Question

Crane Corporation will pay dividends of $2.40, $2.80, and $3.50 in the next three years. After three years, the dividends are expected to grow at a constant rate of 6 percent per year. If the required rate of return is 13.0 percent, what is the current value of the Crane common stock?

Answer 1

$43.47

Step-by-step explanation:

We can use an adapted version of the constant growth model. We will first determine the price of the stock in 3 years and then discount it to the present value.

stock price = [dividend x (1 + growth rate)] / (required rate of return - growth rate)

price in 3 years = [$3.50 x (1 + 6%)] / (13% - 6%) = $3.71 / 7% = $53

current stock price = $2.40/1.13 + $2.80/1.13² + $3.50/1.13³ + $53/1.13³ = $2.12 + $2.19 + $2.43 + $36.73 = $43.47

Answer 2

$39.25

Step-by-step explanation:

The Value of stock is the present value of all future dividend payment. We have to calculate the present value of each dividend and add them up to arrive at a price of stock.

PV of Dividend of first 3 years are as follow

First year = $2.40 ( 1 + 13%)^-1 = $2.12

Second year = $2.80 ( 1 + 13%)^-2 = $2.19

First year = $3.50 ( 1 + 13%)^-3 = 2.43

After 3 year the dividend will grow at 6% per year, we will use the DVM formula to calculate the value after 3 years

Value at year 4 = Dividend ( 1+growth rate) / ( rate of return - growth rate)

Value at year 4 = $3.5 (1+6%) / (13%-6%)

Value at year 4 = $3.71 / 7%

Value at year 4 = $53

PV of Value at year 4 = $53 ( 1 + 13%)^-4 = $32.51

Now Add PV of All dividend.

Current value of Stock = $2.12 + $2.19 + $2.43 + $32.51 = $39.25