**Financial Management**

**Q****-1) Suppose an investor has $100 with him today. There is a 5% chance that he will fall sick after 1 year and then need this cash to pay for his healthcare expenses. He has two investment choices: A and B. A is a liquid investment that gives 2% annual return. If the investment continues from year 1 to 2, the investor keeps getting this 2% return. B is illiquid, and it must remain invested for two years. If investment B is liquidated at year 1, it loses 20% of principal amount, but if it stays in the investment, then it gives a one-time 20% return (i.e. gives $120) after two years.**

**Please answer the following questions based on this information. Only numbers, rounded to two decimal places when applicable, are necessary.**

**What is the expected cash flow need of investor at year 1?**

The expected cash flow is $102 which is the need of the investor in year 1.

**What is the expected cash flow at time 1 from investment A?**

The probable cash flow is $102 at time 1.

**What is the expected cash flow at time 2 from investment A?**

At time 2 the expected cash flow is $104.04

**Assume a discount rate of 2% for investment A. What is the NPV of investment A?**

The Net present value of the investment A is $98 with the assumed discount rate of 2%.

**What is the expected cash flow at time 1 from investment B?**

From the investment B at time 1 the expected cash flow is $80.

**What is the expected cash flow at time 2 from investment B?**

$120

**Assume that investment B has a discount rate of 5%. What is investment B’s NPV?**

The Net Present value of the investment b is $8.84 at the discount rate of 5%.

**Which investment should the investor take? A or B?**

According to NPV (Net Present Value), the investor should select the investment B**.**

**Now assume that investment B gives only $110 at time 2. What is the new NPV of investment B?**

The new NPV of investment B is $-0.23

**Which investment should be taken now?**

The investor should select investment A because it has higher NPV than the investment B

**What is the minimum return (i.e., total cash flow at time 2) that investment B must give at time 2 in order to make it a zero-NPV project?**

Its minimum return is 110.25 at the zero NPV

**Q-2) Suppose a bank pools the money of two investors (A and B), each contributing $100. There is a 5% chance that either one of the investors needs cash after year 1. The probability that they need cash after year 1 is independent of each other. Otherwise, they will need money in year 2. The bank keeps $100 in cash that earns zero interest rate, and it lends the remaining $100 to a borrower who promises to pay $120 at time 2. Assume there is no default risk with the borrower. However, if the borrower’s project gets liquidated at year 1, the project gets only $40 back (called liquidation value) at year 1.**

**Please answer the following questions based on this information. Only numbers, rounded to two decimal places when applicable, are necessary.**

**What is the probability (in %) that only A needs money in year 1?**

The probability of A needs money is approximately 5%

**What is the probability (in %) that the only B needs money in year 1?**

The probability of B is 5%.

**What is the probability (in %) that no one needs money in year 1?**

The probability of no one needs money is 90.25%

**What is the probability (in %) that both need money in year 1?**

The probability that both need money in the year 1 is 0.25%

**What is the expected cash flow to both investors combined at time 1?**

The cash flow of both the investors at time 1 is $40

**What is the expected cash flow to both investors combined at time 2?**

The cash flow of both the investors at time 2 is expected to be $120

**Assuming a discount rate of 5%, what is the NPV of these cash flows?**

The NPV of the cash flows at the discount rate of 5% is -61.9 and 8.8

**What is the minimum payoff in year 2 that the borrower would have to promise to pay in order to make this a zero-NPV project to the bank?**

The minimum amount of payoff that the borrower would have to pay in year 2 in order to make zero-NPV project is $108.84.

**Q-3) Imagine a company has a manager who gets a fixed salary of $100 if the company remains solvent, and he has no equity stake in the company. If the company goes bankrupt, the manager loses his job and hence gets no salary. The company is considering two projects: A and B. The required investment for each project is $1000, which will come from the shareholders. Both are one-year projects.**

**Project A has a success probability of 5%, in which case it pays $100,000. With the remaining 95% probability, the project fails and gives no return. Project B has a 50% chance of success, and it pays $1500 in success. With the remaining 50% chance, the project fails and pays nothing. If either of the new projects fails, the company will be bankrupt. Assume a discount rate, r, of 0 (i.e. you can ignore the discount rate here).**

**Please answer the following questions based on this information. Only numbers, rounded to two decimal places when applicable, are necessary.**

**What is the NPV of project A?**

The NPV of the project A is $4000

**What is the NPV of project B?**

The NPV of the project B is $-250

**Which project should be taken by the shareholders? A or B?**

Project A should be selected by shareholders because it has a higher NPV.

**What is the expected payoff of the manager in project A?**

The probable payoff of the manager in project A is $5.

**What is the expected payoff of the manager in project B?**

The expected payoff of the manager in project B is $50

**If left to the manager, which project is he likely to take? A or B?**

The manager wants to take project B because it has a low risk and managers take rational decisions.

**Q-4) Suppose a company has a market value of assets of $50, and it owes $100 of debt to its lender. The company is considering two projects, A and B. Each project requires an investment of $50 that will come from selling the current assets at the market price for $50. Project A has a 5% chance of paying off $500 and a 95% chance of paying nothing. Project B has a 50% chance of paying $120 and a 50% chance of paying nothing. Ignore discounting rate for this problem.**

**What is the NPV of project A?**

The NPV of project A is $-25

**What is the NPV of project B?**

The NPV of project B is $10.

**From the firm’s perspective, which project should be taken? A or B?**According to the perspective of the firm, they select B project.**What is the shareholders’ NPV of project A?**

The Shareholders NPV from project A is $-25

**What is the shareholders’ NPV of project B?**

The shareholders NPV from Project B is $10

**Which project is more desirable to shareholders? A or B?**

The Project B is more desirable to the shareholders because it will pay off $500 and has a higher NPV

**What is the debtholders’ NPV from project A?**

The debtholders NPV from project A is $-75

**What is the debtholders’ NPV from project B?**

The debtholders NPV from project B is $-40.

**Which project is an undesirable one from the debtholder’s perspective? A or B?**

Project B is undesirable for the debtholders.

**Q-5) Suppose an investor lends $100 to a business that promises to repay $120 after two years. Assume there is no default risk with the business at year 2 repayment. If the investor needs money after one year, the business will not be able to pay him back his entire money. Assume that the penalty for early withdrawal is 25%. Now assume there is a 10% chance the investor will need his money after one year. The project’s discount rate is 8%.**

**If the investor invests in this business, what is his expected cash flow in year 1?**

The expected cash flow is $115.5

**If the investor invests in this business, what is his expected cash flow in year 2?**

In year 2 the expected cash flow is $120

**What is the NPV of this project to the investor?**

The NPV of this project is $2.88

**Now imagine that the early withdrawal penalty is 0% (i.e. he gets back his $100 at year 1 if needed). What is the new NPV?**

The new NPV is $-7.40741

**What is the highest penalty (in %) for early withdrawal that keeps the project from becoming a negative-NPV project?**

$-30.56% penalty deduct from the return total.

**Q-6) Suppose there are two loans, A and B that you want to pool in a Mortgage-Backed-Security. Each has a principal value of $100. Loan A’s default risk is 5%; B’s is 10%. Both of these loans mature after one year. Assume that loan A pays interest of 10% per annum, and B pays 15% per annum. Assume further that their default rate is independent of each other. If a loan defaults you lose all the interest and recover 70% of the principal value.**

**What is the probability (in %) that both loans are in default at year 1?**

The probability of loans are in default in year 1 is only 0.50%

**What is the probability (in %) that neither loan is in default at year 1?**

The probability of no loan default in year 1 is 85.500%

**What is the probability (in %) that loan A is in default, but B is not?**

The probability that loan A will default is only 5.00%

**What is the probability (in %) that loan B is in default, but A is not?**

The probability that loan B will default is 10.0%

**What is the payoff from this pool if both loans are in default?**

If both loans default than the amount of payoff would be $140

**What is the payoff from this pool if neither loan is in default?**

If neither loan default than the amount of payoff would be $225

**What is the payoff from this pool if A is in default, but B is not?**

The amount of payoff would be $185

**What is the payoff from this pool if B is in default, but A is not?**

The amount of payoff would be $180

**What is the expected cash flow from this pool?**

The expected cash flows the pool are $78.15, $82.45 and $160.6

**Suppose you want to create two tranches from this pool: an AAA tranche and a subordinated tranche. If the AAA-tranche carries an interest rate of 3% and if it must have less than 1% default probability, what is the amount of pool that you can sell as AAA?**

The amount of pool that can be sold to AAA would be $102.67