Dynamic Duo is considering the two projects below. The riskier one Project 2 also has a lower expected return. Each requires investment of $800. There are only 2 outcomes possible based on the times, either depression (D), or prosperity (P), and the probability of either is a coin flip (0.5).

Project Value if D Value if P Expected Value Expected Return

1 $500 $1500 $1000 200/800 = 25%

2 $0 $1551 $775.5 -24.5/800 = -3.06%

If our Dynamic Duo represents an owner-managed firm with no debt, they would clearly select Project 1 b/c its the better investment.

But what happens when an owner-managed firm has borrowed for one-period with debt of face value $600? Here it can be seen the $600 payment is sunk cost: if the firm is going to default, then it couldnt care less about how big the default is. In this case, the Dynamic Duo would want to generate more income when not in default. Note the cash flows to equity when the debt of $600 are as follows:

Project Value if Depr. Value if Props. Expected Value

1 0 $1500 600 = $900 $450

2 0 $1551 600 = $951 $475.5

Hence the Dynamic Duo representing the interests of a leveraged firm would select Project 2, flying over its lower net present value, b/c it has a higher present value conditional based on it not leading to default.

Alternatively, if the Dynamic Duo represents EQUITY OWNER (owns upper tail) with main concerns revolving around returns owned, and given their values and the cash flows if prosperity state is reached, Project 2 would be preferred. This is b/c although both projects have the same cash flows if depression state occurs, BUT notably Project 2 has greater value ( higher cash flow) if the prosperity state occurs.

Questions:

A). Suppose an alternative financing option is to issue bonds with a face value of $200, and further suppose that the owner had enough capital to finance the remainder of the project. Which project would the owner select with these bonds in place? Show the expected value to the equity holders for the two projects.

B). Given the project choice that these bonds induce above (A), please compute the cash flows to bondholders, the expected payment to bondholders, and the amount of money these bonds would raise if bondholders require a 10% expected rate of return.

C). If bonds raise the amount you computed above (B), how much does the owner have to put up to raise the $800? What expected payment does she receive for this investment? If she can earn 10% expected return on this alternative investment, is this better or worse than the return she receives with the debt of $600? Which capital structure would she choose?