without leverage, the equity is worth either $15 million or $80 million at year-end. Because the risk is diversifiable, no risk premium is necessary and we can discount the expected value of the firm at the risk-free rate to determine its value without leverage at the start of the year. the solution is : value unlevered = 1//2 (150)+1/2(80)/1.05= 109.52

My questions are:

1. why did they put 1/2 ( I know it says equally likely ) but what does it mean?

2. what is risk diversifiable?

3. what is the risk premium?

and why did they use 26% instead of 1/2in this problem (Gladstone Corporation is about to launch a new product? Depending on the success of the new product, Gladstone may have one of four values next year: $147 million, $136 million, $91 million, or $82 million. These outcomes are all equally likely, and this risk is diversifiable. Suppose the risk-free interest rate is 5% and that, in the event of default, 26% of the value of Gladstones assets will be lost to bankruptcy costs. (Ignore all other market imperfections, such as taxes.) Thank you