investment beta vs company beta.

Hi, I am an intern who is green and still learning, so forgiveness please. I am very confused as to the difference, if any, between the beta of a company vs that of an investment. I have included an example and any advice would be appreciated.

"Managers of Company ABC have been told that their shares have a covariance with the market portfolio of 0.75 and the variance with the market portfolio is 0.3. The current risk-free rate is 3% and the market risk premium is 4%.

Required: (i) Calculate ABC’s cost of equity. (Show all your calculations). (ii) ABC’s managers believe that their company beta (β) will be same as the beta for the investment they want to make. Are they correct and if not why not? "

From the above, I have managed to work out that the beta for the cost of equity is 2.5 and the cost of equity should therefore be 13%. Is that right?

I am very unsure about part 2 because I don't know if the terms in this question are correct. Is this related to levered and unlevered betas? What is the answer to part 2 and why? Any help and/or links would be appreciated.

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