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Question

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 it’s 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 couldn’t 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:

What are the cash flows to debt with face value of $600 given Project 2?

What is the expected payment received by debt holders in this case?

What if debt holders require a 10% expected rate of return, how much is raised initially when bonds with a face value of $600 are sold?

Given all projects require $800 of initial capital, the owner will have to put up his own capital, equal to $800 minus the amount raised from debt holders. How much is this? Call this amount of capital “K”. This investment entitles the owner of the cash flows described above when Project 2 is undertaken (i.e., 0 if “depression” occurs and $951 if “prosperity” occurs). Would the owner be satisfied with this result?