Question

You announce that you will issue $100M worth of one-year bonds tomorrow, and you would like to determine the promised yield to offer on these bonds. Potential debt investors expect a return of 4 percent on these bonds, which is the same as the risk-free rate because the cash flows on these bonds do not have any systematic risk.

a. There is a 12 percent chance you will only be able to pay bondholders $20M next year (state B), and there is an 88 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 4 percent expected return? What is the promised yield for this debt issuance?
b. The market learns that there will be a $15M bankruptcy cost in the default state. What promised cash flow must you provide to bondholders in state G so that they still receive a 4 percent expected return?
c. Before the announcement of the debt issuance, the shares in your firm were priced at $50 per share. The announcement of the debt issuance negatively affects the share price because of the expected bankruptcy cost mentioned in part (b). What is the new share price following the announcement of the debt issuance? Assume that there are 3M shares outstanding. (Hint: equity value is impaired by the present value of the expected bankruptcy cost.)

Answer 1

To provide bondholders with a 4 percent expected return, the promised cash flow in state G must be $42.73M. The promised yield for this debt issuance is 134%.

Step-by-step explanation:

In state G, to provide bondholders with a 4 percent expected return, the promised cash flow must be calculated. The probability-weighted return is calculated using the following formula:

(Probability of State B x Cash Flow in State B) + (Probability of State G x Cash Flow in State G) = 0.12 * 20M + 0.88 * Cash Flow in State G = 100M * 0.04.

Solving for Cash Flow in State G, we get: Cash Flow in State G = ($100M * 0.04 - (0.12 * 20M)) / 0.88 = $42.73M. Therefore, the promised cash flow to bondholders in state G must be $42.73M.

The promised yield for this debt issuance can be calculated as follows:

($100M - $42.73M) / $42.73M = 1.34 or 134%.