Analysis of Stock Opportunity Cost and Equilibrium Price

Given the information about the stock’s beta, current price, expected year-end dividend, T-bill rate, and market risk premium, we can calculate the opportunity cost of capital and determine if the stock is a good or bad buy. Additionally, we can find the equilibrium price at which the stock is perceived as fairly priced today.

Calculation of Opportunity Cost of Capital

Given:

– Beta (β): 0.69
– Current Stock Price (P₀): $50
– Expected Year-End Dividend: $4
– Expected Year-End Stock Price (P₁): $52
– T-bill Rate: 6%
– Market Risk Premium: 9%

Required Rate of Return (Rᵣ):

Rᵣ = Risk-Free Rate + (Beta × Market Risk Premium)
Rᵣ = 6% + (0.69 × 9%)
Rᵣ = 6% + 6.21%
Rᵣ = 12.21%

Opportunity Cost of Capital:

Opportunity Cost of Capital = (Dividends + (P₁ – P₀)) / P₀
Opportunity Cost of Capital = ($4 + ($52 – $50)) / $50
Opportunity Cost of Capital = ($4 + $2) / $50
Opportunity Cost of Capital = $6 / $50
Opportunity Cost of Capital = 0.12 or 12%

Evaluation of Stock as Investment

The calculated opportunity cost of capital is 12%, which is lower than the required rate of return of 12.21%. This indicates that the stock is not a good buy at the current price of $50 because it does not provide a return that meets investors’ expectations. Investors are likely to avoid investing in the stock given the mismatch between the opportunity cost of capital and the required rate of return.

Calculation of Equilibrium Price

To find the equilibrium price at which the stock is perceived as fairly priced today, we need to calculate the price at which the expected rate of return equals the required rate of return.

Equilibrium Price Calculation:

Equilibrium Price = (Dividends + (Required Rate of Return × P₀)) / (1 + Required Rate of Return)
Equilibrium Price = ($4 + (0.1221 × $50)) / (1 + 0.1221)
Equilibrium Price = ($4 + $6.105) / 1.1221
Equilibrium Price = $10.105 / 1.1221
Equilibrium Price ≈ $9

Therefore, the equilibrium price at which the stock is perceived as fairly priced today is approximately $9.

Conclusion

In conclusion, the stock is not a good buy at the current price of $50 as the opportunity cost of capital is lower than the required rate of return. Investors are likely to avoid investing in the stock at this price. The equilibrium price, at which the stock is perceived as fairly priced today, is approximately $9. Investors should consider this fair value when making investment decisions regarding this stock to ensure they achieve an appropriate rate of return relative to their risk tolerance and market expectations.