You are an original owner of an online shoe company called Feet First . Your most current balance sheet states that your company has a book value of $32M, which includes $10M of cash that is invested in short-term, riskless government bonds. This cash was raised in a recent IPO. The stock is currently worth $30 per share and there are 1M shares outstanding. The firm also has long-term debt outstanding - specifically, it has 6,000 bonds outstanding (rated B), and each bond has a market value of $1,200. The firm has no other debt.
Analysis of past data tells us that the bonds have a beta of 0.2 and the equity has a beta of 0.8. The market risk premium is 7.0 percent and the risk-free rate is 3.0 percent.

a) What is the beta of the firm?

Suppose instead that you want to know the beta of the firm's operating assets. That is, you want to know the beta of the operating assets directly involved in shoe production, and not include those assets (cash) tied up in government bond investments. The beta of assets can be decomposed into individual asset projects, where a "project" can also include a cash investment in government bonds:

b) What is the beta of the firm's operating assets?

When you and your friends started this company five years ago, the riskiness of the cash flows involved in operating an online-retail shoe business was similar to now. Suppose that you and your friends are well-diversified across many stocks.

c) In starting this business with your friends, what was your expected return?

d) Start-up entrepreneurs typically have one investment, their start-up company, and no others, meaning they are not well-diversified across many assets. What does this imply for the expected return on this investment? No numbers are required for this answer.