1. **Problem 1: Calculate the return offered by Tesco’s shares** The shares were worth £2.51 initially and £1.90 one year later with no dividends paid. The formula for return is: $$\text{Return} = \frac{\text{Ending Price} - \text{Beginning Price} + \text{Dividends}}{\text{Beginning Price}}$$ Since no dividends were paid, dividends = 0. Calculate: $$\text{Return} = \frac{1.90 - 2.51 + 0}{2.51} = \frac{-0.61}{2.51} \approx -0.2430$$ So, the return is approximately -24.30%. 2. **Problem 2: Calculate the rate of return on Plasticoat shares** Initial price = €32, dividend = £3.50 (assuming currency consistency), ending price = €40. Return formula: $$\text{Return} = \frac{40 - 32 + 3.50}{32} = \frac{11.50}{32} \approx 0.3594$$ So, the return is approximately 35.94%. 3. **Problem 3: Calculate expected return and standard deviation for B. J. Gautney Enterprises' security** Given probabilities and returns: | Probability | Return | |-------------|---------| | 0.15 | -3% | | 0.30 | 2% | | 0.40 | 4% | | 0.15 | 6% | **Step 1: Calculate expected return $E(R)$:** $$E(R) = \sum p_i r_i = 0.15(-0.03) + 0.30(0.02) + 0.40(0.04) + 0.15(0.06)$$ $$= -0.0045 + 0.006 + 0.016 + 0.009 = 0.0265$$ Expected return is 2.65%. **Step 2: Calculate variance $\sigma^2$:** $$\sigma^2 = \sum p_i (r_i - E(R))^2$$ Calculate each term: $$0.15(-0.03 - 0.0265)^2 = 0.15(-0.0565)^2 = 0.15(0.003192) = 0.000479$$ $$0.30(0.02 - 0.0265)^2 = 0.30(-0.0065)^2 = 0.30(0.000042) = 0.000013$$ $$0.40(0.04 - 0.0265)^2 = 0.40(0.0135)^2 = 0.40(0.000182) = 0.000073$$ $$0.15(0.06 - 0.0265)^2 = 0.15(0.0335)^2 = 0.15(0.001122) = 0.000168$$ Sum: $$0.000479 + 0.000013 + 0.000073 + 0.000168 = 0.000733$$ **Step 3: Calculate standard deviation $\sigma$:** $$\sigma = \sqrt{0.000733} \approx 0.0271$$ Standard deviation is approximately 2.71%. **Step 4: Investment decision** The one-year Treasury bill pays 2.9%, which is slightly higher than the expected return of 2.65% for this security. Since the security has a lower expected return and some risk (standard deviation 2.71%), Gautney should prefer the risk-free Treasury bills unless other factors justify the risk. --- **Final answers:** 1. Tesco shares return: **-24.30%** 2. Plasticoat shares return: **35.94%** 3. Expected return: **2.65%**, Standard deviation: **2.71%**, Investment recommendation: **Do not invest** (Treasury bills offer better risk-return).