Kramer Ltd last paid a dividend of $0.20 three years ago.  Today the company announced they will resume paying dividends.  The planned dividends are $0.40 in one year's time, $0.50 in two years' time, and thereafter dividends will increase by a constant rate of 3% p.a. indefinitely.  If the required rate of return for Kramer is 11%, what is a fair price for one share today?


Group of answer choices

$5.63

$6.19

$6.25

$5.99

$0.36

To determine the fair price of a share today for Kramer Ltd, given the future dividends and the required rate of return, we will use the Dividend Discount Model (DDM). 

Here's the step-by-step process:

1. **Calculate the present value of dividends for the first two years:**

   - Dividend in Year 1 ($D_1$) = $0.40
   - Dividend in Year 2 ($D_2$) = $0.50

   The present value of these dividends is given by:

   \[
   PV(D_1) = \frac{D_1}{(1 + r)^1} = \frac{0.40}{(1 + 0.11)^1} = \frac{0.40}{1.11} \approx 0.3604
   \]

   \[
   PV(D_2) = \frac{D_2}{(1 + r)^2} = \frac{0.50}{(1 + 0.11)^2} = \frac{0.50}{1.2321} \approx 0.4059
   \]

2. **Calculate the present value of dividends starting from Year 3 onwards (perpetual growth model):**

   From Year 3 onwards, dividends will grow at a constant rate of 3% per annum. The dividend in Year 3 ($D_3$) will be:

   \[
   D_3 = D_2 \times (1 + g) = 0.50 \times 1.03 = 0.515
   \]

   The present value of all future dividends from Year 3 onwards (using the Gordon Growth Model) is calculated as follows:

   \[
   PV_{D_3 \text{ onwards}} = \frac{D_3}{r - g} = \frac{0.515}{0.11 - 0.03} = \frac{0.515}{0.08} = 6.4375
   \]

   This present value is at Year 2, so we need to discount it back to today's value (Year 0):

   \[
   PV_{D_3 \text{ onwards (today)}} = \frac{6.4375}{(1 + 0.11)^2} = \frac{6.4375}{1.2321} \approx 5.224
   \]

3. **Sum the present values to find the fair price of the share today:**

   \[
   \text{Fair price} = PV(D_1) + PV(D_2) + PV_{D_3 \text{ onwards (today)}} = 0.3604 + 0.4059 + 5.224 \approx 5.9903
   \]

Thus, the fair price for one share today is approximately $5.99.

The correct answer from the given choices is **$5.99**.

Would you like further details on this calculation or have any questions? Here are some related questions you might find interesting:

1. How does the required rate of return affect the fair price of a stock?
2. What is the significance of the constant growth rate in the Gordon Growth Model?
3. How would a change in the initial dividends affect the stock price?
4. Can the Dividend Discount Model be used for companies that do not pay dividends?
5. What are the limitations of the Dividend Discount Model?

**Tip:** Always check the assumptions behind the growth rates and required returns when using the Dividend Discount Model to ensure they are realistic and applicable to the company being analyzed.

Kramer Ltd last paid a dividend of $0.20 three years ago. Today the company announced they will resume paying dividends. The planned dividends are $0.40 in one year's time, $0.50 in two years' time, and thereafter dividends will increase by a constant rate of 3% p.a. indefinitely. If the required rate of return for Kramer is 11%, what is a fair price for one share today?

Determine the fair price of Kramer Ltd stock today using the Dividend Discount Model, factoring in future dividends and a perpetual growth rate. Step-by-step calculations are included for present value, dividends, and the Gordon Growth Model, making this a great resource for undergraduate finance students.

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