Question 1:
You announce that you will issue $10M worth of one-year bonds tomorrow and would like to determine the proper yield (i.e. the promised cash flow) to offer on these bonds. Because your asset cash flows are independent of market conditions, investors expect a return of 5 percent (the risk-free rate) on this debt investment. Your firm has 2M shares outstanding priced at $20 per share prior to this announcement.
a) There is a 10 percent chance you will only be able to pay bondholders $6M next year (state B). There is a 90 percent chance you will be able to fully repay your bondholders the promised cash flow (state G). For now, assume no bankruptcy costs. What promised cash flow must you provide to bondholders in state G so that they receive a 5 percent expected return?
b) What is the promised return for this debt issuance?
c) Following the debt issuance announcement, suppose also that the market learns there will be a $3M bankruptcy cost in the default state. What promised cash flow must you provide to bondholders in state G so that they receive a 5 percent expected return?
d) The expected bankruptcy cost will negatively affect the share price. What will be the new share price following the announcement of the debt issuance?
Question 2:
You are currently doing research on Annex Corporation (symbol: ANX), a levered firm that appears to be financially distressed. Your goal is to infer the probability that this firm goes into default and the estimated bond repayment in the default state using available market data. The firm has two bonds outstanding: Bond A and Bond B. Bond A is senior to Bond B, meaning that it has first claim to the cash flows generated by the firm.
a) Bond B has a current price of $800, one year until maturity, a promised cash flow of $1,100 next year, and an expected return of 6 percent. If ANX defaults, then Bond B pays a cash flow of zero (this is because Bond A claims all available cash flows first). What is the probability of default implied by this information?
b) Bond A has a current price of $900, one year until maturity, a promised cash flow of $1,075 next year, and an expected return of 5 percent. The probability of default is given by your answer in part (a). Based on this information, what is the cash flow to Bond A in the default state? (the cash flow in the default state is also known as the recovery cash flow)
Question 3:
Your firm is considering an expansion into a new investment project. The investment would cost $1,000K and there are two states of the world that will determine the values of your existing assets and new investment project today. As the manager, assume your objective is to maximize the value to current shareholders. The following table provides you with financial information for your firm in each state of the world (all values are in thousands of $):
| |
State G |
State B |
| Probability of State |
50% |
50% |
| Value of Existing Assets |
8,000 |
4,000 |
| Cost of New Investment |
1,000 |
1,000 |
| Value of New Investment |
2,500 |
1,500 |
| NPV of New Investment |
1,500 |
500 |
| Value with Investment (no frictions) |
10,500 |
5,500 |
The manager announces that he will invest in the new project. The public does not know the true state of the world, but knows that the manager knows the true state of the world. Suppose first that the manager will raise the $1,000K by issuing equity.
a) What percentage of the firm will these new shareholders demand in exchange for $1,000K?
b) What is the APV of the new investment project (NPV of the new investment plus the NPV of financing) if the manager knows that the true state of the world is State G?
c) What is the APV of the new investment project (NPV of the new investment plus the NPV of financing) if the manager knows that the true state of the world is State B?
Suppose that the manager could also raise the $1,000K from bondholders in the form of perpetual par- valued debt. Assume that these bondholders know nothing about the firm and that the bonds are fairly priced. Assume a tax rate of 20 percent for determining the tax shield benefit from issuing this debt. There are no bankruptcy costs.
d) What is the APV of the new investment project if the manager raises the $1,000K via debt markets and knows that the true state of the world is State G? What is the APV in State B?
e) Will the manager issue debt or equity to finance the project in State G? What about State B?
f) Investors can now infer the true state of the world based on the manager's decision to invest and whether he issues debt or equity to pay for the new project. Given this, what percentage of the firm will these new shareholders demand in exchange for $1,000K if the manager announces he will pay for this new project by issuing equity?