Suppose XYZ is a very small, privately held company that has decided to go public. You have been charged with analyzing XYZ’s expected return. The company has been around for a long time (they are not a start-up anymore), but they are a privately held company and they do not have historical return data. Your analysis includes the following information:

Bond yields = 7%
Equity risk premium = 12%
Micro-cap premium = 5%
Start-up premium = 4%

What are the expected returns for this company, given the information above?

Question

Suppose XYZ is a very small, privately held company that has decided to go public. You have been charged with analyzing XYZ’s expected return. The company has been around for a long time (they are not a start-up anymore), but they are a privately held company and they do not have historical return data. Your analysis includes the following information:

Bond yields = 7%
Equity risk premium = 12%
Micro-cap premium = 5%
Start-up premium = 4%

What are the expected returns for this company, given the information above?

BlackTom AI · Accepted Answer

First, I’ll restate the key data to ensure we’re using the same numbers in our calculation. The question provides: bond yields (risk-free rate) = 7%, the equity risk premium = 12%, a micro-cap premium = 5%, and a start-up premium = 4%. The company is a very small privately held firm about to go public, with no historical return data, so we’re asked to assemble an expected return using these premia.

Option A: 19% — This would correspond to 7% + 12% = 19%, i.e., taking the risk-free rate plus the broad equity risk premium, but overlooking both the micro-cap premium and the start-up premium. The small size and private-to-public status typically imply extra risk, so omitting those premiums underestimates expected return.

Option B: 22% — This would be 7% + 12% + 3%, where the extra 3% is not one of the provided premia. Since the question supplies 5% (micro-cap) and 4% (start-up) as applicable adjustments for small, early-stage firms, this 22% figure ignores these explicit premiums. It’s missing both adjustments and thus is not consistent with the given data.

Option C: 24% — This would be 7% + 12% + 5% = 24%, i.e., adding the micro-cap premium on top of the risk-free rate and the broad equity premium, but it leaves out the start-up premium. Since the company is extremely small and privately held transitioning to public, both small size and private-to-public status would reasonably warrant multiple premiums, not just one.

Option D: 28% — This equals 7% + 12% + 5% + 4% = 28%, i.e., risk-free rate plus the broad equity premium, plus both the micro-cap premium (for very small firm size) and the start-up premium (reflecting the risk of moving from private to public status and the early-stage nature associated with private firms entering the public arena).

To evaluate the options, consider the logic of risk premia: the risk-free rate serves as a baseline for safe returns. The equity risk premium adds compensation for bearing overall equity risk. Since XYZ is extremely small (micro-cap category) and privately held before going public (start-up-like risk), you would typically apply both the micro-cap premium and the start-up premium in addition to the baseline equity premium. Therefore, the combination 7% + 12% + 5% + 4% = 28% aligns with applying all relevant risk premia explicitly provided in the question. The other options each omit one or more premia that would be justified given the company’s size and transition from private to public status.

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