cash flow exceeds interest and principal payments. In these situations the bondholders are paid in full, and the stockholders receive any residual. However, the most interesting of the four columns involves Day Corporation in a recession. Here the bondholders are owed $60, but the firm has only $50 in cash. Because we assume that the firm has no other assets, the bondholders cannot be satisfied in full. If bankruptcy occurs, the bondholders will receive all of the firm’s cash, and the stockholders will receive nothing. Importantly, the stockholders do not have to come up with the additional $10 (=$60 – $50). Corporations have limited liability in America and most other countries, implying that bondholders cannot sue the stockholders for the extra $10. 1 We assume that (1) both bondholders and stockholders are risk-neutral and (2) the interest rate is 10 percent. Due to this risk neutrality, cash flows to both stockholders and bondholders are to be discounted at the 10 percent rate. 2 We can evaluate the debt, the equity, and the entire firm for both Knight and Day as follows: For simplicity, we assume in this example. This means that investors are indifferent to the level of risk. Here, = because risk-neutral investors do not demand compensation for bearing risk. In addition, neither nor rises with leverage. Because the interest rate is 10 percent, our assumption of risk neutrality implies that = 10% as well. Though financial economists believe that investors are risk-averse, they frequently develop examples based on risk neutrality to isolate a point unrelated to risk. This is our approach because we want to focus on bankruptcy costs—not bankruptcy risk. The same qualitative conclusions from this example can be drawn in a world of risk aversion, albeit with more difficulty for the reader. Note that the two firms have the same value, even though Day runs the risk of bankruptcy. Furthermore, notice that Day’s bondholders are valuing the bonds with “their eyes open.” Though the promised payment of principal and interest is $60, the bondholders are willing to pay only $50. Hence their return or yield is: Day’s debt can be viewed as a because the probability of default is so high. As with all junk bonds, Day’s bondholders demand a high promised yield. Day’s example is not realistic because it ignores an important cash flow to be discussed next. A
more realistic set of numbers might be these: Why do the bondholders receive only $35 in a recession? If cash flow is only $50, bondholders will be informed that they will not be paid in full. These bondholders are likely to hire lawyers to negotiate or even to sue the company. Similarly, the firm is likely to hire lawyers to defend itself. Further costs will be incurred if the case gets to a bankruptcy court. These fees are always paid before the bondholders get paid. In this example, we are assuming that bankruptcy costs total $15 (=$50 – $35).
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