QuestionCalculate the stock value of Delphi Products with a current dividend of \$2, growing at varying rates and an 18% return.

Studdy Solution

STEP 1

Assumptions1. The current dividend per share is \$. The dividend growth rate is15% for the first three years,10% for the next three years, and5% thereafter indefinitely3. The required rate of return is18%

STEP 2

We can calculate the stock value using the Gordon Growth Model, which is a version of the Dividend Discount Model (DDM) that assumes dividends grow at a constant rate. However, since the growth rate changes over time in this problem, we need to calculate the present value of dividends for each period separately.

STEP 3

First, calculate the dividends for the first three years using the growth rate of15%.
$1 = D0 \times (1 + g1)$ $2 = D1 \times (1 + g1)$ $3 = D2 \times (1 + g1)$ where $0$ is the current dividend, $g1$ is the growth rate for the first three years.

STEP 4

Plug in the given values for the current dividend and the growth rate to calculate the dividends for the first three years.
$1 = \$2 \times (1 +15\%)$ $2 = D1 \times (1 +15\%)$ $3 = D2 \times (1 +15\%)$

STEP 5

Calculate the dividends for the next three years using the growth rate of10%.
$4 = D3 \times (1 + g2)$ $5 = D4 \times (1 + g2)$ $= D5 \times (1 + g2)$ where $g2$ is the growth rate for the next three years.

STEP 6

Calculate the dividends for the years after the sixth year using the growth rate of5%.
$= D6 \times (1 + g3)$ where $g3$ is the growth rate for the years after the sixth year.

STEP 7

Now, calculate the present value of these dividends. The present value of a future cash flow can be calculated using the formula $PV = \frac{CF}{(1 + r)^n}$ where $CF$ is the future cash flow, $r$ is the discount rate, and $n$ is the number of periods.

STEP 8

Calculate the present value of the dividends for the first six years.
$PV1 = \frac{1}{(1 + r)^1}$ $PV2 = \frac{2}{(1 + r)^2}$ $PV3 = \frac{3}{(1 + r)^3}$ $PV4 = \frac{4}{(1 + r)^4}$ $PV5 = \frac{5}{(1 + r)^5}$ $PV6 = \frac{6}{(1 + r)^6}$ where $r$ is the required rate of return.

STEP 9

The present value of the dividends from the seventh year onwards can be calculated using the Gordon Growth Model $PV_{7+} = \frac{7}{r - g3}$

STEP 10

Finally, the value of the stock is the sum of the present values of the dividends.
$Stock\, value = PV + PV2 + PV3 + PV4 + PV5 + PV6 + PV_{7+}$

STEP 11

Calculate the stock value by plugging in the values for the present values of the dividends.

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