Question

1. The loans provided by banks have three elements: (L, r, C). Where L is the amount of the loan, r is the interest rate on the loan and C is the security for the loan. At this time, businessman X received a loan (500 million, 10%, 200 million) from the bank. At this time, businessman X is a person who wants to maximize the expected rate of return, and there are two types of projects X can invest in, and each income R is as follows. (30 points)

(Hint: If collateral businessman X declares default, it can be used by the bank to make up for the default.)

Project A

R = 400 million probability 0.5

= 800 million probability 0.5

Project B

R = 200 million probability 0.5

= 900 million probability 0.5

(a) If the bank doesn't know which project X is choosing, X is

Would you like to do a project?

(b) Suppose the bank has increased the amount of collateral from C = 200 million to C = 300 million. If the bank doesn't know which project X is choosing, what project does X want to do?

(c) If the answers in (a) and (b) are the same, explain the same reason, if different, explain the other reason.

Type or paste question here

Answer 1

Amount to be returned to the bank = 10% of 500 million + 500 million = 550 million

Income from A if earning is less = 400 million.

Amount to be paid to the bank = $550 million.

So return of security from Bank = $200 - ($550 - $400) million = $50 million. Loss to the businessman = $200 - $50 = $150 million

Income from A if earning is more = 800 million.

Amount to be paid to the bank = $550 million.

Since earning is more than what needs to be paid to the bank, so the security deposit will be returned.

Profit to the businessman = $800 - $550 million = $250 million

So expected earnings from A = 0.5 * (-150) + 0.5 * 250 = -75 + 125 = $50 million

Income from B if earning is less = 200 million.

Amount to be paid to the bank = $550 million.

So return of security from Bank = $200 - ($550 - $200) million = -$150 million.
Bank can recover a maximum of $200. So the businessman will face a loss of this amount only.

Income from B if earning is more = 900 million.

Amount to be paid to the bank = $550 million.

Since earning is more than what needs to be paid to the bank, so the security deposit will be returned.

Profit to the businessman = $900 - $550 million = $350 million

So expected earnings from B = 0.5 * (-200) + 0.5 * 350 = -100 + 175 = $75 million

a) So it is advisable for X to choose project B as his expected earning is more.

b) If bank increases security to $300 million,

Income from A if earning is less = 400 million.

Amount to be paid to the bank = $550 million.

So return of security from Bank = $300 - ($550 - $400) million = $150 million. Loss to the businessman = $300 - $150 = $150 million

Income from A if earning is more = 800 million.

Amount to be paid to the bank = $550 million.

Since earning is more than what needs to be paid to the bank, so the security deposit will be returned.

Profit to the businessman = $800 - $550 million = $250 million

So expected earnings from A = 0.5 * (-150) + 0.5 * 250 = -75 + 125 = $50 million

Income from B if earning is less = 200 million.

Amount to be paid to the bank = $550 million.

So return of security from Bank = $300 - ($550 - $200) million = -$50 million.
Bank can recover a maximum of $300. So the businessman will face a loss of this amount only.

Income from B if earning is more = 900 million.

Amount to be paid to the bank = $550 million.

Since earning is more than what needs to be paid to the bank, so the security deposit will be returned.

Profit to the businessman = $900 - $550 million = $350 million

So expected earnings from B = 0.5 * (-300) + 0.5 * 350 = -150 + 175 = $25 million

So in this case, Businessman should go for project A.

c) In project B, if the businessman defaults, the amount for the bank to recover was $350 million. However, since in the first case the deposit was $200 million only, the bank could not recover anything more than that. So the losses of the businessman was limited to $200 million. In the second case, with the same logic, the maximum loss of the businessman would have been $300 pounds.

As the loss was limited in the first case, the potential earnings or expected earnings was also limited in the downside. This went down further in the second case. So businessman had to change his profits.

If the security deposit was more than $350 million (which is the maximum loss in both the projects) always, then Businessman would always have gone with A. However, since the security deposit is lesser than the max loss, so to protect the downside, the businessman had to change his decision.

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