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Let's go through the problem step by step to calculate the expected return and risk.

### Problem Breakdown:

- Current price of the share = ₹43
- Two possible prices at the year-end:
  - ₹55 (50% chance)
  - ₹60 (50% chance)
- Number of shares acquired = 250 shares
- 80% of the funds used are borrowed.
- Cost of borrowed funds = 12%

### Calculating Expected Return:

1. **Initial Investment (Equity Contribution):**
   The investor is purchasing 250 shares, and the total investment will be:
   \[
   \text{Total Investment} = 250 \times 43 = ₹10,750
   \]

2. **Borrowed Amount (80% of Total Investment):**
   \[
   \text{Borrowed Amount} = 0.80 \times 10,750 = ₹8,600
   \]

3. **Investor's Own Equity (20% of Total Investment):**
   \[
   \text{Equity Contribution} = 0.20 \times 10,750 = ₹2,150
   \]

4. **Possible Values at Year-End:**
   - If the price is ₹55:
     \[
     \text{Portfolio Value} = 250 \times 55 = ₹13,750
     \]
   - If the price is ₹60:
     \[
     \text{Portfolio Value} = 250 \times 60 = ₹15,000
     \]

5. **Loan Repayment (12% Interest):**
   The amount to be repaid on the borrowed ₹8,600 at 12% interest:
   \[
   \text{Loan Repayment} = 8,600 + (0.12 \times 8,600) = 8,600 + 1,032 = ₹9,632
   \]

6. **Net Value for Investor:**
   - If the price is ₹55:
     \[
     \text{Net Value} = 13,750 - 9,632 = ₹4,118
     \]
   - If the price is ₹60:
     \[
     \text{Net Value} = 15,000 - 9,632 = ₹5,368
     \]

7. **Return Calculation:**
   The return for each outcome can be calculated based on the investor's initial equity contribution of ₹2,150:
   - Return if price is ₹55:
     \[
     \text{Return} = \frac{4,118 - 2,150}{2,150} \times 100 = 91.16\%
     \]
   - Return if price is ₹60:
     \[
     \text{Return} = \frac{5,368 - 2,150}{2,150} \times 100 = 149.67\%
     \]

8. **Expected Return:**
   Since there is a 50% chance for each price outcome, the expected return is the average of the two possible returns:
   \[
   \text{Expected Return} = \frac{91.16 + 149.67}{2} = 120.42\%
   \]

Now let's calculate the **risk** (i.e., standard deviation) associated with the investment.The **expected return** on the investment is approximately **120.41%**, and the **risk** (standard deviation of returns) is around **29.26%**.

Would you like more details or have any further questions?

Here are 5 related questions to further explore this topic:
1. How does the leverage (borrowed funds) affect the risk of the investment?
2. How would the expected return change if the interest rate on borrowed funds was different?
3. What impact would different probabilities (other than 50%) for each outcome have on the expected return?
4. How does the inclusion of dividends affect the expected return and risk in stock investments?
5. What is the significance of systematic and unsystematic risk in portfolio management?

**Tip:** Leverage amplifies both potential returns and risks, so it's important to carefully consider the interest rates and likelihood of outcomes when borrowing to invest.

An investor has analysed a share for a one-year holding period. The share is currently selling for Rs. 43 but pays no dividends, and there is a fifty-fifty chance that the share will sell for either Rs. 55 or Rs. 60 by the year end. What is the expected return and risk if 250 shares are acquired with 80% borrowed funds? Assume the cost of borrowed funds to be 12%.

This problem involves calculating the expected return and risk (standard deviation) for a leveraged investment in a share priced at Rs. 43 with two possible outcomes. Learn how leverage affects the return on investment and risk, with borrowed funds contributing to 80% of the investment, and 12% interest applied. Suitable for finance students at the university level.

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