A man buys Rs 20 shares that pay a 9% annual dividend. He wants to earn 12% interest on his investment. What should be the market value of each share?

Introduction / Context:
This problem belongs to the topic of stocks and shares. It tests understanding of how dividend, face value, market value, and required rate of return are related. Such questions are very common in banking and finance related aptitude tests.

Given Data / Assumptions:

• Face value of each share = Rs 20.
• Dividend rate = 9 percent per annum on face value.
• The investor wants a 12 percent return on the money he actually invests, that is, on the market value.
• We assume dividends are paid once a year and there are no additional taxes or charges.

Concept / Approach:
Dividend is calculated on the face value, but the investor pays the market value. The effective yield or return is (annual dividend / market value) * 100 percent. To achieve a desired yield, we equate this expression to the required percentage and solve for the market value.

Step-by-Step Solution:
Step 1: Compute the annual dividend per share.Step 2: Dividend = 9 percent of Rs 20 = (9/100) * 20 = Rs 1.80 per share.Step 3: Let the market value of each share be Rs P.Step 4: The investor wants a 12 percent return, so yield = (dividend / P) * 100 = 12.Step 5: Substitute dividend = 1.80: (1.80 / P) * 100 = 12.Step 6: Simplify: 180 / P = 12.Step 7: Solve for P: P = 180 / 12 = 15.Step 8: Therefore, the market value of each share should be Rs 15.

Verification / Alternative check:
Check the yield if the market price is Rs 15: yield = (1.80 / 15) * 100 percent. Compute 1.80 / 15 = 0.12, then 0.12 * 100 percent = 12 percent. This matches the investor requirement, confirming the correctness of the result.

Why Other Options Are Wrong:

• Rs 12: If P = 12, yield would be (1.80 / 12) * 100 = 15 percent, which is higher than required.
• Rs 18: If P = 18, yield would be (1.80 / 18) * 100 = 10 percent, lower than required.
• Rs 20: If P = 20, yield would be (1.80 / 20) * 100 = 9 percent, which is just the dividend rate, not the desired 12 percent on investment.

Common Pitfalls:
Students sometimes mistakenly compute dividend on the market value instead of face value, or they confuse dividend rate with required yield. It is crucial to remember that dividend is always declared on face value, while the investor cares about return on the actual price paid in the market.

Final Answer:
The market value of each share should be Rs 15.