Question

A 12 % stock is yielding 10 %. The market value of stock is

• A. 83.33
• B. 110
• C. 120
• D. 112

Hint:

If the actual yield is lower than the face-value coupon rate (\(10\% < 12\%\delta\)), the stock is trading at a premium (market value is greater than the face value of 100). This immediately eliminates Option A (83.33).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Stock yields and market values are calculated based on face value.
- The coupon rate (or stock percentage) is the dividend paid on the face value of the stock.
- The yield is the actual percentage return realized based on the current market price of the stock.
Key Formula or Approach:
The relationship between yield, dividend, and market value is:
\[ \text{Yield \%} = \frac{\text{Dividend}}{\text{Market Value}} \times 100 \]
Or equivalently, since the dividend is calculated on the face value (assumed to be Rs. 100):
\[ \text{Market Value} = \frac{\text{Face Value} \times \text{Stock \%}}{\text{Yield \%}} \]

Step 2: Detailed Explanation:
Let us perform the calculations:
1. Assume the standard face value of the stock is \(\text{Rs. } 100\).
2. A \(12\%\) stock pays a dividend of:
\[ \text{Dividend} = 12\% \text{ of } 100 = \text{Rs. } 12 \]
3. This stock is yielding an actual return of \(10\%\) on its market value (MV).
Using our formula:
\[ 10\% = \frac{12}{\text{Market Value}} \times 100 \]
\[ 10 = \frac{1200}{\text{Market Value}} \]
\[ \text{Market Value} = \frac{1200}{10} = \text{Rs. } 120 \]
This matches Option C.

Step 3: Final Answer:
The market value of the stock is 120.