I need an explain of the solution. Where do we get .667 from ?

Problem 1: Assume that Casper Manufacturing Inc. has $3.5 billion in assets and total debt amounting to $3.3 billion. The debt must be paid off in the next month and at that time equityholders will only receive $200 million. However management has an opportunity to invest $700 million with a potential payoff of either $1.5 billion or $0.

Assuming what the probability of the high payoff is 33.3%, what is the expect value of the equity if the firm takes the investment?

NPV = (.333*1.5) + (.667*0) - 0.7 = $ -200 million NPV of project

Expected value of equity in total: [.333*(((3.5-.7) +1.5) - 3.3)] + (.667*0) = $ 333 million

What is equitys value without the project?

$200 million

Would equity holders recommend this?

Yes. The expected value of the equity with the project ($333 million) is higher than the expected value of equity without the project ($200 million).

What do debt holders get without the project?

$3.3 billion (the lesser value between value of the firm and face value).

What do debt holders get with the project?

Total loss to debt is $333 million, $133 million transfer from debt to equity and $200 million from the negative NPV of the project.