1. **Stating the problem:** We want to analyze if investing in BlueTech Innovations is worthwhile based on given financial data. 2. **Key formulas and concepts:** - Price-to-Earnings (P/E) ratio: $$\text{P/E} = \frac{\text{Price per Share}}{\text{Earnings per Share}}$$ - Growth of EPS over time: $$\text{EPS}_t = \text{EPS}_0 \times (1 + g)^t$$ where $g$ is growth rate and $t$ is years. - Dividend Yield: $$\text{Dividend Yield} = \frac{\text{Dividend per Share}}{\text{Price per Share}}$$ - Required rate of return (discount rate) is 8%. 3. **Calculate current P/E ratio:** $$\text{P/E} = \frac{50}{5} = 10$$ 4. **Compare current P/E to industry average:** - Industry average P/E is 20, BlueTech's P/E is 10, which is lower, possibly indicating undervaluation or lower growth expectations. 5. **Calculate projected EPS after 5 years:** $$\text{EPS}_5 = 5 \times (1 + 0.10)^5 = 5 \times 1.61051 = 8.05255$$ 6. **Estimate future price using industry average P/E:** $$\text{Future Price} = \text{EPS}_5 \times 20 = 8.05255 \times 20 = 161.051$$ 7. **Calculate expected price appreciation:** $$\text{Price Increase} = 161.051 - 50 = 111.051$$ 8. **Calculate dividend yield:** $$\text{Dividend Yield} = \frac{2}{50} = 0.04 = 4\%$$ 9. **Estimate total expected return:** - Price appreciation yield over 5 years: $$\frac{111.051}{50} = 2.221 = 222.1\%$$ - Annualized price growth rate: $$\left(\frac{161.051}{50}\right)^{\frac{1}{5}} - 1 = 1.221 - 1 = 0.221 = 22.1\%$$ - Total expected annual return including dividends: $$22.1\% + 4\% = 26.1\%$$ 10. **Compare expected return to required return:** - Expected return (26.1%) is much higher than required return (8%), indicating a potentially worthwhile investment. **Final conclusion:** Based on the projected EPS growth, dividend, and industry P/E, investing in BlueTech Innovations appears attractive with an expected return significantly above the required rate of return.