the bank invests the same in Safe loans today
Total Liabilities of the Bank = Time Deposits =$ 80 Million
Total Assets of the Bank = Amount invested in Loans = $ 80 Million
After 1 year, if the assets are less than $ 80 Million then
Loans = $ 80 Million - X where X is the erosion in value of assets
Amount of Government Bailout = X
Total Assets = ($ 80 Million - X) + X = $ 80 Million = Total Liabilities
And the Bank will be closed
Answer (b)
If the Bank invests in safe loans
After 1 Year Value of the Safe Loans = (105/100) * $ 80 Million = $ 84 Million
Assets
Value of Safe Loans = $ 84 Million = Total Liabilities
Amount of Government Bailout = 0
Liabilities
Time Deposits Payable = $ 80 Million
Addition to Networth = $ 4 Million
Total Liabilities = $ 84 Million
As the value of safe loans are expected to be the amount mentioned above with certainty, the probability of the Bank fails is 0.
Answer (d)
In case the Bank invests in risky assets. There is a equal probability of bank holding assets worth less than the original investment or more than original investment after one year
In case the assets are worth less than original investment (50% probability)
Assets
Value of Risky Loans = $ 80 Million * (70/100) = $ 56 Million
Amount of Government Bailout = (80 – 56) = $ 24 Million
Total Assets = $ 80 Million
Liabilities
Time Deposits Payable = $ 80 Million
Total Liabilities = $ 80 Million
In case the assets are worth more than original investment (50% probability)
Assets
Value of Risky Loans = $ 80 Million * (130/100) = $ 104 Million
Amount of Government Bailout = $ 0 Million
Total Assets = $ 104 Million
Liabilities
Time Deposits Payable = $ 80 Million
Addition to Networth = (104 – 80) = $ 24 Million
Total Liabilities = $ 104 Million
As both the outcomes are equally possible, there is a 50% probability that the Bank will fail.
Answer (e)
As Banks deal with public money and there is an element of cost involved for government in the form of insurance money to be paid in case of a reduction in value of assets, the government prefers the banks to invest in safe loans.
Banks also prefer to invest in safe loans as survival is their primary objective and maximizing the expected networth is a secondary objective.
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