Part 1Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin's equity beta is 0.850.85, the risk-free rate is 4 %4%, and the market risk premium is 5 %5%. If your firm's project is all-equity financed, estimate its cost of capital. Part 1Harburtin's cost of capital is [input]enter your response here %. (Round to two decimal places.)

Question

Part 1Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an​ all-equity firm that specializes in this business. Suppose Harburtin​'s equity beta is 0.850.85​, the​ risk-free rate is 4 %4%​, and the market risk premium is 5 %5%. If your​ firm's project is​ all-equity financed, estimate its cost of capital. Part 1Harburtin​'s cost of capital is [input]enter your response here ​%. ​(Round to two decimal​ places.)

BlackTom AI · Accepted Answer

Using the Capital Asset Pricing Model (CAPM): the required return on equity (and thus the project’s cost of capital for an all‑equity project) equals the risk‑free rate plus the equity beta times the market risk premium.

1. Relevant knowledge points and concepts
- CAPM formula: rE = rF + βE × (rM − rF).  
- rF is the risk‑free rate, βE is the equity beta (measure of systematic risk), and (rM − rF) is the market risk premium.  
- For an all‑equity financed project, the project’s cost of capital equals the cost of equity.

2. Step‑by‑step reasoning and calculation
- Given: rF = 4% (0.04), βE = 0.85, market risk premium = 5% (0.05).  
- Apply CAPM: rE = 0.04 + 0.85 × 0.05.

3. Intermediate arithmetic steps
- Multiply beta by the market premium: 0.85 × 0.05 = 0.0425 (4.25%).  
- Add the risk‑free rate: 0.04 + 0.0425 = 0.0825.

4. Why this is correct
- The result 0.0825 is the required return on equity expressed as a decimal; converting to percent gives 8.25%. Because the project is financed entirely with equity, there is no debt to change the firm’s overall cost of capital, so the CAPM equity cost is the appropriate discount rate.

5. Common incorrect approaches (brief)
- Using the market return instead of the market risk premium (i.e., rF + β × rM) would overstate the return.  
- Forgetting to convert percentages to decimals when multiplying (e.g., 5 vs 0.05) yields wrong results.  
- Using a levered/unlevered beta adjustment is unnecessary here because the firm and project are all‑equity financed.

Conclusion: The computed cost of capital is 8.25%, which matches the provided answer.

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